Mixed Models Tutorial: Contrast Coding

Author

Reinhold Kliegl

Published

2025-09-03

This script uses a subset of data reported in Fühner et al. (2021).

To circumvent delays associated with model fitting we work with models that are less complex than those in the reference publication. All the data to reproduce the models in the publication are used here, too; the script requires only a few changes to specify the more complex models in the paper.

All children were between 6.0 and 6.99 years at legal keydate (30 September) of school enrollment, that is in their ninth year of life in the third grade. To avoid delays associated with model fitting we work with a reduced data set and less complex models than those in the reference publication. The script requires only a few changes to specify the more complex models in the paper.

The script is structured in three main sections:

Setup with reading and examining the data
Contrasts coding

Effect and sequential difference contrasts
Helmert contrast
Hypothesis contrast
PCA-based contrast

Other topics

LMM goodness of fit does not depend on contrast (i.e., reparameterization)
VCs and CPs depend on contrast
VCs and CPs depend on random factor

1 Setup

1.1 Packages and functions

Code

using AlgebraOfGraphics
using CairoMakie
using Chain
using CategoricalArrays
using DataFrames
using DataFrameMacros
using MixedModels
using ProgressMeter
using SMLP2026: dataset
using Statistics
using StatsBase

ProgressMeter.ijulia_behavior(:clear);

1.2 Readme for `dataset("fggk21")`

Number of scores: 525126

Cohort: 9 levels; 2011-2019
School: 515 levels
Child: 108295 levels; all children are between 8.0 and 8.99 years old
Sex: “Girls” (n=55,086), “Boys” (n= 53,209)
age: testdate - middle of month of birthdate
Test: 5 levels
- Endurance (Run): 6 minute endurance run [m]; to nearest 9m in 9x18m field
- Coordination (Star_r): star coordination run [m/s]; 9x9m field, 4 x diagonal = 50.912 m
- Speed(S20_r): 20-meters sprint [m/s]
- Muscle power low (SLJ): standing long jump [cm]
- Muscle power up (BPT): 1-kg medicine ball push test [m]
score - see units

1.3 Preprocessing

1.3.1 Read data

tbl = dataset(:fggk21)

Arrow.Table with 525126 rows, 7 columns, and schema:
 :Cohort  String
 :School  String
 :Child   String
 :Sex     String
 :age     Float64
 :Test    String
 :score   Float64

df = DataFrame(tbl)
describe(df)

7×7 DataFrame

Row	variable	mean	min	median	max	nmissing	eltype
	Symbol	Union…	Any	Union…	Any	Int64	DataType
1	Cohort		2011		2019	0	String
2	School		S100043		S800200	0	String
3	Child		C002352		C117966	0	String
4	Sex		female		male	0	String
5	age	8.56073	7.99452	8.55852	9.10609	0	Float64
6	Test		BPT		Star_r	0	String
7	score	226.141	1.14152	4.65116	1530.0	0	Float64

1.3.2 Extract a stratified subsample

We extract a random sample of 500 children from the Sex (2) x Test (5) cells of the design. Cohort and School are random.

dat = @chain df begin
  @transform(:Sex = :Sex == "female" ? "Girls" : "Boys")
  @groupby(:Test, :Sex)
  combine(x -> x[sample(1:nrow(x), 500), :])
end

5000×7 DataFrame

4975 rows omitted

Row	Test	Sex	Cohort	School	Child	age	score
	String	String	String	String	String	Float64	Float64
1	S20_r	Boys	2019	S100560	C075635	8.71732	5.55556
2	S20_r	Boys	2011	S100973	C088051	8.83231	4.54545
3	S20_r	Boys	2013	S103512	C049554	8.49829	4.34783
4	S20_r	Boys	2018	S103445	C101340	8.93908	4.44444
5	S20_r	Boys	2019	S100912	C019065	8.22177	5.26316
6	S20_r	Boys	2012	S102260	C022248	8.24914	4.34783
7	S20_r	Boys	2019	S106410	C096215	8.88433	4.65116
8	S20_r	Boys	2013	S104504	C039985	8.41342	4.87805
9	S20_r	Boys	2015	S102933	C112569	9.0486	5.12821
10	S20_r	Boys	2019	S113207	C077100	8.71732	4.44444
11	S20_r	Boys	2019	S105466	C038086	8.38877	4.44444
12	S20_r	Boys	2019	S100122	C027916	8.3039	4.25532
13	S20_r	Boys	2015	S103548	C025356	8.27652	4.08163
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
4989	Run	Girls	2019	S100572	C065319	8.63244	1080.0
4990	Run	Girls	2016	S102301	C111954	9.04586	1134.0
4991	Run	Girls	2016	S106677	C036969	8.38056	981.0
4992	Run	Girls	2017	S103937	C115483	9.08145	945.0
4993	Run	Girls	2014	S101485	C017015	8.20808	997.0
4994	Run	Girls	2019	S103470	C037732	8.38877	1260.0
4995	Run	Girls	2018	S100146	C062074	8.6078	1278.0
4996	Run	Girls	2017	S101345	C100297	8.91992	1066.0
4997	Run	Girls	2012	S110346	C022819	8.24914	1071.0
4998	Run	Girls	2019	S103354	C019452	8.22177	1080.0
4999	Run	Girls	2013	S103354	C097952	8.9117	1089.0
5000	Run	Girls	2019	S113001	C077078	8.71732	936.0

1.3.3 Transformations

transform!(dat, :age, :age => (x -> x .- 8.5) => :a1) # centered age (linear)
select!(groupby(dat, :Test), :, :score => zscore => :zScore) # z-score

5000×9 DataFrame

4975 rows omitted

Row	Test	Sex	Cohort	School	Child	age	score	a1	zScore
	String	String	String	String	String	Float64	Float64	Float64	Float64
1	S20_r	Boys	2019	S100560	C075635	8.71732	5.55556	0.217317	2.51057
2	S20_r	Boys	2011	S100973	C088051	8.83231	4.54545	0.332307	0.0525415
3	S20_r	Boys	2013	S103512	C049554	8.49829	4.34783	-0.00171116	-0.428377
4	S20_r	Boys	2018	S103445	C101340	8.93908	4.44444	0.439083	-0.193261
5	S20_r	Boys	2019	S100912	C019065	8.22177	5.26316	-0.278234	1.79903
6	S20_r	Boys	2012	S102260	C022248	8.24914	4.34783	-0.250856	-0.428377
7	S20_r	Boys	2019	S106410	C096215	8.88433	4.65116	0.384326	0.309777
8	S20_r	Boys	2013	S104504	C039985	8.41342	4.87805	-0.0865845	0.861892
9	S20_r	Boys	2015	S102933	C112569	9.0486	5.12821	0.548597	1.47063
10	S20_r	Boys	2019	S113207	C077100	8.71732	4.44444	0.217317	-0.193261
11	S20_r	Boys	2019	S105466	C038086	8.38877	4.44444	-0.111225	-0.193261
12	S20_r	Boys	2019	S100122	C027916	8.3039	4.25532	-0.196099	-0.653487
13	S20_r	Boys	2015	S103548	C025356	8.27652	4.08163	-0.223477	-1.07614
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
4989	Run	Girls	2019	S100572	C065319	8.63244	1080.0	0.132444	0.507184
4990	Run	Girls	2016	S102301	C111954	9.04586	1134.0	0.545859	0.879253
4991	Run	Girls	2016	S106677	C036969	8.38056	981.0	-0.119439	-0.174941
4992	Run	Girls	2017	S103937	C115483	9.08145	945.0	0.581451	-0.422987
4993	Run	Girls	2014	S101485	C017015	8.20808	997.0	-0.291923	-0.0646986
4994	Run	Girls	2019	S103470	C037732	8.38877	1260.0	-0.111225	1.74741
4995	Run	Girls	2018	S100146	C062074	8.6078	1278.0	0.107803	1.87143
4996	Run	Girls	2017	S101345	C100297	8.91992	1066.0	0.419918	0.410722
4997	Run	Girls	2012	S110346	C022819	8.24914	1071.0	-0.250856	0.445173
4998	Run	Girls	2019	S103354	C019452	8.22177	1080.0	-0.278234	0.507184
4999	Run	Girls	2013	S103354	C097952	8.9117	1089.0	0.411704	0.569196
5000	Run	Girls	2019	S113001	C077078	8.71732	936.0	0.217317	-0.484998

dat2 = combine(
  groupby(dat, [:Test, :Sex]),
  :score => mean,
  :score => std,
  :zScore => mean,
  :zScore => std,
)

10×6 DataFrame

Row	Test	Sex	score_mean	score_std	zScore_mean	zScore_std
	String	String	Float64	Float64	Float64	Float64
1	S20_r	Boys	4.56863	0.413395	0.108948	1.00597
2	BPT	Boys	3.9896	0.698676	0.346344	0.971427
3	SLJ	Boys	127.562	19.7226	0.174235	1.03256
4	Star_r	Boys	2.09069	0.306015	0.12132	1.04269
5	Run	Boys	1037.11	146.774	0.211693	1.0113
6	S20_r	Girls	4.47909	0.403942	-0.108948	0.982971
7	BPT	Girls	3.4914	0.650471	-0.346344	0.904403
8	SLJ	Girls	120.906	17.8668	-0.174235	0.935405
9	Star_r	Girls	2.01948	0.276144	-0.12132	0.940908
10	Run	Girls	975.666	136.879	-0.211693	0.94312

1.3.4 Figure of age x Sex x Test interactions

The main results of relevance here are shown in Figure 2 of Scientific Reports 11:17566.

2 Contrast coding

Contrast coding is part of StatsModels.jl. Here is the primary author’s (i.e., Dave Kleinschmidt’s) documentation of Modeling Categorical Data.

The random factors Child, School, and Cohort are assigned a Grouping contrast. This contrast is needed when the number of groups (i.e., units, levels) is very large. This is the case for Child (i.e., the 108,925 children in the full and probably also the 11,566 children in the reduced data set). The assignment is not necessary for the typical sample size of experiments. However, we use this coding of random factors irrespective of the number of units associated with them to be transparent about the distinction between random and fixed factors.

A couple of general remarks about the following examples. First, all contrasts defined in this tutorial return an estimate of the Grand Mean (GM) in the intercept, that is they are so-called sum-to-zero contrasts. In both Julia and R the default contrast is Dummy coding which is not a sum-to-zero contrast, but returns the mean of the reference (control) group - unfortunately for (quasi-)experimentally minded scientists.

Second, The factor Sex has only two levels. We use EffectCoding (also known as Sum coding in R) to estimate the difference of the levels from the Grand Mean. Unlike in R, the default sign of the effect is for the second level (base is the first, not the last level), but this can be changed with the base kwarg in the command. Effect coding is a sum-to-zero contrast, but when applied to factors with more than two levels does not yield orthogonal contrasts.

Finally, contrasts for the five levels of the fixed factor Test represent the hypotheses about differences between them. In this tutorial, we use this factor to illustrate various options.

We (initially) include only Test as fixed factor and Child as random factor. More complex LMMs can be specified by simply adding other fixed or random factors to the formula.

2.1 SeqDiffCoding: `contr1`

SeqDiffCoding was used in the publication. This specification tests pairwise differences between the five neighboring levels of Test, that is:

SDC1: 2-1
SDC2: 3-2
SDC3: 4-3
SDC4: 5-4

The levels were sorted such that these contrasts map onto four a priori hypotheses; in other words, they are theoretically motivated pairwise comparisons. The motivation also encompasses theoretically motivated interactions with Sex. The order of levels can also be explicitly specified during contrast construction. This is very useful if levels are in a different order in the dataframe. We recommend the explicit specification to increase transparency of the code.

The statistical disadvantage of SeqDiffCoding is that the contrasts are not orthogonal, that is the contrasts are correlated. This is obvious from the fact that levels 2, 3, and 4 are all used in two contrasts. One consequence of this is that correlation parameters estimated between neighboring contrasts (e.g., 2-1 and 3-2) are difficult to interpret. Usually, they will be negative because assuming some practical limitation on the overall range (e.g., between levels 1 and 3), a small “2-1” effect “correlates” negatively with a larger “3-2” effect for mathematical reasons.

Obviously, the tradeoff between theoretical motivation and statistical purity is something that must be considered carefully when planning the analysis.

contr1 = merge(
  Dict(nm => Grouping() for nm in (:School, :Child, :Cohort)),
  Dict(
    :Sex => EffectsCoding(; levels=["Girls", "Boys"]),
    :Test => SeqDiffCoding(;
      levels=["Run", "Star_r", "S20_r", "SLJ", "BPT"]
    ),
  ),
)

Dict{Symbol, StatsModels.AbstractContrasts} with 5 entries:
  :Child  => Grouping()
  :School => Grouping()
  :Test   => SeqDiffCoding(["Run", "Star_r", "S20_r", "SLJ", "BPT"])
  :Cohort => Grouping()
  :Sex    => EffectsCoding(nothing, ["Girls", "Boys"])

f_ovi_1 = @formula zScore ~ 1 + Test + (1 | Child);

m_ovi_SeqDiff_1 = fit(MixedModel, f_ovi_1, dat; contrasts=contr1)

	Est.	SE	z	p	σ_Child
(Intercept)	0.0002	0.0143	0.01	0.9914	0.7127
Test: Star_r	0.0013	0.0442	0.03	0.9760
Test: S20_r	-0.0036	0.0442	-0.08	0.9345
Test: SLJ	-0.0018	0.0444	-0.04	0.9685
Test: BPT	0.0015	0.0443	0.03	0.9727
Residual	0.7006

In this case, any differences between tests identified by the contrasts would be spurious because each test was standardized (i.e., M=0, \(SD\)=1). The differences could also be due to an imbalance in the number of boys and girls or in the number of missing observations for each test.

The primary interest in this study related to interactions of the test contrasts with and age and Sex. We start with age (linear) and its interaction with the four test contrasts.

m_ovi_SeqDiff_2 = let
  form = @formula zScore ~ 1 + Test * a1 + (1 | Child)
  fit(MixedModel, form, dat; contrasts=contr1)
end

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0226	0.0145	-1.56	0.1191	0.7108
Test: Star_r	-0.0110	0.0449	-0.25	0.8056
Test: S20_r	-0.0050	0.0450	-0.11	0.9108
Test: SLJ	0.0189	0.0451	0.42	0.6756
Test: BPT	-0.0297	0.0450	-0.66	0.5097
a1	0.3593	0.0495	7.27	<1e-12
Test: Star_r & a1	0.2718	0.1534	1.77	0.0764
Test: S20_r & a1	-0.0524	0.1568	-0.33	0.7383
Test: SLJ & a1	-0.2802	0.1545	-1.81	0.0697
Test: BPT & a1	0.4455	0.1513	2.95	0.0032
Residual	0.6935

The difference between older and younger children is larger for Star_r than for Run (0.2473). S20_r did not differ significantly from Star_r (-0.0377) and SLJ (-0.0113) The largest difference in developmental gain was between BPT and SLJ (0.3355).

Please note that standard errors of this LMM are anti-conservative because the LMM is missing a lot of information in the RES (e..g., contrast-related VCs snd CPs for Child, School, and Cohort.

Next we add the main effect of Sex and its interaction with the four test contrasts.

m_ovi_SeqDiff_3 = let
  form = @formula zScore ~ 1 + Test * (a1 + Sex) + (1 | Child)
  fit(MixedModel, form, dat; contrasts=contr1)
end

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0220	0.0142	-1.55	0.1211	0.6729
Test: Star_r	-0.0137	0.0440	-0.31	0.7546
Test: S20_r	-0.0048	0.0441	-0.11	0.9135
Test: SLJ	0.0179	0.0441	0.41	0.6846
Test: BPT	-0.0315	0.0440	-0.71	0.4747
a1	0.3480	0.0484	7.19	<1e-12
Sex: Boys	0.1874	0.0139	13.51	<1e-40
Test: Star_r & a1	0.2970	0.1507	1.97	0.0487
Test: S20_r & a1	-0.0587	0.1541	-0.38	0.7034
Test: SLJ & a1	-0.2449	0.1516	-1.61	0.1063
Test: BPT & a1	0.4705	0.1481	3.18	0.0015
Test: Star_r & Sex: Boys	-0.0846	0.0431	-1.96	0.0497
Test: S20_r & Sex: Boys	-0.0288	0.0432	-0.67	0.5054
Test: SLJ & Sex: Boys	0.0854	0.0433	1.97	0.0487
Test: BPT & Sex: Boys	0.1709	0.0431	3.96	<1e-04
Residual	0.6999

The significant interactions with Sex reflect mostly differences related to muscle power, where the physiological constitution gives boys an advantage. The sex difference is smaller when coordination and cognition play a role – as in the Star_r test. (Caveat: SEs are estimated with an underspecified RES.)

The final step in this first series is to add the interactions between the three covariates. A significant interaction between any of the four Test contrasts and age (linear) x Sex was hypothesized to reflect a prepubertal signal (i.e., hormones start to rise in girls’ ninth year of life). However, this hypothesis is linked to a specific shape of the interaction: Girls would need to gain more than boys in tests of muscular power.

f_ovi = @formula zScore ~ 1 + Test * a1 * Sex + (1 | Child)
m_ovi_SeqDiff = fit(MixedModel, f_ovi, dat; contrasts=contr1)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0206	0.0142	-1.45	0.1463	0.6729
Test: Star_r	-0.0128	0.0441	-0.29	0.7719
Test: S20_r	-0.0005	0.0442	-0.01	0.9908
Test: SLJ	0.0115	0.0442	0.26	0.7947
Test: BPT	-0.0302	0.0440	-0.69	0.4929
a1	0.3508	0.0484	7.25	<1e-12
Sex: Boys	0.1914	0.0142	13.49	<1e-40
Test: Star_r & a1	0.2992	0.1506	1.99	0.0470
Test: S20_r & a1	-0.0603	0.1541	-0.39	0.6956
Test: SLJ & a1	-0.2378	0.1516	-1.57	0.1168
Test: BPT & a1	0.4635	0.1481	3.13	0.0018
Test: Star_r & Sex: Boys	-0.0811	0.0441	-1.84	0.0655
Test: S20_r & Sex: Boys	-0.0210	0.0442	-0.48	0.6346
Test: SLJ & Sex: Boys	0.0812	0.0442	1.84	0.0662
Test: BPT & Sex: Boys	0.1554	0.0440	3.53	0.0004
a1 & Sex: Boys	-0.0684	0.0484	-1.41	0.1575
Test: Star_r & a1 & Sex: Boys	-0.0698	0.1506	-0.46	0.6430
Test: S20_r & a1 & Sex: Boys	-0.1061	0.1541	-0.69	0.4911
Test: SLJ & a1 & Sex: Boys	0.0399	0.1516	0.26	0.7925
Test: BPT & a1 & Sex: Boys	0.2594	0.1481	1.75	0.0799
Residual	0.6990

The results are very clear: Despite an abundance of statistical power there is no evidence for the differences between boys and girls in how much they gain in the ninth year of life in these five tests. The authors argue that, in this case, absence of evidence looks very much like evidence of absence of a hypothesized interaction.

In the next two sections we use different contrasts. Does this have a bearing on this result? We still ignore for now that we are looking at anti-conservative test statistics.

2.2 HelmertCoding: `contr2`

The second set of contrasts uses HelmertCoding. Helmert coding codes each level as the difference from the average of the lower levels. With the default order of Test levels we get the following test statistics which we describe in reverse order of appearance in model output

HeC4: 5 - mean(1,2,3,4)
HeC3: 4 - mean(1,2,3)
HeC2: 3 - mean(1,2)
HeC1: 2 - 1

In the model output, HeC1 will be reported first and HeC4 last.

There is some justification for the HeC4 specification in a post-hoc manner because the fifth test (BPT) turned out to be different from the other four tests in that high performance is most likely not only related to physical fitness, but also to overweight/obesity, that is for a subset of children high scores on this test might be indicative of physical unfitness. A priori the SDC4 contrast 5-4 between BPT (5) and SLJ (4) was motivated because conceptually both are tests of the physical fitness component Muscular Power, BPT for upper limbs and SLJ for lower limbs, respectively.

One could argue that there is justification for HeC3 because Run (1), Star_r (2), and S20 (3) involve running but SLJ (4) does not. Sports scientists, however, recoil. For them it does not make much sense to average the different running tests, because they draw on completely different physiological resources; it is a variant of the old apples-and-oranges problem.

The justification for HeC3 is thatRun (1) and Star_r (2) draw more strongly on cardiorespiratory Endurance than S20 (3) due to the longer duration of the runs compared to sprinting for 20 m which is a pure measure of the physical-fitness component Speed. Again, sports scientists are not very happy with this proposal.

Finally, HeC1 contrasts the fitness components Endurance, indicated best by Run (1), and Coordination, indicated by Star_r (2). Endurance (i.e., running for 6 minutes) is considered to be the best indicator of health-related status among the five tests because it is a rather pure measure of cardiorespiratory fitness. The Star_r test requires execution of a pre-instructed sequence of forward, sideways, and backward runs. This coordination of body movements implies a demand on working memory (i.e., remembering the order of these subruns) and executive control processes, but performance also depends on endurance. HeC1 yields a measure of Coordination “corrected” for the contribution of Endurance.

The statistical advantage of HelmertCoding is that the resulting contrasts are orthogonal (uncorrelated). This allows for optimal partitioning of variance and statistical power. It is also more efficient to estimate “orthogonal” than “non-orthogonal” random-effect structures.

contr2 = Dict(
  :School => Grouping(),
  :Child => Grouping(),
  :Cohort => Grouping(),
  :Sex => EffectsCoding(; levels=["Girls", "Boys"]),
  :Test => HelmertCoding(;
    levels=["Run", "Star_r", "S20_r", "SLJ", "BPT"],
  ),
);

m_ovi_Helmert = fit(MixedModel, f_ovi, dat; contrasts=contr2)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0206	0.0142	-1.45	0.1463	0.6729
Test: Star_r	-0.0064	0.0220	-0.29	0.7719
Test: S20_r	-0.0023	0.0128	-0.18	0.8574
Test: SLJ	0.0017	0.0090	0.19	0.8474
Test: BPT	-0.0050	0.0070	-0.72	0.4740
a1	0.3508	0.0484	7.25	<1e-12
Sex: Boys	0.1914	0.0142	13.49	<1e-40
Test: Star_r & a1	0.1496	0.0753	1.99	0.0470
Test: S20_r & a1	0.0298	0.0443	0.67	0.5020
Test: SLJ & a1	-0.0446	0.0304	-1.46	0.1432
Test: BPT & a1	0.0660	0.0236	2.80	0.0051
Test: Star_r & Sex: Boys	-0.0406	0.0220	-1.84	0.0655
Test: S20_r & Sex: Boys	-0.0205	0.0128	-1.60	0.1086
Test: SLJ & Sex: Boys	0.0100	0.0090	1.12	0.2633
Test: BPT & Sex: Boys	0.0371	0.0070	5.31	<1e-06
a1 & Sex: Boys	-0.0684	0.0484	-1.41	0.1575
Test: Star_r & a1 & Sex: Boys	-0.0349	0.0753	-0.46	0.6430
Test: S20_r & a1 & Sex: Boys	-0.0470	0.0443	-1.06	0.2892
Test: SLJ & a1 & Sex: Boys	-0.0135	0.0304	-0.44	0.6567
Test: BPT & a1 & Sex: Boys	0.0438	0.0236	1.86	0.0632
Residual	0.6990

We forego a detailed discussion of the effects, but note that again none of the interactions between age x Sex with the four test contrasts was significant.

The default labeling of Helmert contrasts may lead to confusions with other contrasts. Therefore, we could provide our own labels:

labels=["c2.1", "c3.12", "c4.123", "c5.1234"]

Once the order of levels is memorized the proposed labelling is very transparent.

2.3 HypothesisCoding: `contr3`

The third set of contrasts uses HypothesisCoding. Hypothesis coding allows the user to specify their own a priori contrast matrix, subject to the mathematical constraint that the matrix has full rank. For example, sport scientists agree that the first four tests can be contrasted with BPT, because the difference is akin to a correction of overall physical fitness. However, they want to keep the pairwise comparisons for the first four tests.

HyC1: BPT - mean(1,2,3,4)
HyC2: Star_r - Run_r
HyC3: Run_r - S20_r
HyC4: S20_r - SLJ

contr3 = Dict(
  :School => Grouping(),
  :Child => Grouping(),
  :Cohort => Grouping(),
  :Sex => EffectsCoding(; levels=["Girls", "Boys"]),
  :Test => HypothesisCoding(
    [
      -1 -1 -1 -1 +4
      -1 +1  0  0  0
       0 -1 +1  0  0
       0  0 -1 +1  0
    ];
    levels=["Run", "Star_r", "S20_r", "SLJ", "BPT"],
    labels=["BPT-other", "Star-End", "S20-Star", "SLJ-S20"],
  ),
);

m_ovi_Hypo = fit(MixedModel, f_ovi, dat; contrasts=contr3)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0206	0.0142	-1.45	0.1463	0.6729
Test: BPT-other	-0.1000	0.1397	-0.72	0.4740
Test: Star-End	-0.0128	0.0441	-0.29	0.7719
Test: S20-Star	-0.0005	0.0442	-0.01	0.9908
Test: SLJ-S20	0.0115	0.0442	0.26	0.7947
a1	0.3508	0.0484	7.25	<1e-12
Sex: Boys	0.1914	0.0142	13.49	<1e-40
Test: BPT-other & a1	1.3191	0.4711	2.80	0.0051
Test: Star-End & a1	0.2992	0.1506	1.99	0.0470
Test: S20-Star & a1	-0.0603	0.1541	-0.39	0.6956
Test: SLJ-S20 & a1	-0.2378	0.1516	-1.57	0.1168
Test: BPT-other & Sex: Boys	0.7421	0.1397	5.31	<1e-06
Test: Star-End & Sex: Boys	-0.0811	0.0441	-1.84	0.0655
Test: S20-Star & Sex: Boys	-0.0210	0.0442	-0.48	0.6346
Test: SLJ-S20 & Sex: Boys	0.0812	0.0442	1.84	0.0662
a1 & Sex: Boys	-0.0684	0.0484	-1.41	0.1575
Test: BPT-other & a1 & Sex: Boys	0.8754	0.4711	1.86	0.0632
Test: Star-End & a1 & Sex: Boys	-0.0698	0.1506	-0.46	0.6430
Test: S20-Star & a1 & Sex: Boys	-0.1061	0.1541	-0.69	0.4911
Test: SLJ-S20 & a1 & Sex: Boys	0.0399	0.1516	0.26	0.7925
Residual	0.6990

With HypothesisCoding we must generate our own labels for the contrasts. The default labeling of contrasts is usually not interpretable. Therefore, we provide our own.

Anyway, none of the interactions between age x Sex with the four Test contrasts was significant for these contrasts.

contr1b = Dict(
  :School => Grouping(),
  :Child => Grouping(),
  :Cohort => Grouping(),
  :Sex => EffectsCoding(; levels=["Girls", "Boys"]),
  :Test => HypothesisCoding(
    [
      -1 +1  0  0  0
       0 -1 +1  0  0
       0  0 -1 +1  0
       0  0  0 -1 +1
    ];
    levels=["Run", "Star_r", "S20_r", "SLJ", "BPT"],
    labels=["Star-Run", "S20-Star", "SLJ-S20", "BPT-SLJ"],
  ),
);

m_ovi_SeqDiff_v2 = fit(MixedModel, f_ovi, dat; contrasts=contr1b)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0206	0.0142	-1.45	0.1463	0.6729
Test: Star-Run	-0.0128	0.0441	-0.29	0.7719
Test: S20-Star	-0.0005	0.0442	-0.01	0.9908
Test: SLJ-S20	0.0115	0.0442	0.26	0.7947
Test: BPT-SLJ	-0.0302	0.0440	-0.69	0.4929
a1	0.3508	0.0484	7.25	<1e-12
Sex: Boys	0.1914	0.0142	13.49	<1e-40
Test: Star-Run & a1	0.2992	0.1506	1.99	0.0470
Test: S20-Star & a1	-0.0603	0.1541	-0.39	0.6956
Test: SLJ-S20 & a1	-0.2378	0.1516	-1.57	0.1168
Test: BPT-SLJ & a1	0.4635	0.1481	3.13	0.0018
Test: Star-Run & Sex: Boys	-0.0811	0.0441	-1.84	0.0655
Test: S20-Star & Sex: Boys	-0.0210	0.0442	-0.48	0.6346
Test: SLJ-S20 & Sex: Boys	0.0812	0.0442	1.84	0.0662
Test: BPT-SLJ & Sex: Boys	0.1554	0.0440	3.53	0.0004
a1 & Sex: Boys	-0.0684	0.0484	-1.41	0.1575
Test: Star-Run & a1 & Sex: Boys	-0.0698	0.1506	-0.46	0.6430
Test: S20-Star & a1 & Sex: Boys	-0.1061	0.1541	-0.69	0.4911
Test: SLJ-S20 & a1 & Sex: Boys	0.0399	0.1516	0.26	0.7925
Test: BPT-SLJ & a1 & Sex: Boys	0.2594	0.1481	1.75	0.0799
Residual	0.6990

m_zcp_SeqD = let
  form = @formula(
    zScore ~ 1 + Test * a1 * Sex + zerocorr(1 + Test | Child)
  )
  fit(MixedModel, form, dat; contrasts=contr1b)
end

Minimizing 18    Time: 0:00:00 ( 5.64 ms/it)
   objective: 13853.453855515327


Minimizing 81    Time: 0:00:00 ( 8.91 ms/it)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0205	0.0142	-1.44	0.1489	0.6926
Test: Star-Run	-0.0161	0.0446	-0.36	0.7181	0.0000
Test: S20-Star	0.0010	0.0441	0.02	0.9813	0.6127
Test: SLJ-S20	0.0102	0.0436	0.23	0.8142	0.3684
Test: BPT-SLJ	-0.0279	0.0436	-0.64	0.5221	0.0000
a1	0.3510	0.0484	7.25	<1e-12
Sex: Boys	0.1913	0.0142	13.47	<1e-40
Test: Star-Run & a1	0.2998	0.1526	1.96	0.0495
Test: S20-Star & a1	-0.0628	0.1538	-0.41	0.6828
Test: SLJ-S20 & a1	-0.2409	0.1493	-1.61	0.1066
Test: BPT-SLJ & a1	0.4692	0.1466	3.20	0.0014
Test: Star-Run & Sex: Boys	-0.0791	0.0446	-1.77	0.0762
Test: S20-Star & Sex: Boys	-0.0212	0.0441	-0.48	0.6315
Test: SLJ-S20 & Sex: Boys	0.0781	0.0436	1.79	0.0730
Test: BPT-SLJ & Sex: Boys	0.1590	0.0436	3.65	0.0003
a1 & Sex: Boys	-0.0681	0.0484	-1.41	0.1600
Test: Star-Run & a1 & Sex: Boys	-0.1004	0.1526	-0.66	0.5105
Test: S20-Star & a1 & Sex: Boys	-0.0883	0.1538	-0.57	0.5659
Test: SLJ-S20 & a1 & Sex: Boys	0.0388	0.1493	0.26	0.7951
Test: BPT-SLJ & a1 & Sex: Boys	0.2642	0.1466	1.80	0.0714
Residual	0.5829

m_zcp_SeqD_2 = let
  form = @formula(
    zScore ~ 1 + Test * a1 * Sex + (0 + Test | Child)
  )
  fit(MixedModel, form, dat; contrasts=contr1b)
end

Minimizing 10    Time: 0:00:00 (10.32 ms/it)
   objective: 13960.322216747365


Minimizing 19    Time: 0:00:00 (11.03 ms/it)
   objective: 13917.647769395386


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   objective: 13920.4884153477


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   objective: 13855.468352556034


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   objective: 13855.10126611991


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   objective: 13854.59302644577


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   objective: 13851.67690974522


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   objective: 13849.077329110234


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   objective: 13846.825945956134


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   objective: 13846.349678977756


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   objective: 13840.939691528643


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   objective: 13834.486065713321


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   objective: 13823.169304377483


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   objective: 13819.581419007161


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   objective: 13813.95898367808


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   objective: 13811.044310369387


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   objective: 13805.033848580173


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   objective: 13803.590101058933


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   objective: 13803.232512711753


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   objective: 13802.977374867942


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   objective: 13802.562023112341


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   objective: 13800.934853798208


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   objective: 13799.46696007519


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   objective: 13797.617420619992


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   objective: 13797.43938404541


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   objective: 13796.438608447108


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   objective: 13790.300765736674


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   objective: 13789.468781355179


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   objective: 13791.15540746535


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   objective: 13788.06453382311


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   objective: 13786.591240524429


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   objective: 13785.647579858316


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   objective: 13785.274177600902


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   objective: 13784.473306174259


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   objective: 13782.687177485754


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   objective: 13782.437290364014


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   objective: 13781.095202666776


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   objective: 13780.749998640695


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   objective: 13780.484586039362


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   objective: 13778.644325490188


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   objective: 13778.18053806284


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   objective: 13774.371912177172


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   objective: 13772.841089574329


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   objective: 13772.716621466556


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   objective: 13771.15402360491


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   objective: 13770.418964524159


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   objective: 13766.43960565934


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   objective: 13763.241357549181


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   objective: 13762.813224331867


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   objective: 13762.012797845799


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   objective: 13760.75894313459


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   objective: 13760.360949443238


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   objective: 13759.405726811781


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   objective: 13756.706293060568


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   objective: 13751.112102723015


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   objective: 13747.250733119292


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   objective: 13746.959611426153


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   objective: 13745.085267592967


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   objective: 13738.31116675269


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   objective: 13736.672179272036


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   objective: 13735.272449961762


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   objective: 13734.607544974542


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   objective: 13732.837722223703


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   objective: 13729.959435957779


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   objective: 13729.65187697325


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   objective: 13728.912055870358


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   objective: 13726.985199144754


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   objective: 13725.523280327208


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   objective: 13724.292841829341


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   objective: 13722.38862156979


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   objective: 13719.312452098158


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   objective: 13719.221770883469


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   objective: 13718.561108741073


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   objective: 13718.122319225458


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   objective: 13717.210114960279


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   objective: 13716.128409860463


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   objective: 13715.969326788145


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   objective: 13715.680131623332


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   objective: 13715.013342384143


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   objective: 13713.487058727758


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   objective: 13713.283884705339


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   objective: 13713.093843474802


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   objective: 13712.58339329503


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   objective: 13712.3522045131


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   objective: 13712.256825402423


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   objective: 13711.820721961238


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   objective: 13711.391782631235


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   objective: 13708.891947353244


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   objective: 13708.689072126745


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   objective: 13708.517480677448


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   objective: 13707.915777301645


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   objective: 13707.544425163072


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   objective: 13707.318637167209


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   objective: 13706.038654338907


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   objective: 13705.011994962817


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   objective: 13704.331332362028


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   objective: 13697.374458173996


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   objective: 13696.156472956289


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   objective: 13693.516475011897


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   objective: 13690.855122305435


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   objective: 13688.279961426924


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   objective: 13677.256244910444


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   objective: 13674.151935431102


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   objective: 13673.15427696882


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   objective: 13672.872690884768


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   objective: 13670.484710394772


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   objective: 13663.997120029722


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   objective: 13663.44945931826


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   objective: 13660.817606723387


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Minimizing 1616    Time: 0:00:15 ( 9.69 ms/it)
   objective: 13634.10356477151


Minimizing 1627    Time: 0:00:15 ( 9.69 ms/it)
   objective: 13632.87047121759


Minimizing 1638    Time: 0:00:15 ( 9.69 ms/it)
   objective: 13632.549551439479


Minimizing 1649    Time: 0:00:15 ( 9.68 ms/it)
   objective: 13632.157225777068


Minimizing 1660    Time: 0:00:16 ( 9.69 ms/it)
   objective: 13630.728581028583


Minimizing 1671    Time: 0:00:16 ( 9.69 ms/it)
   objective: 13630.392176067267


Minimizing 1682    Time: 0:00:16 ( 9.68 ms/it)
   objective: 13627.098933356727


Minimizing 1693    Time: 0:00:16 ( 9.68 ms/it)
   objective: 13626.06177216235


Minimizing 1704    Time: 0:00:16 ( 9.68 ms/it)
   objective: 13633.29911357777


Minimizing 1715    Time: 0:00:16 ( 9.68 ms/it)
   objective: 13615.84736006894


Minimizing 1726    Time: 0:00:16 ( 9.67 ms/it)
   objective: 13615.427486872279


Minimizing 1737    Time: 0:00:16 ( 9.67 ms/it)
   objective: 13614.60682127477


Minimizing 1748    Time: 0:00:16 ( 9.67 ms/it)
   objective: 13609.723114096101


Minimizing 1759    Time: 0:00:17 ( 9.67 ms/it)
   objective: 13608.310974650376


Minimizing 1770    Time: 0:00:17 ( 9.67 ms/it)
   objective: 13602.374296590075


Minimizing 1781    Time: 0:00:17 ( 9.67 ms/it)
   objective: 13579.553326793364


Minimizing 1792    Time: 0:00:17 ( 9.66 ms/it)
   objective: 13578.33593726014


Minimizing 1803    Time: 0:00:17 ( 9.66 ms/it)
   objective: 13572.627200195886


Minimizing 1814    Time: 0:00:17 ( 9.66 ms/it)
   objective: 13572.389550071333


Minimizing 1825    Time: 0:00:17 ( 9.66 ms/it)
   objective: 13572.084000734321


Minimizing 1836    Time: 0:00:17 ( 9.65 ms/it)
   objective: 13571.152281376686


Minimizing 1847    Time: 0:00:17 ( 9.65 ms/it)
   objective: 13570.333791088131


Minimizing 1858    Time: 0:00:17 ( 9.65 ms/it)
   objective: 13570.273383237341


Minimizing 1869    Time: 0:00:18 ( 9.64 ms/it)
   objective: 13570.241483038197


Minimizing 1880    Time: 0:00:18 ( 9.64 ms/it)
   objective: 13569.908557268318


Minimizing 1891    Time: 0:00:18 ( 9.64 ms/it)
   objective: 13569.835464293326


Minimizing 1902    Time: 0:00:18 ( 9.64 ms/it)
   objective: 13569.79371586212


Minimizing 1913    Time: 0:00:18 ( 9.63 ms/it)
   objective: 13569.541459383661


Minimizing 1925    Time: 0:00:18 ( 9.63 ms/it)
   objective: 13569.490233143457


Minimizing 1936    Time: 0:00:18 ( 9.63 ms/it)
   objective: 13569.17329498555


Minimizing 1948    Time: 0:00:18 ( 9.63 ms/it)
   objective: 13569.069263535886


Minimizing 1959    Time: 0:00:18 ( 9.62 ms/it)
   objective: 13569.018630697843


Minimizing 1970    Time: 0:00:18 ( 9.62 ms/it)
   objective: 13568.762408588838


Minimizing 1981    Time: 0:00:19 ( 9.62 ms/it)
   objective: 13568.484830029287


Minimizing 1992    Time: 0:00:19 ( 9.62 ms/it)
   objective: 13568.45964841055


Minimizing 2003    Time: 0:00:19 ( 9.62 ms/it)
   objective: 13568.145155691927


Minimizing 2015    Time: 0:00:19 ( 9.62 ms/it)
   objective: 13568.029128848226


Minimizing 2026    Time: 0:00:19 ( 9.62 ms/it)
   objective: 13567.364785610705


Minimizing 2037    Time: 0:00:19 ( 9.62 ms/it)
   objective: 13566.824803759657


Minimizing 2048    Time: 0:00:19 ( 9.61 ms/it)
   objective: 13566.261797712526


Minimizing 2059    Time: 0:00:19 ( 9.61 ms/it)
   objective: 13565.887091196317


Minimizing 2070    Time: 0:00:19 ( 9.61 ms/it)
   objective: 13564.194159192455


Minimizing 2156    Time: 0:00:20 ( 9.68 ms/it)
   objective: 13553.445249903409


Minimizing 2170    Time: 0:00:21 ( 9.68 ms/it)
   objective: 13544.930818233384


Minimizing 2181    Time: 0:00:21 ( 9.68 ms/it)
   objective: 13543.939672618719


Minimizing 2192    Time: 0:00:21 ( 9.68 ms/it)
   objective: 13543.097345871058


Minimizing 2203    Time: 0:00:21 ( 9.67 ms/it)
   objective: 13541.826854051513


Minimizing 2214    Time: 0:00:21 ( 9.67 ms/it)
   objective: 13540.103855550537


Minimizing 2226    Time: 0:00:21 ( 9.67 ms/it)
   objective: 13538.571868760584


Minimizing 2237    Time: 0:00:21 ( 9.67 ms/it)
   objective: 13535.109035860078


Minimizing 2248    Time: 0:00:21 ( 9.66 ms/it)
   objective: 13534.54623050992


Minimizing 2259    Time: 0:00:21 ( 9.66 ms/it)
   objective: 13534.188693434262


Minimizing 2270    Time: 0:00:21 ( 9.66 ms/it)
   objective: 13532.869857137659


Minimizing 2281    Time: 0:00:22 ( 9.66 ms/it)
   objective: 13529.790646862559


Minimizing 2292    Time: 0:00:22 ( 9.66 ms/it)
   objective: 13529.36531017421


Minimizing 2303    Time: 0:00:22 ( 9.65 ms/it)
   objective: 13529.086270051135


Minimizing 2314    Time: 0:00:22 ( 9.65 ms/it)
   objective: 13527.440154835422


Minimizing 2325    Time: 0:00:22 ( 9.65 ms/it)
   objective: 13527.071831789712


Minimizing 2336    Time: 0:00:22 ( 9.65 ms/it)
   objective: 13526.34862771118


Minimizing 2347    Time: 0:00:22 ( 9.65 ms/it)
   objective: 13525.485923227985


Minimizing 2358    Time: 0:00:22 ( 9.64 ms/it)
   objective: 13523.274366858954


Minimizing 2369    Time: 0:00:22 ( 9.64 ms/it)
   objective: 13521.345045605558


Minimizing 2380    Time: 0:00:22 ( 9.64 ms/it)
   objective: 13516.423891844242


Minimizing 2391    Time: 0:00:23 ( 9.64 ms/it)
   objective: 13516.158614244297


Minimizing 2402    Time: 0:00:23 ( 9.64 ms/it)
   objective: 13515.627594639009


Minimizing 2413    Time: 0:00:23 ( 9.64 ms/it)
   objective: 13514.678163249948


Minimizing 2424    Time: 0:00:23 ( 9.64 ms/it)
   objective: 13514.213953674203


Minimizing 2435    Time: 0:00:23 ( 9.64 ms/it)
   objective: 13513.666128174576


Minimizing 2446    Time: 0:00:23 ( 9.64 ms/it)
   objective: 13511.38193084039


Minimizing 2457    Time: 0:00:23 ( 9.64 ms/it)
   objective: 13509.232157366976


Minimizing 2468    Time: 0:00:23 ( 9.64 ms/it)
   objective: 13509.056448816715


Minimizing 2479    Time: 0:00:23 ( 9.63 ms/it)
   objective: 13508.870175077725


Minimizing 2490    Time: 0:00:23 ( 9.63 ms/it)
   objective: 13508.65551483215


Minimizing 2501    Time: 0:00:24 ( 9.63 ms/it)
   objective: 13508.191863384272


Minimizing 2512    Time: 0:00:24 ( 9.63 ms/it)
   objective: 13507.919097982362


Minimizing 2523    Time: 0:00:24 ( 9.63 ms/it)
   objective: 13507.555056678786


Minimizing 2534    Time: 0:00:24 ( 9.63 ms/it)
   objective: 13507.001086878241


Minimizing 2545    Time: 0:00:24 ( 9.63 ms/it)
   objective: 13506.746396578063


Minimizing 2556    Time: 0:00:24 ( 9.62 ms/it)
   objective: 13506.487933406766


Minimizing 2567    Time: 0:00:24 ( 9.62 ms/it)
   objective: 13504.584122658358


Minimizing 2578    Time: 0:00:24 ( 9.62 ms/it)
   objective: 13504.40225176436


Minimizing 2589    Time: 0:00:24 ( 9.62 ms/it)
   objective: 13504.15678332861


Minimizing 2600    Time: 0:00:25 ( 9.62 ms/it)
   objective: 13503.770707483825


Minimizing 2611    Time: 0:00:25 ( 9.62 ms/it)
   objective: 13503.481241574846


Minimizing 2622    Time: 0:00:25 ( 9.61 ms/it)
   objective: 13502.960260508102


Minimizing 2633    Time: 0:00:25 ( 9.61 ms/it)
   objective: 13501.672983150187


Minimizing 2644    Time: 0:00:25 ( 9.61 ms/it)
   objective: 13501.261657083829


Minimizing 2655    Time: 0:00:25 ( 9.61 ms/it)
   objective: 13501.253614342888


Minimizing 2666    Time: 0:00:25 ( 9.61 ms/it)
   objective: 13501.222631196477


Minimizing 2677    Time: 0:00:25 ( 9.61 ms/it)
   objective: 13501.139258821102


Minimizing 2688    Time: 0:00:25 ( 9.60 ms/it)
   objective: 13501.004697918368


Minimizing 2699    Time: 0:00:25 ( 9.60 ms/it)
   objective: 13500.875075470365


Minimizing 2710    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13500.723859340593


Minimizing 2721    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13500.12104262461


Minimizing 2732    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13499.596549467868


Minimizing 2743    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13499.264982478911


Minimizing 2754    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13497.863130639511


Minimizing 2765    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13496.698605117548


Minimizing 2776    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13496.546450668306


Minimizing 2787    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13496.54273225661


Minimizing 2798    Time: 0:00:26 ( 9.60 ms/it)
   objective: 13496.542789925326


Minimizing 2809    Time: 0:00:26 ( 9.59 ms/it)
   objective: 13496.542535711647


Minimizing 2820    Time: 0:00:27 ( 9.59 ms/it)
   objective: 13496.542817165478


Minimizing 2832    Time: 0:00:27 ( 9.59 ms/it)
   objective: 13496.542488626306


Minimizing 2843    Time: 0:00:27 ( 9.59 ms/it)
   objective: 13496.54247475497


Minimizing 2854    Time: 0:00:27 ( 9.59 ms/it)
   objective: 13496.542581950373


Minimizing 2865    Time: 0:00:27 ( 9.59 ms/it)
   objective: 13496.542522242016


Minimizing 2876    Time: 0:00:27 ( 9.59 ms/it)
   objective: 13496.54247809037


Minimizing 2887    Time: 0:00:27 ( 9.58 ms/it)
   objective: 13496.542283678078


Minimizing 2898    Time: 0:00:27 ( 9.58 ms/it)
   objective: 13496.542448280059


Minimizing 2909    Time: 0:00:27 ( 9.58 ms/it)
   objective: 13496.542370044932


Minimizing 2920    Time: 0:00:27 ( 9.58 ms/it)
   objective: 13496.54228990787


Minimizing 2931    Time: 0:00:28 ( 9.58 ms/it)
   objective: 13496.542350734962


Minimizing 2942    Time: 0:00:28 ( 9.58 ms/it)
   objective: 13496.542286761876


Minimizing 2953    Time: 0:00:28 ( 9.58 ms/it)
   objective: 13496.54223769874


Minimizing 2964    Time: 0:00:28 ( 9.57 ms/it)
   objective: 13496.542363798377


Minimizing 2975    Time: 0:00:28 ( 9.57 ms/it)
   objective: 13496.542272039398


Minimizing 2986    Time: 0:00:28 ( 9.57 ms/it)
   objective: 13496.542430458474


Minimizing 2997    Time: 0:00:28 ( 9.57 ms/it)
   objective: 13496.542245101038


Minimizing 3009    Time: 0:00:28 ( 9.57 ms/it)
   objective: 13496.542277439788


Minimizing 3019    Time: 0:00:28 ( 9.57 ms/it)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0197	0.0142	-1.39	0.1636
Test: Star-Run	-0.0154	0.0440	-0.35	0.7265
Test: S20-Star	-0.0015	0.0449	-0.03	0.9741
Test: SLJ-S20	0.0120	0.0447	0.27	0.7885
Test: BPT-SLJ	-0.0298	0.0432	-0.69	0.4898
a1	0.3548	0.0483	7.35	<1e-12
Sex: Boys	0.1919	0.0142	13.56	<1e-41
Test: Star-Run & a1	0.3081	0.1508	2.04	0.0411
Test: S20-Star & a1	-0.0408	0.1567	-0.26	0.7943
Test: SLJ-S20 & a1	-0.2624	0.1535	-1.71	0.0873
Test: BPT-SLJ & a1	0.4622	0.1456	3.17	0.0015
Test: Star-Run & Sex: Boys	-0.0827	0.0440	-1.88	0.0604
Test: S20-Star & Sex: Boys	-0.0242	0.0449	-0.54	0.5904
Test: SLJ-S20 & Sex: Boys	0.0847	0.0447	1.89	0.0581
Test: BPT-SLJ & Sex: Boys	0.1577	0.0432	3.65	0.0003
a1 & Sex: Boys	-0.0670	0.0483	-1.39	0.1655
Test: Star-Run & a1 & Sex: Boys	-0.0871	0.1508	-0.58	0.5636
Test: S20-Star & a1 & Sex: Boys	-0.0777	0.1567	-0.50	0.6199
Test: SLJ-S20 & a1 & Sex: Boys	0.0220	0.1535	0.14	0.8860
Test: BPT-SLJ & a1 & Sex: Boys	0.2683	0.1456	1.84	0.0653
Test: Run					0.9712
Test: Star_r					0.9851
Test: S20_r					0.9866
Test: SLJ					0.9759
Test: BPT					0.9206
Residual	0.0001

m_cpx_0_SeqDiff = let
  f_cpx_0 = @formula(
    zScore ~ 1 + Test * a1 * Sex + (0 + Test | Child)
  )
  fit(MixedModel, f_cpx_0, dat; contrasts=contr1b)
end

Minimizing 11    Time: 0:00:00 ( 9.24 ms/it)
   objective: 14015.92257854082


Minimizing 22    Time: 0:00:00 ( 9.61 ms/it)
   objective: 14072.366682023294


Minimizing 33    Time: 0:00:00 ( 9.70 ms/it)
   objective: 13856.369659160984


Minimizing 44    Time: 0:00:00 ( 9.56 ms/it)
   objective: 13855.53208712221


Minimizing 55    Time: 0:00:00 ( 9.57 ms/it)
   objective: 13855.74059996676


Minimizing 65    Time: 0:00:00 ( 9.70 ms/it)
   objective: 13852.84351809056


Minimizing 75    Time: 0:00:00 ( 9.79 ms/it)
   objective: 13850.584868490663


Minimizing 86    Time: 0:00:00 ( 9.78 ms/it)
   objective: 13847.901091360854


Minimizing 96    Time: 0:00:00 ( 9.81 ms/it)
   objective: 13844.879199408384


Minimizing 106    Time: 0:00:01 ( 9.86 ms/it)
   objective: 13840.583298224967


Minimizing 117    Time: 0:00:01 ( 9.85 ms/it)
   objective: 13832.795458573662


Minimizing 128    Time: 0:00:01 ( 9.85 ms/it)
   objective: 13822.906825216749


Minimizing 139    Time: 0:00:01 ( 9.81 ms/it)
   objective: 13820.220935697595


Minimizing 150    Time: 0:00:01 ( 9.77 ms/it)
   objective: 13815.314777803009


Minimizing 161    Time: 0:00:01 ( 9.74 ms/it)
   objective: 13807.508308019233


Minimizing 172    Time: 0:00:01 ( 9.71 ms/it)
   objective: 13806.067627613016


Minimizing 183    Time: 0:00:01 ( 9.68 ms/it)
   objective: 13803.96075575856


Minimizing 194    Time: 0:00:01 ( 9.65 ms/it)
   objective: 13803.243801358583


Minimizing 205    Time: 0:00:01 ( 9.64 ms/it)
   objective: 13803.068221136882


Minimizing 216    Time: 0:00:02 ( 9.62 ms/it)
   objective: 13802.702554770645


Minimizing 227    Time: 0:00:02 ( 9.60 ms/it)
   objective: 13801.501578709443


Minimizing 238    Time: 0:00:02 ( 9.59 ms/it)
   objective: 13799.937734607203


Minimizing 249    Time: 0:00:02 ( 9.57 ms/it)
   objective: 13798.181609332487


Minimizing 260    Time: 0:00:02 ( 9.55 ms/it)
   objective: 13797.49456742328


Minimizing 271    Time: 0:00:02 ( 9.54 ms/it)
   objective: 13797.053387656906


Minimizing 282    Time: 0:00:02 ( 9.53 ms/it)
   objective: 13792.092055646553


Minimizing 293    Time: 0:00:02 ( 9.51 ms/it)
   objective: 13789.546454640556


Minimizing 305    Time: 0:00:02 ( 9.50 ms/it)
   objective: 13788.921536501233


Minimizing 315    Time: 0:00:02 ( 9.52 ms/it)
   objective: 13788.230418516678


Minimizing 326    Time: 0:00:03 ( 9.51 ms/it)
   objective: 13787.32202956283


Minimizing 337    Time: 0:00:03 ( 9.50 ms/it)
   objective: 13785.773587324773


Minimizing 350    Time: 0:00:03 ( 9.54 ms/it)
   objective: 13785.321472935637


Minimizing 363    Time: 0:00:03 ( 9.53 ms/it)
   objective: 13784.289853092683


Minimizing 374    Time: 0:00:03 ( 9.52 ms/it)
   objective: 13782.610502619431


Minimizing 385    Time: 0:00:03 ( 9.50 ms/it)
   objective: 13782.327273140156


Minimizing 396    Time: 0:00:03 ( 9.50 ms/it)
   objective: 13781.254634022273


Minimizing 407    Time: 0:00:03 ( 9.49 ms/it)
   objective: 13780.672172135812


Minimizing 418    Time: 0:00:03 ( 9.48 ms/it)
   objective: 13778.972807571852


Minimizing 429    Time: 0:00:04 ( 9.48 ms/it)
   objective: 13778.330881559443


Minimizing 440    Time: 0:00:04 ( 9.47 ms/it)
   objective: 13775.940462826089


Minimizing 451    Time: 0:00:04 ( 9.46 ms/it)
   objective: 13773.188439152269


Minimizing 462    Time: 0:00:04 ( 9.45 ms/it)
   objective: 13772.693291580583


Minimizing 474    Time: 0:00:04 ( 9.44 ms/it)
   objective: 13771.309477095281


Minimizing 486    Time: 0:00:04 ( 9.44 ms/it)
   objective: 13770.418964524159


Minimizing 497    Time: 0:00:04 ( 9.43 ms/it)
   objective: 13766.43960565934


Minimizing 508    Time: 0:00:04 ( 9.43 ms/it)
   objective: 13763.241357549181


Minimizing 519    Time: 0:00:04 ( 9.43 ms/it)
   objective: 13762.813224331867


Minimizing 530    Time: 0:00:05 ( 9.44 ms/it)
   objective: 13762.012797845799


Minimizing 541    Time: 0:00:05 ( 9.44 ms/it)
   objective: 13760.79148650394


Minimizing 552    Time: 0:00:05 ( 9.44 ms/it)
   objective: 13760.38981851256


Minimizing 563    Time: 0:00:05 ( 9.44 ms/it)
   objective: 13759.464924837526


Minimizing 574    Time: 0:00:05 ( 9.44 ms/it)
   objective: 13757.48279713933


Minimizing 585    Time: 0:00:05 ( 9.44 ms/it)
   objective: 13751.523525099674


Minimizing 596    Time: 0:00:05 ( 9.44 ms/it)
   objective: 13747.339429763288


Minimizing 607    Time: 0:00:05 ( 9.43 ms/it)
   objective: 13747.044039877706


Minimizing 618    Time: 0:00:05 ( 9.43 ms/it)
   objective: 13745.42677432337


Minimizing 629    Time: 0:00:05 ( 9.44 ms/it)
   objective: 13739.89813824988


Minimizing 640    Time: 0:00:06 ( 9.43 ms/it)
   objective: 13736.915630627858


Minimizing 652    Time: 0:00:06 ( 9.43 ms/it)
   objective: 13735.569370972125


Minimizing 663    Time: 0:00:06 ( 9.42 ms/it)
   objective: 13734.635046387664


Minimizing 674    Time: 0:00:06 ( 9.42 ms/it)
   objective: 13733.131387417774


Minimizing 685    Time: 0:00:06 ( 9.41 ms/it)
   objective: 13730.15297131693


Minimizing 696    Time: 0:00:06 ( 9.41 ms/it)
   objective: 13729.667984687272


Minimizing 707    Time: 0:00:06 ( 9.40 ms/it)
   objective: 13729.109809795122


Minimizing 718    Time: 0:00:06 ( 9.40 ms/it)
   objective: 13726.985199144754


Minimizing 729    Time: 0:00:06 ( 9.40 ms/it)
   objective: 13725.523280327208


Minimizing 740    Time: 0:00:06 ( 9.40 ms/it)
   objective: 13724.368444819225


Minimizing 751    Time: 0:00:07 ( 9.40 ms/it)
   objective: 13724.292841829341


Minimizing 762    Time: 0:00:07 ( 9.41 ms/it)
   objective: 13722.38862156979


Minimizing 773    Time: 0:00:07 ( 9.40 ms/it)
   objective: 13719.312452098158


Minimizing 785    Time: 0:00:07 ( 9.40 ms/it)
   objective: 13719.21499107503


Minimizing 796    Time: 0:00:07 ( 9.40 ms/it)
   objective: 13718.561108741073


Minimizing 807    Time: 0:00:07 ( 9.39 ms/it)
   objective: 13718.062941203974


Minimizing 818    Time: 0:00:07 ( 9.39 ms/it)
   objective: 13716.816921466565


Minimizing 829    Time: 0:00:07 ( 9.39 ms/it)
   objective: 13716.131452979764


Minimizing 840    Time: 0:00:07 ( 9.38 ms/it)
   objective: 13715.96260131904


Minimizing 851    Time: 0:00:07 ( 9.38 ms/it)
   objective: 13715.652967803351


Minimizing 862    Time: 0:00:08 ( 9.38 ms/it)
   objective: 13714.902839845105


Minimizing 873    Time: 0:00:08 ( 9.38 ms/it)
   objective: 13713.637987797832


Minimizing 884    Time: 0:00:08 ( 9.37 ms/it)
   objective: 13713.280088628202


Minimizing 896    Time: 0:00:08 ( 9.37 ms/it)
   objective: 13712.930453360816


Minimizing 907    Time: 0:00:08 ( 9.37 ms/it)
   objective: 13712.38337143463


Minimizing 919    Time: 0:00:08 ( 9.36 ms/it)
   objective: 13712.346666040103


Minimizing 930    Time: 0:00:08 ( 9.36 ms/it)
   objective: 13712.0994867941


Minimizing 941    Time: 0:00:08 ( 9.36 ms/it)
   objective: 13711.717929847433


Minimizing 952    Time: 0:00:08 ( 9.36 ms/it)
   objective: 13711.078537165933


Minimizing 963    Time: 0:00:09 ( 9.37 ms/it)
   objective: 13708.759328631084


Minimizing 973    Time: 0:00:09 ( 9.38 ms/it)
   objective: 13708.679742889246


Minimizing 984    Time: 0:00:09 ( 9.38 ms/it)
   objective: 13708.44235351188


Minimizing 995    Time: 0:00:09 ( 9.38 ms/it)
   objective: 13707.852539793086


Minimizing 1006    Time: 0:00:09 ( 9.39 ms/it)
   objective: 13707.495397136885


Minimizing 1017    Time: 0:00:09 ( 9.39 ms/it)
   objective: 13707.214453358349


Minimizing 1028    Time: 0:00:09 ( 9.39 ms/it)
   objective: 13705.952328657466


Minimizing 1039    Time: 0:00:09 ( 9.38 ms/it)
   objective: 13705.110657761794


Minimizing 1051    Time: 0:00:09 ( 9.38 ms/it)
   objective: 13703.979243885107


Minimizing 1062    Time: 0:00:09 ( 9.38 ms/it)
   objective: 13698.816150196471


Minimizing 1073    Time: 0:00:10 ( 9.39 ms/it)
   objective: 13696.135711311203


Minimizing 1084    Time: 0:00:10 ( 9.38 ms/it)
   objective: 13695.28864920529


Minimizing 1095    Time: 0:00:10 ( 9.39 ms/it)
   objective: 13694.570334744934


Minimizing 1106    Time: 0:00:10 ( 9.38 ms/it)
   objective: 13693.339458732076


Minimizing 1117    Time: 0:00:10 ( 9.38 ms/it)
   objective: 13691.940704971916


Minimizing 1128    Time: 0:00:10 ( 9.38 ms/it)
   objective: 13689.991414959735


Minimizing 1139    Time: 0:00:10 ( 9.38 ms/it)
   objective: 13687.965263586826


Minimizing 1150    Time: 0:00:10 ( 9.39 ms/it)
   objective: 13686.990555785007


Minimizing 1161    Time: 0:00:10 ( 9.38 ms/it)
   objective: 13684.451819958522


Minimizing 1172    Time: 0:00:11 ( 9.39 ms/it)
   objective: 13681.30229815617


Minimizing 1183    Time: 0:00:11 ( 9.39 ms/it)
   objective: 13679.711505239324


Minimizing 1194    Time: 0:00:11 ( 9.39 ms/it)
   objective: 13679.017381830192


Minimizing 1205    Time: 0:00:11 ( 9.38 ms/it)
   objective: 13678.355435914269


Minimizing 1216    Time: 0:00:11 ( 9.38 ms/it)
   objective: 13677.256244910444


Minimizing 1227    Time: 0:00:11 ( 9.38 ms/it)
   objective: 13674.255073440458


Minimizing 1238    Time: 0:00:11 ( 9.38 ms/it)
   objective: 13673.514276925373


Minimizing 1249    Time: 0:00:11 ( 9.38 ms/it)
   objective: 13672.903696407044


Minimizing 1260    Time: 0:00:11 ( 9.38 ms/it)
   objective: 13671.93125154659


Minimizing 1271    Time: 0:00:11 ( 9.38 ms/it)
   objective: 13667.651647697086


Minimizing 1282    Time: 0:00:12 ( 9.38 ms/it)
   objective: 13666.486388232297


Minimizing 1293    Time: 0:00:12 ( 9.38 ms/it)
   objective: 13666.37532655782


Minimizing 1304    Time: 0:00:12 ( 9.38 ms/it)
   objective: 13664.497410032593


Minimizing 1315    Time: 0:00:12 ( 9.37 ms/it)
   objective: 13663.47774446645


Minimizing 1326    Time: 0:00:12 ( 9.37 ms/it)
   objective: 13663.338971219368


Minimizing 1337    Time: 0:00:12 ( 9.37 ms/it)
   objective: 13661.249964863535


Minimizing 1348    Time: 0:00:12 ( 9.37 ms/it)
   objective: 13660.255356034831


Minimizing 1359    Time: 0:00:12 ( 9.37 ms/it)
   objective: 13659.256765327562


Minimizing 1370    Time: 0:00:12 ( 9.37 ms/it)
   objective: 13658.224684935332


Minimizing 1381    Time: 0:00:12 ( 9.37 ms/it)
   objective: 13655.777137186982


Minimizing 1392    Time: 0:00:13 ( 9.37 ms/it)
   objective: 13648.686430876296


Minimizing 1403    Time: 0:00:13 ( 9.37 ms/it)
   objective: 13645.223752633203


Minimizing 1417    Time: 0:00:13 ( 9.39 ms/it)
   objective: 13643.699873513244


Minimizing 1430    Time: 0:00:13 ( 9.38 ms/it)
   objective: 13642.732099888344


Minimizing 1441    Time: 0:00:13 ( 9.39 ms/it)
   objective: 13642.643347215839


Minimizing 1452    Time: 0:00:13 ( 9.39 ms/it)
   objective: 13641.42235765094


Minimizing 1463    Time: 0:00:13 ( 9.39 ms/it)
   objective: 13639.825175838254


Minimizing 1474    Time: 0:00:13 ( 9.39 ms/it)
   objective: 13638.692364038136


Minimizing 1485    Time: 0:00:13 ( 9.39 ms/it)
   objective: 13638.499733019831


Minimizing 1496    Time: 0:00:14 ( 9.40 ms/it)
   objective: 13638.134370721338


Minimizing 1507    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13637.629452057903


Minimizing 1518    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13636.811688102054


Minimizing 1529    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13636.587054262323


Minimizing 1540    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13636.383441839076


Minimizing 1551    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13636.004479977404


Minimizing 1562    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13635.853811584173


Minimizing 1573    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13635.659761971714


Minimizing 1584    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13635.356546571209


Minimizing 1595    Time: 0:00:14 ( 9.39 ms/it)
   objective: 13634.871861886626


Minimizing 1606    Time: 0:00:15 ( 9.39 ms/it)
   objective: 13634.168393889267


Minimizing 1617    Time: 0:00:15 ( 9.39 ms/it)
   objective: 13634.091486092286


Minimizing 1628    Time: 0:00:15 ( 9.40 ms/it)
   objective: 13632.743634726641


Minimizing 1639    Time: 0:00:15 ( 9.40 ms/it)
   objective: 13632.540805841862


Minimizing 1650    Time: 0:00:15 ( 9.40 ms/it)
   objective: 13631.850645347018


Minimizing 1661    Time: 0:00:15 ( 9.39 ms/it)
   objective: 13630.86743678974


Minimizing 1672    Time: 0:00:15 ( 9.39 ms/it)
   objective: 13630.307474752437


Minimizing 1683    Time: 0:00:15 ( 9.39 ms/it)
   objective: 13626.836051208746


Minimizing 1694    Time: 0:00:15 ( 9.39 ms/it)
   objective: 13625.989409280926


Minimizing 1705    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13618.586463778825


Minimizing 1716    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13615.821101115274


Minimizing 1727    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13615.233738915354


Minimizing 1738    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13614.435935696696


Minimizing 1749    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13609.672791105979


Minimizing 1760    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13608.19111973518


Minimizing 1771    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13598.274277536628


Minimizing 1782    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13578.585570721232


Minimizing 1793    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13578.271469235988


Minimizing 1804    Time: 0:00:16 ( 9.39 ms/it)
   objective: 13572.73134602348


Minimizing 1815    Time: 0:00:17 ( 9.40 ms/it)
   objective: 13572.384534579738


Minimizing 1826    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13572.077360947027


Minimizing 1837    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13570.933042012104


Minimizing 1848    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13570.311106842186


Minimizing 1859    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13570.273261930262


Minimizing 1870    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13570.211714620826


Minimizing 1881    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13569.922967139566


Minimizing 1892    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13569.839354018106


Minimizing 1903    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13569.76708476719


Minimizing 1914    Time: 0:00:17 ( 9.39 ms/it)
   objective: 13569.523841445225


Minimizing 1925    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13569.490233143457


Minimizing 1936    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13569.17329498555


Minimizing 1947    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13569.076127914122


Minimizing 1958    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13569.04079198435


Minimizing 1969    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13568.776358032861


Minimizing 1980    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13568.496859071107


Minimizing 1991    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13568.46193561265


Minimizing 2002    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13568.161612370859


Minimizing 2013    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13568.056094395703


Minimizing 2024    Time: 0:00:18 ( 9.38 ms/it)
   objective: 13567.438920022323


Minimizing 2035    Time: 0:00:19 ( 9.38 ms/it)
   objective: 13567.055056797923


Minimizing 2046    Time: 0:00:19 ( 9.38 ms/it)
   objective: 13566.324221003357


Minimizing 2057    Time: 0:00:19 ( 9.38 ms/it)
   objective: 13566.110862482456


Minimizing 2068    Time: 0:00:19 ( 9.38 ms/it)
   objective: 13564.461769554058


Minimizing 2079    Time: 0:00:19 ( 9.38 ms/it)
   objective: 13563.461343707371


Minimizing 2090    Time: 0:00:19 ( 9.37 ms/it)
   objective: 13563.092508933398


Minimizing 2101    Time: 0:00:19 ( 9.37 ms/it)
   objective: 13562.018625563156


Minimizing 2112    Time: 0:00:19 ( 9.37 ms/it)
   objective: 13560.91713136663


Minimizing 2123    Time: 0:00:19 ( 9.37 ms/it)
   objective: 13559.849729192647


Minimizing 2134    Time: 0:00:20 ( 9.37 ms/it)
   objective: 13556.740991591309


Minimizing 2145    Time: 0:00:20 ( 9.38 ms/it)
   objective: 13553.948087138102


Minimizing 2156    Time: 0:00:20 ( 9.38 ms/it)
   objective: 13553.445249903409


Minimizing 2167    Time: 0:00:20 ( 9.38 ms/it)
   objective: 13546.305770401887


Minimizing 2178    Time: 0:00:20 ( 9.38 ms/it)
   objective: 13543.953980054328


Minimizing 2189    Time: 0:00:20 ( 9.38 ms/it)
   objective: 13543.688506983948


Minimizing 2200    Time: 0:00:20 ( 9.37 ms/it)
   objective: 13542.002110393456


Minimizing 2211    Time: 0:00:20 ( 9.37 ms/it)
   objective: 13540.742595141783


Minimizing 2222    Time: 0:00:20 ( 9.38 ms/it)
   objective: 13539.405861314008


Minimizing 2233    Time: 0:00:20 ( 9.38 ms/it)
   objective: 13536.081904857085


Minimizing 2244    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13534.663389140624


Minimizing 2255    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13534.513124126912


Minimizing 2267    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13533.389494276096


Minimizing 2278    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13531.486562440681


Minimizing 2289    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13529.436500992218


Minimizing 2300    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13529.315596382541


Minimizing 2311    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13527.728611562387


Minimizing 2322    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13527.209931676814


Minimizing 2334    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13526.49055422812


Minimizing 2344    Time: 0:00:21 ( 9.38 ms/it)
   objective: 13525.627060852348


Minimizing 2354    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13525.094274728908


Minimizing 2365    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13518.817118469262


Minimizing 2376    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13516.523988507572


Minimizing 2387    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13516.308985224387


Minimizing 2398    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13515.809599946268


Minimizing 2409    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13515.193227181138


Minimizing 2420    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13514.328005326664


Minimizing 2431    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13514.004516843954


Minimizing 2442    Time: 0:00:22 ( 9.39 ms/it)
   objective: 13512.512453985692


Minimizing 2453    Time: 0:00:23 ( 9.39 ms/it)
   objective: 13509.263957897158


Minimizing 2464    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13509.06136530124


Minimizing 2475    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13509.020647687328


Minimizing 2487    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13508.68390502721


Minimizing 2498    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13508.38033142488


Minimizing 2509    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13507.958357807118


Minimizing 2521    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13507.673819991192


Minimizing 2532    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13507.063781579593


Minimizing 2543    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13506.788002817528


Minimizing 2554    Time: 0:00:23 ( 9.38 ms/it)
   objective: 13506.565697190425


Minimizing 2565    Time: 0:00:24 ( 9.38 ms/it)
   objective: 13504.97478979436


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   objective: 13504.41630393402


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   objective: 13504.26324921845


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   objective: 13503.848172474682


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   objective: 13503.510096394457


Minimizing 2620    Time: 0:00:24 ( 9.37 ms/it)
   objective: 13503.116852583174


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   objective: 13501.562380502713


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   objective: 13501.265037912759


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   objective: 13501.255504780667


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   objective: 13501.235941659339


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   objective: 13501.043064763886


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   objective: 13500.881859113331


Minimizing 2707    Time: 0:00:25 ( 9.38 ms/it)
   objective: 13500.79760484655


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   objective: 13499.710798284199


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   objective: 13499.404685800982


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   objective: 13498.516421302687


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   objective: 13497.22488813028


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   objective: 13496.543072865446


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   objective: 13496.542621310451


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   objective: 13496.54259550423


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   objective: 13496.542837509929


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Minimizing 2859    Time: 0:00:26 ( 9.40 ms/it)
   objective: 13496.542386541245


Minimizing 2870    Time: 0:00:26 ( 9.40 ms/it)
   objective: 13496.542313257756


Minimizing 2881    Time: 0:00:27 ( 9.40 ms/it)
   objective: 13496.542441121288


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   objective: 13496.54223826433


Minimizing 2902    Time: 0:00:27 ( 9.42 ms/it)
   objective: 13496.542304953851


Minimizing 2913    Time: 0:00:27 ( 9.42 ms/it)
   objective: 13496.542456553434


Minimizing 2924    Time: 0:00:27 ( 9.42 ms/it)
   objective: 13496.542459869073


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   objective: 13496.54243196435


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   objective: 13496.542261596041


Minimizing 2958    Time: 0:00:27 ( 9.42 ms/it)
   objective: 13496.542264035044


Minimizing 2969    Time: 0:00:27 ( 9.42 ms/it)
   objective: 13496.542270465856


Minimizing 2980    Time: 0:00:28 ( 9.42 ms/it)
   objective: 13496.54227176118


Minimizing 2991    Time: 0:00:28 ( 9.41 ms/it)
   objective: 13496.542283693401


Minimizing 3002    Time: 0:00:28 ( 9.41 ms/it)
   objective: 13496.5422816059


Minimizing 3013    Time: 0:00:28 ( 9.41 ms/it)
   objective: 13496.542281210553


Minimizing 3019    Time: 0:00:28 ( 9.41 ms/it)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0197	0.0142	-1.39	0.1636
Test: Star-Run	-0.0154	0.0440	-0.35	0.7265
Test: S20-Star	-0.0015	0.0449	-0.03	0.9741
Test: SLJ-S20	0.0120	0.0447	0.27	0.7885
Test: BPT-SLJ	-0.0298	0.0432	-0.69	0.4898
a1	0.3548	0.0483	7.35	<1e-12
Sex: Boys	0.1919	0.0142	13.56	<1e-41
Test: Star-Run & a1	0.3081	0.1508	2.04	0.0411
Test: S20-Star & a1	-0.0408	0.1567	-0.26	0.7943
Test: SLJ-S20 & a1	-0.2624	0.1535	-1.71	0.0873
Test: BPT-SLJ & a1	0.4622	0.1456	3.17	0.0015
Test: Star-Run & Sex: Boys	-0.0827	0.0440	-1.88	0.0604
Test: S20-Star & Sex: Boys	-0.0242	0.0449	-0.54	0.5904
Test: SLJ-S20 & Sex: Boys	0.0847	0.0447	1.89	0.0581
Test: BPT-SLJ & Sex: Boys	0.1577	0.0432	3.65	0.0003
a1 & Sex: Boys	-0.0670	0.0483	-1.39	0.1655
Test: Star-Run & a1 & Sex: Boys	-0.0871	0.1508	-0.58	0.5636
Test: S20-Star & a1 & Sex: Boys	-0.0777	0.1567	-0.50	0.6199
Test: SLJ-S20 & a1 & Sex: Boys	0.0220	0.1535	0.14	0.8860
Test: BPT-SLJ & a1 & Sex: Boys	0.2683	0.1456	1.84	0.0653
Test: Run					0.9712
Test: Star_r					0.9851
Test: S20_r					0.9866
Test: SLJ					0.9759
Test: BPT					0.9206
Residual	0.0001

VarCorr(m_cpx_0_SeqDiff)

	Column	Variance	Std.Dev	Corr.
Child	Test: Run	0.943179402	0.971174238
	Test: Star_r	0.970421012	0.985099493	+0.64
	Test: S20_r	0.973373545	0.986596952	+0.71	+0.03
	Test: SLJ	0.952370839	0.975894891	+0.44	+0.74	+0.28
	Test: BPT	0.847582007	0.920642171	+0.21	+0.29	+0.11	+0.19
Residual		0.000000011	0.000105278

m_cpx_0_SeqDiff.PCA

(Child = 
Principal components based on correlation matrix
 Test: Run     1.0    .     .     .     .
 Test: Star_r  0.64  1.0    .     .     .
 Test: S20_r   0.71  0.03  1.0    .     .
 Test: SLJ     0.44  0.74  0.28  1.0    .
 Test: BPT     0.21  0.29  0.11  0.19  1.0

Normalized cumulative variances:
[0.5127, 0.7417, 0.917, 1.0, 1.0]

Component loadings
                 PC1    PC2    PC3    PC4    PC5
 Test: Run     -0.55   0.32   0.04   0.53   0.57
 Test: Star_r  -0.51  -0.45   0.2    0.37  -0.59
 Test: S20_r   -0.36   0.74  -0.1   -0.31  -0.48
 Test: SLJ     -0.49  -0.29   0.3   -0.7    0.31
 Test: BPT     -0.26  -0.26  -0.93  -0.09   0.05,)

f_cpx_1 = @formula(
  zScore ~ 1 + Test * a1 * Sex + (1 + Test | Child)
)
m_cpx_1_SeqDiff =
fit(MixedModel, f_cpx_1, dat; contrasts=contr1b)

Minimizing 11    Time: 0:00:00 ( 9.27 ms/it)
   objective: 13905.365587289616


Minimizing 22    Time: 0:00:00 ( 9.71 ms/it)
   objective: 13891.169931774632


Minimizing 32    Time: 0:00:00 ( 9.94 ms/it)
   objective: 13925.92599565793


Minimizing 43    Time: 0:00:00 ( 9.81 ms/it)
   objective: 13841.544449419174


Minimizing 54    Time: 0:00:00 ( 9.81 ms/it)
   objective: 13837.39021981755


Minimizing 65    Time: 0:00:00 ( 9.79 ms/it)
   objective: 13832.87035654105


Minimizing 76    Time: 0:00:00 ( 9.82 ms/it)
   objective: 13826.546137875921


Minimizing 87    Time: 0:00:00 ( 9.82 ms/it)
   objective: 13826.007015477113


Minimizing 98    Time: 0:00:00 ( 9.81 ms/it)
   objective: 13824.5848468172


Minimizing 109    Time: 0:00:01 ( 9.79 ms/it)
   objective: 13823.289633409717


Minimizing 120    Time: 0:00:01 ( 9.79 ms/it)
   objective: 13823.460290086936


Minimizing 131    Time: 0:00:01 ( 9.80 ms/it)
   objective: 13821.60072616827


Minimizing 141    Time: 0:00:01 ( 9.82 ms/it)
   objective: 13819.905805017715


Minimizing 152    Time: 0:00:01 ( 9.80 ms/it)
   objective: 13817.842016922752


Minimizing 162    Time: 0:00:01 (10.01 ms/it)
   objective: 13816.267359671298


Minimizing 172    Time: 0:00:01 (10.08 ms/it)
   objective: 13814.777083458293


Minimizing 180    Time: 0:00:01 (10.20 ms/it)
   objective: 13814.695183329797


Minimizing 188    Time: 0:00:01 (10.34 ms/it)
   objective: 13812.954158009925


Minimizing 198    Time: 0:00:02 (10.34 ms/it)
   objective: 13807.68938263755


Minimizing 209    Time: 0:00:02 (10.32 ms/it)
   objective: 13802.180144965178


Minimizing 220    Time: 0:00:02 (10.27 ms/it)
   objective: 13800.802787089462


Minimizing 231    Time: 0:00:02 (10.26 ms/it)
   objective: 13800.152503239071


Minimizing 242    Time: 0:00:02 (10.23 ms/it)
   objective: 13797.370266477568


Minimizing 253    Time: 0:00:02 (10.21 ms/it)
   objective: 13796.017421779527


Minimizing 264    Time: 0:00:02 (10.19 ms/it)
   objective: 13788.449654408065


Minimizing 275    Time: 0:00:02 (10.17 ms/it)
   objective: 13788.109410876732


Minimizing 286    Time: 0:00:02 (10.15 ms/it)
   objective: 13786.40034273266


Minimizing 297    Time: 0:00:03 (10.13 ms/it)
   objective: 13784.970057318158


Minimizing 308    Time: 0:00:03 (10.11 ms/it)
   objective: 13783.749887572927


Minimizing 319    Time: 0:00:03 (10.12 ms/it)
   objective: 13782.97450009279


Minimizing 330    Time: 0:00:03 (10.11 ms/it)
   objective: 13782.108776753965


Minimizing 341    Time: 0:00:03 (10.10 ms/it)
   objective: 13781.95742636447


Minimizing 352    Time: 0:00:03 (10.09 ms/it)
   objective: 13781.527920311673


Minimizing 363    Time: 0:00:03 (10.08 ms/it)
   objective: 13780.902860417906


Minimizing 374    Time: 0:00:03 (10.06 ms/it)
   objective: 13779.8661419389


Minimizing 385    Time: 0:00:03 (10.06 ms/it)
   objective: 13779.737740126824


Minimizing 396    Time: 0:00:03 (10.03 ms/it)
   objective: 13777.713240471065


Minimizing 407    Time: 0:00:04 (10.01 ms/it)
   objective: 13777.354580581708


Minimizing 418    Time: 0:00:04 ( 9.99 ms/it)
   objective: 13776.777008991765


Minimizing 429    Time: 0:00:04 ( 9.98 ms/it)
   objective: 13776.315760030913


Minimizing 440    Time: 0:00:04 ( 9.97 ms/it)
   objective: 13776.05360042063


Minimizing 450    Time: 0:00:04 (10.02 ms/it)
   objective: 13775.592436041534


Minimizing 461    Time: 0:00:04 (10.01 ms/it)
   objective: 13774.325245961969


Minimizing 471    Time: 0:00:04 (10.02 ms/it)
   objective: 13773.284891449086


Minimizing 481    Time: 0:00:04 (10.03 ms/it)
   objective: 13772.364934078116


Minimizing 491    Time: 0:00:04 (10.03 ms/it)
   objective: 13772.203694449872


Minimizing 502    Time: 0:00:05 (10.03 ms/it)
   objective: 13770.23500457091


Minimizing 513    Time: 0:00:05 (10.03 ms/it)
   objective: 13768.966413209097


Minimizing 524    Time: 0:00:05 (10.01 ms/it)
   objective: 13768.889207883105


Minimizing 538    Time: 0:00:05 (10.04 ms/it)
   objective: 13768.416985192205


Minimizing 551    Time: 0:00:05 (10.02 ms/it)
   objective: 13767.809441595131


Minimizing 562    Time: 0:00:05 (10.01 ms/it)
   objective: 13767.086032066123


Minimizing 573    Time: 0:00:05 ( 9.99 ms/it)
   objective: 13766.202578595268


Minimizing 584    Time: 0:00:05 ( 9.98 ms/it)
   objective: 13766.110858025582


Minimizing 595    Time: 0:00:05 ( 9.97 ms/it)
   objective: 13765.921632380996


Minimizing 606    Time: 0:00:06 ( 9.95 ms/it)
   objective: 13765.76233271485


Minimizing 617    Time: 0:00:06 ( 9.94 ms/it)
   objective: 13765.389991212294


Minimizing 628    Time: 0:00:06 ( 9.93 ms/it)
   objective: 13764.134090485255


Minimizing 639    Time: 0:00:06 ( 9.92 ms/it)
   objective: 13761.567868354055


Minimizing 650    Time: 0:00:06 ( 9.91 ms/it)
   objective: 13761.418560237667


Minimizing 661    Time: 0:00:06 ( 9.90 ms/it)
   objective: 13759.932973153804


Minimizing 672    Time: 0:00:06 ( 9.89 ms/it)
   objective: 13758.732708083013


Minimizing 683    Time: 0:00:06 ( 9.88 ms/it)
   objective: 13758.216804892303


Minimizing 694    Time: 0:00:06 ( 9.87 ms/it)
   objective: 13758.126637065789


Minimizing 705    Time: 0:00:06 ( 9.86 ms/it)
   objective: 13756.847920911234


Minimizing 716    Time: 0:00:07 ( 9.87 ms/it)
   objective: 13755.595204556274


Minimizing 727    Time: 0:00:07 ( 9.86 ms/it)
   objective: 13749.977748025203


Minimizing 738    Time: 0:00:07 ( 9.86 ms/it)
   objective: 13741.907631414068


Minimizing 749    Time: 0:00:07 ( 9.88 ms/it)
   objective: 13741.212279380015


Minimizing 758    Time: 0:00:07 ( 9.91 ms/it)
   objective: 13739.344999136258


Minimizing 769    Time: 0:00:07 ( 9.90 ms/it)
   objective: 13736.416976883173


Minimizing 780    Time: 0:00:07 ( 9.89 ms/it)
   objective: 13735.616878591129


Minimizing 791    Time: 0:00:07 ( 9.89 ms/it)
   objective: 13734.85932064169


Minimizing 802    Time: 0:00:07 ( 9.89 ms/it)
   objective: 13732.582895152202


Minimizing 812    Time: 0:00:08 ( 9.90 ms/it)
   objective: 13731.188015986405


Minimizing 823    Time: 0:00:08 ( 9.89 ms/it)
   objective: 13723.181279289394


Minimizing 834    Time: 0:00:08 ( 9.88 ms/it)
   objective: 13720.351292443174


Minimizing 845    Time: 0:00:08 ( 9.88 ms/it)
   objective: 13720.147828331352


Minimizing 855    Time: 0:00:08 ( 9.89 ms/it)
   objective: 13718.23431633081


Minimizing 864    Time: 0:00:08 ( 9.91 ms/it)
   objective: 13716.886107747254


Minimizing 873    Time: 0:00:08 ( 9.93 ms/it)
   objective: 13715.800602507366


Minimizing 882    Time: 0:00:08 ( 9.95 ms/it)
   objective: 13714.34028288384


Minimizing 891    Time: 0:00:08 ( 9.97 ms/it)
   objective: 13713.139895379925


Minimizing 901    Time: 0:00:08 ( 9.98 ms/it)
   objective: 13710.638492100414


Minimizing 909    Time: 0:00:09 (10.01 ms/it)
   objective: 13710.511867247074


Minimizing 919    Time: 0:00:09 (10.02 ms/it)
   objective: 13709.59284198572


Minimizing 929    Time: 0:00:09 (10.03 ms/it)
   objective: 13703.288582936493


Minimizing 938    Time: 0:00:09 (10.07 ms/it)
   objective: 13701.117353948615


Minimizing 948    Time: 0:00:09 (10.08 ms/it)
   objective: 13698.572991010511


Minimizing 957    Time: 0:00:09 (10.10 ms/it)
   objective: 13675.685830137547


Minimizing 966    Time: 0:00:09 (10.11 ms/it)
   objective: 13671.414602426019


Minimizing 976    Time: 0:00:09 (10.11 ms/it)
   objective: 13669.69148281782


Minimizing 986    Time: 0:00:09 (10.11 ms/it)
   objective: 13668.448702402813


Minimizing 997    Time: 0:00:10 (10.11 ms/it)
   objective: 13666.44790093082


Minimizing 1008    Time: 0:00:10 (10.10 ms/it)
   objective: 13658.157730376632


Minimizing 1019    Time: 0:00:10 (10.09 ms/it)
   objective: 13657.870427598958


Minimizing 1030    Time: 0:00:10 (10.09 ms/it)
   objective: 13656.285172294236


Minimizing 1041    Time: 0:00:10 (10.08 ms/it)
   objective: 13649.380555091237


Minimizing 1052    Time: 0:00:10 (10.08 ms/it)
   objective: 13647.025815970104


Minimizing 1062    Time: 0:00:10 (10.08 ms/it)
   objective: 13646.859913098597


Minimizing 1072    Time: 0:00:10 (10.08 ms/it)
   objective: 13645.08312428523


Minimizing 1082    Time: 0:00:10 (10.10 ms/it)
   objective: 13642.366676777048


Minimizing 1093    Time: 0:00:11 (10.10 ms/it)
   objective: 13636.861273050468


Minimizing 1104    Time: 0:00:11 (10.09 ms/it)
   objective: 13631.330032986349


Minimizing 1115    Time: 0:00:11 (10.08 ms/it)
   objective: 13625.376284857564


Minimizing 1126    Time: 0:00:11 (10.08 ms/it)
   objective: 13622.659384904073


Minimizing 1137    Time: 0:00:11 (10.08 ms/it)
   objective: 13620.721672170672


Minimizing 1148    Time: 0:00:11 (10.07 ms/it)
   objective: 13619.3843617214


Minimizing 1159    Time: 0:00:11 (10.07 ms/it)
   objective: 13618.63718323315


Minimizing 1170    Time: 0:00:11 (10.06 ms/it)
   objective: 13617.531733369833


Minimizing 1181    Time: 0:00:11 (10.05 ms/it)
   objective: 13613.980342091781


Minimizing 1192    Time: 0:00:11 (10.05 ms/it)
   objective: 13613.176745378238


Minimizing 1203    Time: 0:00:12 (10.04 ms/it)
   objective: 13610.54405522249


Minimizing 1214    Time: 0:00:12 (10.03 ms/it)
   objective: 13608.405137514164


Minimizing 1225    Time: 0:00:12 (10.03 ms/it)
   objective: 13603.402433533076


Minimizing 1236    Time: 0:00:12 (10.03 ms/it)
   objective: 13597.334531987122


Minimizing 1247    Time: 0:00:12 (10.02 ms/it)
   objective: 13591.935579271485


Minimizing 1258    Time: 0:00:12 (10.01 ms/it)
   objective: 13572.098966613317


Minimizing 1269    Time: 0:00:12 (10.01 ms/it)
   objective: 13570.200980016518


Minimizing 1280    Time: 0:00:12 (10.00 ms/it)
   objective: 13567.510050079443


Minimizing 1291    Time: 0:00:12 ( 9.99 ms/it)
   objective: 13565.010127025686


Minimizing 1302    Time: 0:00:13 ( 9.99 ms/it)
   objective: 13560.660106116891


Minimizing 1313    Time: 0:00:13 ( 9.98 ms/it)
   objective: 13559.338657383661


Minimizing 1324    Time: 0:00:13 ( 9.97 ms/it)
   objective: 13556.574064506443


Minimizing 1335    Time: 0:00:13 ( 9.97 ms/it)
   objective: 13555.482232315553


Minimizing 1346    Time: 0:00:13 ( 9.96 ms/it)
   objective: 13551.966128530396


Minimizing 1357    Time: 0:00:13 ( 9.96 ms/it)
   objective: 13548.440444260399


Minimizing 1368    Time: 0:00:13 ( 9.95 ms/it)
   objective: 13542.004768612067


Minimizing 1379    Time: 0:00:13 ( 9.95 ms/it)
   objective: 13540.357869011234


Minimizing 1390    Time: 0:00:13 ( 9.94 ms/it)
   objective: 13539.989972653522


Minimizing 1401    Time: 0:00:13 ( 9.94 ms/it)
   objective: 13539.053710557157


Minimizing 1412    Time: 0:00:14 ( 9.93 ms/it)
   objective: 13538.468211391853


Minimizing 1423    Time: 0:00:14 ( 9.93 ms/it)
   objective: 13537.821754991222


Minimizing 1434    Time: 0:00:14 ( 9.92 ms/it)
   objective: 13536.449606188282


Minimizing 1445    Time: 0:00:14 ( 9.92 ms/it)
   objective: 13535.633556610002


Minimizing 1456    Time: 0:00:14 ( 9.91 ms/it)
   objective: 13534.277406250592


Minimizing 1467    Time: 0:00:14 ( 9.91 ms/it)
   objective: 13534.25436773857


Minimizing 1478    Time: 0:00:14 ( 9.90 ms/it)
   objective: 13533.758997678087


Minimizing 1489    Time: 0:00:14 ( 9.90 ms/it)
   objective: 13532.978287407692


Minimizing 1500    Time: 0:00:14 ( 9.89 ms/it)
   objective: 13531.31017894455


Minimizing 1511    Time: 0:00:14 ( 9.89 ms/it)
   objective: 13528.440470837872


Minimizing 1522    Time: 0:00:15 ( 9.88 ms/it)
   objective: 13527.996557278253


Minimizing 1533    Time: 0:00:15 ( 9.88 ms/it)
   objective: 13526.298213752743


Minimizing 1544    Time: 0:00:15 ( 9.88 ms/it)
   objective: 13525.098600442681


Minimizing 1555    Time: 0:00:15 ( 9.87 ms/it)
   objective: 13524.197857014136


Minimizing 1566    Time: 0:00:15 ( 9.87 ms/it)
   objective: 13523.838394444989


Minimizing 1577    Time: 0:00:15 ( 9.87 ms/it)
   objective: 13519.796377444363


Minimizing 1588    Time: 0:00:15 ( 9.86 ms/it)
   objective: 13516.973213525765


Minimizing 1599    Time: 0:00:15 ( 9.86 ms/it)
   objective: 13516.513858641323


Minimizing 1610    Time: 0:00:15 ( 9.85 ms/it)
   objective: 13516.113255103468


Minimizing 1621    Time: 0:00:15 ( 9.85 ms/it)
   objective: 13515.474405948087


Minimizing 1632    Time: 0:00:16 ( 9.85 ms/it)
   objective: 13514.648748798878


Minimizing 1643    Time: 0:00:16 ( 9.85 ms/it)
   objective: 13512.45525811147


Minimizing 1654    Time: 0:00:16 ( 9.84 ms/it)
   objective: 13510.642273691381


Minimizing 1665    Time: 0:00:16 ( 9.84 ms/it)
   objective: 13509.15497459432


Minimizing 1676    Time: 0:00:16 ( 9.84 ms/it)
   objective: 13506.43692932371


Minimizing 1687    Time: 0:00:16 ( 9.84 ms/it)
   objective: 13502.799813687307


Minimizing 1698    Time: 0:00:16 ( 9.84 ms/it)
   objective: 13496.521489947889


Minimizing 1708    Time: 0:00:16 ( 9.84 ms/it)
   objective: 13473.981388874032


Minimizing 1718    Time: 0:00:16 ( 9.85 ms/it)
   objective: 13471.97863240527


Minimizing 1727    Time: 0:00:17 ( 9.86 ms/it)
   objective: 13469.859971326281


Minimizing 1736    Time: 0:00:17 ( 9.87 ms/it)
   objective: 13466.887163150473


Minimizing 1745    Time: 0:00:17 ( 9.90 ms/it)
   objective: 13466.027154582902


Minimizing 1752    Time: 0:00:17 ( 9.93 ms/it)
   objective: 13465.823714778351


Minimizing 1759    Time: 0:00:17 ( 9.95 ms/it)
   objective: 13465.223440879185


Minimizing 1770    Time: 0:00:17 ( 9.95 ms/it)
   objective: 13463.974508446438


Minimizing 1781    Time: 0:00:17 ( 9.96 ms/it)
   objective: 13463.966126850122


Minimizing 1792    Time: 0:00:17 ( 9.96 ms/it)
   objective: 13463.960753428604


Minimizing 1803    Time: 0:00:17 ( 9.95 ms/it)
   objective: 13463.961226362386


Minimizing 1814    Time: 0:00:18 ( 9.95 ms/it)
   objective: 13463.96153325637


Minimizing 1825    Time: 0:00:18 ( 9.95 ms/it)
   objective: 13463.961063429626


Minimizing 1836    Time: 0:00:18 ( 9.95 ms/it)
   objective: 13463.960539887208


Minimizing 1847    Time: 0:00:18 ( 9.94 ms/it)
   objective: 13463.96023119244


Minimizing 1858    Time: 0:00:18 ( 9.94 ms/it)
   objective: 13463.960445831093


Minimizing 1869    Time: 0:00:18 ( 9.94 ms/it)
   objective: 13463.960434418448


Minimizing 1880    Time: 0:00:18 ( 9.93 ms/it)
   objective: 13463.960765794793


Minimizing 1891    Time: 0:00:18 ( 9.93 ms/it)
   objective: 13463.960057589647


Minimizing 1901    Time: 0:00:18 ( 9.93 ms/it)
   objective: 13463.960754612635


Minimizing 1912    Time: 0:00:18 ( 9.93 ms/it)
   objective: 13463.960295826153


Minimizing 1923    Time: 0:00:19 ( 9.93 ms/it)
   objective: 13463.960120262578


Minimizing 1934    Time: 0:00:19 ( 9.93 ms/it)
   objective: 13463.960298238715


Minimizing 1945    Time: 0:00:19 ( 9.93 ms/it)
   objective: 13463.960691543281


Minimizing 1956    Time: 0:00:19 ( 9.92 ms/it)
   objective: 13463.96030180312


Minimizing 1967    Time: 0:00:19 ( 9.92 ms/it)
   objective: 13463.960831609773


Minimizing 1978    Time: 0:00:19 ( 9.92 ms/it)
   objective: 13463.960530837285


Minimizing 1989    Time: 0:00:19 ( 9.91 ms/it)
   objective: 13463.960852884265


Minimizing 1998    Time: 0:00:19 ( 9.91 ms/it)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0200	0.0142	-1.41	0.1576	0.6986
Test: Star-Run	-0.0187	0.0436	-0.43	0.6676	0.6958
Test: S20-Star	-0.0006	0.0448	-0.01	0.9885	1.1740
Test: SLJ-S20	0.0122	0.0449	0.27	0.7865	1.0915
Test: BPT-SLJ	-0.0278	0.0432	-0.64	0.5194	0.9761
a1	0.3548	0.0483	7.34	<1e-12
Sex: Boys	0.1915	0.0142	13.52	<1e-40
Test: Star-Run & a1	0.3053	0.1494	2.04	0.0410
Test: S20-Star & a1	-0.0488	0.1562	-0.31	0.7549
Test: SLJ-S20 & a1	-0.2572	0.1541	-1.67	0.0950
Test: BPT-SLJ & a1	0.4648	0.1454	3.20	0.0014
Test: Star-Run & Sex: Boys	-0.0779	0.0436	-1.78	0.0743
Test: S20-Star & Sex: Boys	-0.0275	0.0448	-0.61	0.5393
Test: SLJ-S20 & Sex: Boys	0.0815	0.0449	1.81	0.0697
Test: BPT-SLJ & Sex: Boys	0.1611	0.0432	3.73	0.0002
a1 & Sex: Boys	-0.0683	0.0483	-1.41	0.1579
Test: Star-Run & a1 & Sex: Boys	-0.1249	0.1494	-0.84	0.4028
Test: S20-Star & a1 & Sex: Boys	-0.0646	0.1562	-0.41	0.6791
Test: SLJ-S20 & a1 & Sex: Boys	0.0311	0.1541	0.20	0.8398
Test: BPT-SLJ & a1 & Sex: Boys	0.2670	0.1454	1.84	0.0662
Residual	0.0000

m_cpx_1_SeqDiff.PCA

(Child = 
Principal components based on correlation matrix
 (Intercept)      1.0     .      .      .      .
 Test: Star-Run   0.11   1.0     .      .      .
 Test: S20-Star  -0.12  -0.77   1.0     .      .
 Test: SLJ-S20    0.04   0.99  -0.71   1.0     .
 Test: BPT-SLJ   -0.23  -0.19  -0.01  -0.24   1.0

Normalized cumulative variances:
[0.5433, 0.7809, 0.9438, 1.0, 1.0]

Component loadings
                   PC1    PC2    PC3    PC4    PC5
 (Intercept)     -0.11   0.69   0.7   -0.14  -0.05
 Test: Star-Run  -0.6   -0.07  -0.04  -0.32   0.73
 Test: S20-Star   0.52   0.19  -0.26  -0.79   0.08
 Test: SLJ-S20   -0.58  -0.07  -0.15  -0.42  -0.68
 Test: BPT-SLJ    0.16  -0.69   0.64  -0.28  -0.03,)

2.4 PCA-based HypothesisCoding: `contr4`

The fourth set of contrasts uses HypothesisCoding to specify the set of contrasts implementing the loadings of the four principal components of the published LMM based on test scores, not test effects (contrasts) — coarse-grained, that is roughly according to their signs. This is actually a very interesting and plausible solution nobody had proposed a priori.

PC1: BPT - Run_r
PC2: (Star_r + S20_r + SLJ) - (BPT + Run_r)
PC3: Star_r - (S20_r + SLJ)
PC4: S20_r - SLJ

PC1 contrasts the worst and the best indicator of physical health; PC2 contrasts these two against the core indicators of physical fitness; PC3 contrasts the cognitive and the physical tests within the narrow set of physical fitness components; and PC4, finally, contrasts two types of lower muscular fitness differing in speed and power.

contr4 = Dict(
  :School => Grouping(),
  :Child => Grouping(),
  :Cohort => Grouping(),
  :Sex => EffectsCoding(; levels=["Girls", "Boys"]),
  :Test => HypothesisCoding(
    [
      -1  0  0  0 +1
      -3 +2 +2 +2 -3
       0 +2 -1 -1  0
       0  0 +1 -1  0
    ];
    levels=["Run", "Star_r", "S20_r", "SLJ", "BPT"],
    labels=["c5.1", "c234.15", "c2.34", "c3.4"],
  ),
);

m_cpx_1_PC = fit(MixedModel, f_cpx_1, dat; contrasts=contr4)

Minimizing 12    Time: 0:00:00 ( 8.93 ms/it)
   objective: 13847.871580147708


Minimizing 23    Time: 0:00:00 ( 9.40 ms/it)
   objective: 13858.986492102911


Minimizing 34    Time: 0:00:00 ( 9.55 ms/it)
   objective: 13841.49228594995


Minimizing 45    Time: 0:00:00 ( 9.52 ms/it)
   objective: 13840.859908936854


Minimizing 56    Time: 0:00:00 ( 9.64 ms/it)
   objective: 13839.337089949211


Minimizing 67    Time: 0:00:00 ( 9.70 ms/it)
   objective: 13837.536899012863


Minimizing 77    Time: 0:00:00 ( 9.76 ms/it)
   objective: 13832.968668450281


Minimizing 87    Time: 0:00:00 ( 9.80 ms/it)
   objective: 13829.228896040524


Minimizing 98    Time: 0:00:00 ( 9.82 ms/it)
   objective: 13822.217783121301


Minimizing 108    Time: 0:00:01 ( 9.87 ms/it)
   objective: 13815.932241908298


Minimizing 118    Time: 0:00:01 ( 9.89 ms/it)
   objective: 13815.436414513213


Minimizing 128    Time: 0:00:01 ( 9.93 ms/it)
   objective: 13813.550192353563


Minimizing 139    Time: 0:00:01 ( 9.87 ms/it)
   objective: 13809.418712775156


Minimizing 150    Time: 0:00:01 ( 9.82 ms/it)
   objective: 13803.35756603884


Minimizing 161    Time: 0:00:01 ( 9.81 ms/it)
   objective: 13802.84013299839


Minimizing 172    Time: 0:00:01 ( 9.77 ms/it)
   objective: 13799.219679345984


Minimizing 183    Time: 0:00:01 ( 9.74 ms/it)
   objective: 13797.201919382305


Minimizing 194    Time: 0:00:01 ( 9.73 ms/it)
   objective: 13795.383638092702


Minimizing 205    Time: 0:00:01 ( 9.70 ms/it)
   objective: 13794.779235468864


Minimizing 216    Time: 0:00:02 ( 9.68 ms/it)
   objective: 13794.028834725439


Minimizing 227    Time: 0:00:02 ( 9.67 ms/it)
   objective: 13792.887247794257


Minimizing 238    Time: 0:00:02 ( 9.65 ms/it)
   objective: 13791.705770994133


Minimizing 249    Time: 0:00:02 ( 9.63 ms/it)
   objective: 13791.35902451339


Minimizing 260    Time: 0:00:02 ( 9.62 ms/it)
   objective: 13790.797349613165


Minimizing 271    Time: 0:00:02 ( 9.60 ms/it)
   objective: 13789.580965434867


Minimizing 282    Time: 0:00:02 ( 9.61 ms/it)
   objective: 13788.646347601467


Minimizing 293    Time: 0:00:02 ( 9.61 ms/it)
   objective: 13788.391860166183


Minimizing 304    Time: 0:00:02 ( 9.59 ms/it)
   objective: 13787.038169591211


Minimizing 315    Time: 0:00:03 ( 9.58 ms/it)
   objective: 13785.813230975557


Minimizing 326    Time: 0:00:03 ( 9.58 ms/it)
   objective: 13785.444794367879


Minimizing 337    Time: 0:00:03 ( 9.56 ms/it)
   objective: 13782.684211750946


Minimizing 348    Time: 0:00:03 ( 9.55 ms/it)
   objective: 13782.188238715502


Minimizing 359    Time: 0:00:03 ( 9.54 ms/it)
   objective: 13781.38127351409


Minimizing 370    Time: 0:00:03 ( 9.53 ms/it)
   objective: 13779.872733552475


Minimizing 381    Time: 0:00:03 ( 9.52 ms/it)
   objective: 13775.928018374858


Minimizing 392    Time: 0:00:03 ( 9.52 ms/it)
   objective: 13774.901587443208


Minimizing 403    Time: 0:00:03 ( 9.52 ms/it)
   objective: 13774.53022147467


Minimizing 414    Time: 0:00:03 ( 9.51 ms/it)
   objective: 13774.008266509018


Minimizing 425    Time: 0:00:04 ( 9.51 ms/it)
   objective: 13773.646572846304


Minimizing 436    Time: 0:00:04 ( 9.50 ms/it)
   objective: 13773.60469100704


Minimizing 447    Time: 0:00:04 ( 9.50 ms/it)
   objective: 13773.311699883789


Minimizing 459    Time: 0:00:04 ( 9.56 ms/it)
   objective: 13772.374351544524


Minimizing 469    Time: 0:00:04 ( 9.57 ms/it)
   objective: 13772.06105057388


Minimizing 479    Time: 0:00:04 ( 9.58 ms/it)
   objective: 13771.504199732004


Minimizing 490    Time: 0:00:04 ( 9.59 ms/it)
   objective: 13770.611470746811


Minimizing 501    Time: 0:00:04 ( 9.58 ms/it)
   objective: 13770.507511520565


Minimizing 512    Time: 0:00:04 ( 9.57 ms/it)
   objective: 13769.680472941578


Minimizing 523    Time: 0:00:05 ( 9.58 ms/it)
   objective: 13768.90529190972


Minimizing 534    Time: 0:00:05 ( 9.58 ms/it)
   objective: 13766.974013260935


Minimizing 545    Time: 0:00:05 ( 9.59 ms/it)
   objective: 13765.149411487206


Minimizing 556    Time: 0:00:05 ( 9.59 ms/it)
   objective: 13764.360373336725


Minimizing 567    Time: 0:00:05 ( 9.59 ms/it)
   objective: 13762.883032309604


Minimizing 578    Time: 0:00:05 ( 9.58 ms/it)
   objective: 13761.71594850239


Minimizing 589    Time: 0:00:05 ( 9.60 ms/it)
   objective: 13760.74901216127


Minimizing 600    Time: 0:00:05 ( 9.59 ms/it)
   objective: 13756.53008094543


Minimizing 611    Time: 0:00:05 ( 9.59 ms/it)
   objective: 13753.116145311798


Minimizing 622    Time: 0:00:05 ( 9.59 ms/it)
   objective: 13750.429689077251


Minimizing 633    Time: 0:00:06 ( 9.59 ms/it)
   objective: 13746.440244227517


Minimizing 644    Time: 0:00:06 ( 9.58 ms/it)
   objective: 13742.771822210143


Minimizing 655    Time: 0:00:06 ( 9.58 ms/it)
   objective: 13742.52680790472


Minimizing 666    Time: 0:00:06 ( 9.57 ms/it)
   objective: 13741.191633775226


Minimizing 677    Time: 0:00:06 ( 9.56 ms/it)
   objective: 13739.911554478902


Minimizing 688    Time: 0:00:06 ( 9.56 ms/it)
   objective: 13738.581455576754


Minimizing 699    Time: 0:00:06 ( 9.55 ms/it)
   objective: 13734.38856519846


Minimizing 710    Time: 0:00:06 ( 9.55 ms/it)
   objective: 13730.323432505127


Minimizing 721    Time: 0:00:06 ( 9.54 ms/it)
   objective: 13728.929207248144


Minimizing 732    Time: 0:00:06 ( 9.54 ms/it)
   objective: 13726.354106202376


Minimizing 743    Time: 0:00:07 ( 9.54 ms/it)
   objective: 13723.361604503705


Minimizing 754    Time: 0:00:07 ( 9.53 ms/it)
   objective: 13723.29756773022


Minimizing 765    Time: 0:00:07 ( 9.53 ms/it)
   objective: 13721.540293153954


Minimizing 776    Time: 0:00:07 ( 9.53 ms/it)
   objective: 13718.982835799441


Minimizing 787    Time: 0:00:07 ( 9.53 ms/it)
   objective: 13717.681818593737


Minimizing 798    Time: 0:00:07 ( 9.53 ms/it)
   objective: 13717.374823938502


Minimizing 809    Time: 0:00:07 ( 9.52 ms/it)
   objective: 13717.308170854994


Minimizing 820    Time: 0:00:07 ( 9.52 ms/it)
   objective: 13716.680173019584


Minimizing 831    Time: 0:00:07 ( 9.54 ms/it)
   objective: 13715.911614431858


Minimizing 842    Time: 0:00:08 ( 9.54 ms/it)
   objective: 13714.54876476149


Minimizing 853    Time: 0:00:08 ( 9.54 ms/it)
   objective: 13712.992383162567


Minimizing 864    Time: 0:00:08 ( 9.53 ms/it)
   objective: 13711.377688055883


Minimizing 875    Time: 0:00:08 ( 9.53 ms/it)
   objective: 13710.43188974297


Minimizing 886    Time: 0:00:08 ( 9.53 ms/it)
   objective: 13707.804364659522


Minimizing 897    Time: 0:00:08 ( 9.52 ms/it)
   objective: 13706.483410465957


Minimizing 908    Time: 0:00:08 ( 9.52 ms/it)
   objective: 13705.126084567353


Minimizing 919    Time: 0:00:08 ( 9.52 ms/it)
   objective: 13699.501515304222


Minimizing 930    Time: 0:00:08 ( 9.51 ms/it)
   objective: 13697.701594214417


Minimizing 941    Time: 0:00:08 ( 9.51 ms/it)
   objective: 13696.11535809985


Minimizing 952    Time: 0:00:09 ( 9.51 ms/it)
   objective: 13687.29642711348


Minimizing 963    Time: 0:00:09 ( 9.52 ms/it)
   objective: 13678.241460479028


Minimizing 974    Time: 0:00:09 ( 9.52 ms/it)
   objective: 13677.960846505226


Minimizing 985    Time: 0:00:09 ( 9.52 ms/it)
   objective: 13677.159039665057


Minimizing 996    Time: 0:00:09 ( 9.52 ms/it)
   objective: 13675.612633289908


Minimizing 1007    Time: 0:00:09 ( 9.52 ms/it)
   objective: 13672.454231599098


Minimizing 1018    Time: 0:00:09 ( 9.52 ms/it)
   objective: 13667.104263621703


Minimizing 1029    Time: 0:00:09 ( 9.51 ms/it)
   objective: 13666.043900787605


Minimizing 1040    Time: 0:00:09 ( 9.51 ms/it)
   objective: 13665.996309355098


Minimizing 1051    Time: 0:00:09 ( 9.51 ms/it)
   objective: 13664.075101277274


Minimizing 1062    Time: 0:00:10 ( 9.51 ms/it)
   objective: 13663.204629457774


Minimizing 1073    Time: 0:00:10 ( 9.50 ms/it)
   objective: 13658.852421637901


Minimizing 1084    Time: 0:00:10 ( 9.50 ms/it)
   objective: 13658.205079760308


Minimizing 1095    Time: 0:00:10 ( 9.49 ms/it)
   objective: 13658.121363513965


Minimizing 1106    Time: 0:00:10 ( 9.49 ms/it)
   objective: 13657.027573870335


Minimizing 1117    Time: 0:00:10 ( 9.49 ms/it)
   objective: 13656.714285629787


Minimizing 1128    Time: 0:00:10 ( 9.49 ms/it)
   objective: 13656.137358674503


Minimizing 1139    Time: 0:00:10 ( 9.49 ms/it)
   objective: 13654.880067019403


Minimizing 1150    Time: 0:00:10 ( 9.49 ms/it)
   objective: 13653.345397207573


Minimizing 1162    Time: 0:00:11 ( 9.49 ms/it)
   objective: 13653.165930450254


Minimizing 1173    Time: 0:00:11 ( 9.49 ms/it)
   objective: 13652.50728298445


Minimizing 1184    Time: 0:00:11 ( 9.49 ms/it)
   objective: 13651.496164043652


Minimizing 1195    Time: 0:00:11 ( 9.49 ms/it)
   objective: 13648.546323903269


Minimizing 1206    Time: 0:00:11 ( 9.49 ms/it)
   objective: 13648.241198382391


Minimizing 1217    Time: 0:00:11 ( 9.48 ms/it)
   objective: 13647.441494019004


Minimizing 1228    Time: 0:00:11 ( 9.49 ms/it)
   objective: 13646.065390998716


Minimizing 1238    Time: 0:00:11 ( 9.50 ms/it)
   objective: 13645.489455529714


Minimizing 1248    Time: 0:00:11 ( 9.50 ms/it)
   objective: 13644.374298439863


Minimizing 1259    Time: 0:00:11 ( 9.50 ms/it)
   objective: 13639.195725754871


Minimizing 1270    Time: 0:00:12 ( 9.51 ms/it)
   objective: 13637.833441767762


Minimizing 1281    Time: 0:00:12 ( 9.50 ms/it)
   objective: 13637.07019628337


Minimizing 1292    Time: 0:00:12 ( 9.50 ms/it)
   objective: 13633.581019405356


Minimizing 1303    Time: 0:00:12 ( 9.50 ms/it)
   objective: 13632.917996470744


Minimizing 1314    Time: 0:00:12 ( 9.49 ms/it)
   objective: 13629.128485339468


Minimizing 1325    Time: 0:00:12 ( 9.49 ms/it)
   objective: 13620.37607894191


Minimizing 1336    Time: 0:00:12 ( 9.49 ms/it)
   objective: 13593.518281106633


Minimizing 1347    Time: 0:00:12 ( 9.49 ms/it)
   objective: 13586.318855982849


Minimizing 1358    Time: 0:00:12 ( 9.49 ms/it)
   objective: 13585.592923125696


Minimizing 1369    Time: 0:00:12 ( 9.49 ms/it)
   objective: 13579.267535122817


Minimizing 1380    Time: 0:00:13 ( 9.49 ms/it)
   objective: 13578.63033361818


Minimizing 1391    Time: 0:00:13 ( 9.49 ms/it)
   objective: 13575.417052594006


Minimizing 1402    Time: 0:00:13 ( 9.49 ms/it)
   objective: 13573.443524678849


Minimizing 1413    Time: 0:00:13 ( 9.49 ms/it)
   objective: 13566.744258471626


Minimizing 1424    Time: 0:00:13 ( 9.48 ms/it)
   objective: 13566.183491591903


Minimizing 1435    Time: 0:00:13 ( 9.48 ms/it)
   objective: 13565.210254599791


Minimizing 1446    Time: 0:00:13 ( 9.48 ms/it)
   objective: 13561.705723031453


Minimizing 1457    Time: 0:00:13 ( 9.48 ms/it)
   objective: 13559.10099408045


Minimizing 1468    Time: 0:00:13 ( 9.48 ms/it)
   objective: 13554.31955403401


Minimizing 1479    Time: 0:00:14 ( 9.47 ms/it)
   objective: 13549.011249161922


Minimizing 1490    Time: 0:00:14 ( 9.47 ms/it)
   objective: 13548.775582741917


Minimizing 1501    Time: 0:00:14 ( 9.47 ms/it)
   objective: 13546.479853601253


Minimizing 1512    Time: 0:00:14 ( 9.47 ms/it)
   objective: 13543.376671927574


Minimizing 1523    Time: 0:00:14 ( 9.47 ms/it)
   objective: 13542.646427482658


Minimizing 1534    Time: 0:00:14 ( 9.47 ms/it)
   objective: 13541.6882988539


Minimizing 1545    Time: 0:00:14 ( 9.47 ms/it)
   objective: 13534.913290371653


Minimizing 1556    Time: 0:00:14 ( 9.47 ms/it)
   objective: 13527.365286990142


Minimizing 1567    Time: 0:00:14 ( 9.46 ms/it)
   objective: 13526.305257859945


Minimizing 1578    Time: 0:00:14 ( 9.46 ms/it)
   objective: 13523.559880623376


Minimizing 1589    Time: 0:00:15 ( 9.46 ms/it)
   objective: 13522.501978579501


Minimizing 1600    Time: 0:00:15 ( 9.46 ms/it)
   objective: 13519.70012369426


Minimizing 1611    Time: 0:00:15 ( 9.47 ms/it)
   objective: 13514.24476017445


Minimizing 1622    Time: 0:00:15 ( 9.47 ms/it)
   objective: 13509.520547885651


Minimizing 1633    Time: 0:00:15 ( 9.46 ms/it)
   objective: 13501.009673121342


Minimizing 1644    Time: 0:00:15 ( 9.46 ms/it)
   objective: 13495.410019434988


Minimizing 1655    Time: 0:00:15 ( 9.46 ms/it)
   objective: 13494.882478854634


Minimizing 1666    Time: 0:00:15 ( 9.46 ms/it)
   objective: 13492.466197401867


Minimizing 1677    Time: 0:00:15 ( 9.46 ms/it)
   objective: 13491.879914663863


Minimizing 1688    Time: 0:00:15 ( 9.46 ms/it)
   objective: 13489.132733929888


Minimizing 1699    Time: 0:00:16 ( 9.46 ms/it)
   objective: 13487.296067046671


Minimizing 1710    Time: 0:00:16 ( 9.46 ms/it)
   objective: 13486.654752724717


Minimizing 1721    Time: 0:00:16 ( 9.46 ms/it)
   objective: 13486.517237244247


Minimizing 1732    Time: 0:00:16 ( 9.46 ms/it)
   objective: 13475.888947724932


Minimizing 1743    Time: 0:00:16 ( 9.46 ms/it)
   objective: 13474.796502550496


Minimizing 1754    Time: 0:00:16 ( 9.46 ms/it)
   objective: 13472.368011997343


Minimizing 1765    Time: 0:00:16 ( 9.46 ms/it)
   objective: 13469.78664111685


Minimizing 1776    Time: 0:00:16 ( 9.46 ms/it)
   objective: 13462.730585368


Minimizing 1787    Time: 0:00:16 ( 9.45 ms/it)
   objective: 13459.82038952384


Minimizing 1798    Time: 0:00:17 ( 9.46 ms/it)
   objective: 13459.041094740605


Minimizing 1809    Time: 0:00:17 ( 9.46 ms/it)
   objective: 13455.566908685621


Minimizing 1820    Time: 0:00:17 ( 9.46 ms/it)
   objective: 13455.014075844054


Minimizing 1831    Time: 0:00:17 ( 9.45 ms/it)
   objective: 13450.90435665015


Minimizing 1842    Time: 0:00:17 ( 9.47 ms/it)
   objective: 13446.93345653692


Minimizing 1853    Time: 0:00:17 ( 9.47 ms/it)
   objective: 13436.87836223036


Minimizing 1864    Time: 0:00:17 ( 9.47 ms/it)
   objective: 13436.112392024515


Minimizing 1875    Time: 0:00:17 ( 9.47 ms/it)
   objective: 13436.063345552917


Minimizing 1886    Time: 0:00:17 ( 9.47 ms/it)
   objective: 13436.042620872875


Minimizing 1897    Time: 0:00:17 ( 9.47 ms/it)
   objective: 13436.042773799883


Minimizing 1908    Time: 0:00:18 ( 9.47 ms/it)
   objective: 13436.041646856524


Minimizing 1919    Time: 0:00:18 ( 9.47 ms/it)
   objective: 13436.047364911457


Minimizing 1929    Time: 0:00:18 ( 9.49 ms/it)
   objective: 13436.051403563572


Minimizing 1937    Time: 0:00:18 ( 9.51 ms/it)
   objective: 13436.050692490724


Minimizing 1944    Time: 0:00:18 ( 9.53 ms/it)
   objective: 13436.04425220433


Minimizing 1951    Time: 0:00:18 ( 9.56 ms/it)
   objective: 13436.046039917986


Minimizing 1958    Time: 0:00:18 ( 9.58 ms/it)
   objective: 13436.044741103062


Minimizing 1966    Time: 0:00:18 ( 9.59 ms/it)
   objective: 13436.043478779131


Minimizing 1975    Time: 0:00:18 ( 9.60 ms/it)
   objective: 13436.042363177898


Minimizing 1986    Time: 0:00:19 ( 9.61 ms/it)
   objective: 13436.044947257658


Minimizing 1995    Time: 0:00:19 ( 9.61 ms/it)
   objective: 13436.042358875653


Minimizing 2005    Time: 0:00:19 ( 9.62 ms/it)
   objective: 13436.044418583158


Minimizing 2015    Time: 0:00:19 ( 9.64 ms/it)
   objective: 13436.04169420847


Minimizing 2024    Time: 0:00:19 ( 9.65 ms/it)
   objective: 13436.045907601176


Minimizing 2033    Time: 0:00:19 ( 9.66 ms/it)
   objective: 13436.043359685573


Minimizing 2043    Time: 0:00:19 ( 9.66 ms/it)
   objective: 13436.042808602244


Minimizing 2053    Time: 0:00:19 ( 9.67 ms/it)
   objective: 13436.041118682391


Minimizing 2064    Time: 0:00:19 ( 9.67 ms/it)
   objective: 13436.040493162523


Minimizing 2075    Time: 0:00:20 ( 9.66 ms/it)
   objective: 13436.042906443428


Minimizing 2076    Time: 0:00:20 ( 9.66 ms/it)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0201	0.0142	-1.41	0.1578	0.7704
Test: c5.1	-0.0349	0.0426	-0.82	0.4118	1.1136
Test: c234.15	0.0063	0.1669	0.04	0.9697	0.7795
Test: c2.34	-0.0011	0.0769	-0.01	0.9882	1.3053
Test: c3.4	-0.0009	0.0448	-0.02	0.9833	1.2942
a1	0.3534	0.0486	7.27	<1e-12
Sex: Boys	0.1916	0.0142	13.46	<1e-40
Test: c5.1 & a1	0.4738	0.1430	3.31	0.0009
Test: c234.15 & a1	-0.2440	0.5658	-0.43	0.6663
Test: c2.34 & a1	0.4090	0.2682	1.52	0.1273
Test: c3.4 & a1	0.2684	0.1537	1.75	0.0808
Test: c5.1 & Sex: Boys	0.1384	0.0426	3.25	0.0012
Test: c234.15 & Sex: Boys	-0.7903	0.1669	-4.74	<1e-05
Test: c2.34 & Sex: Boys	-0.0223	0.0769	-0.29	0.7720
Test: c3.4 & Sex: Boys	-0.0832	0.0448	-1.86	0.0631
a1 & Sex: Boys	-0.0694	0.0486	-1.43	0.1535
Test: c5.1 & a1 & Sex: Boys	0.1003	0.1430	0.70	0.4831
Test: c234.15 & a1 & Sex: Boys	-1.2668	0.5658	-2.24	0.0252
Test: c2.34 & a1 & Sex: Boys	0.1666	0.2682	0.62	0.5345
Test: c3.4 & a1 & Sex: Boys	0.0048	0.1537	0.03	0.9749
Residual	0.0000

VarCorr(m_cpx_1_PC)

	Column	Variance	Std.Dev	Corr.
Child	(Intercept)	0.59345437	0.77035990
	Test: c5.1	1.24016299	1.11362605	-0.11
	Test: c234.15	0.60757415	0.77947043	+0.24	-0.47
	Test: c2.34	1.70391375	1.30534047	+0.26	-0.11	+0.85
	Test: c3.4	1.67495660	1.29420114	-0.14	-0.11	-0.72	-0.69
Residual		0.00000000	0.00001476

m_cpx_1_PC.PCA

(Child = 
Principal components based on correlation matrix
 (Intercept)     1.0     .      .      .      .
 Test: c5.1     -0.11   1.0     .      .      .
 Test: c234.15   0.24  -0.47   1.0     .      .
 Test: c2.34     0.26  -0.11   0.85   1.0     .
 Test: c3.4     -0.14  -0.11  -0.72  -0.69   1.0

Normalized cumulative variances:
[0.53, 0.7589, 0.9387, 0.9943, 1.0]

Component loadings
                  PC1    PC2    PC3    PC4    PC5
 (Intercept)    -0.23  -0.22  -0.94   0.09   0.01
 Test: c5.1      0.19   0.85  -0.26  -0.19   0.37
 Test: c234.15  -0.59  -0.14   0.18   0.0    0.77
 Test: c2.34    -0.56   0.15   0.04  -0.7   -0.41
 Test: c3.4      0.5   -0.43  -0.08  -0.68   0.32,)

There is a numerical interaction with a z-value > 2.0 for the first PCA (i.e., BPT - Run_r). This interaction would really need to be replicated to be taken seriously. It is probably due to larger “unfitness” gains in boys than girls (i.e., in BPT) relative to the slightly larger health-related “fitness” gains of girls than boys (i.e., in Run_r).

contr4b = merge(
  Dict(nm => Grouping() for nm in (:School, :Child, :Cohort)),
  Dict(
    :Sex => EffectsCoding(; levels=["Girls", "Boys"]),
    :Test => HypothesisCoding(
      [
        0.49 -0.04  0.20  0.03 -0.85
        0.70 -0.56 -0.21 -0.13  0.37
        0.31  0.68 -0.56 -0.35  0.00
        0.04  0.08  0.61 -0.78  0.13
      ];
      levels=["Run", "Star_r", "S20_r", "SLJ", "BPT"],
      labels=["c5.1", "c234.15", "c12.34", "c3.4"],
    ),
  ),
);

m_cpx_1_PC_2 = fit(MixedModel, f_cpx_1, dat; contrasts=contr4b)

Minimizing 11    Time: 0:00:00 ( 9.11 ms/it)
   objective: 13884.449730318192


Minimizing 22    Time: 0:00:00 ( 9.58 ms/it)
   objective: 13844.34546749528


Minimizing 33    Time: 0:00:00 ( 9.68 ms/it)
   objective: 13868.678932458995


Minimizing 44    Time: 0:00:00 ( 9.63 ms/it)
   objective: 13836.275783170946


Minimizing 58    Time: 0:00:00 ( 9.97 ms/it)
   objective: 13835.655497702037


Minimizing 72    Time: 0:00:00 ( 9.82 ms/it)
   objective: 13829.713261997349


Minimizing 83    Time: 0:00:00 ( 9.74 ms/it)
   objective: 13823.848299019184


Minimizing 94    Time: 0:00:00 ( 9.67 ms/it)
   objective: 13821.883815668163


Minimizing 105    Time: 0:00:01 ( 9.63 ms/it)
   objective: 13816.773517924845


Minimizing 116    Time: 0:00:01 ( 9.59 ms/it)
   objective: 13809.640124440291


Minimizing 127    Time: 0:00:01 ( 9.56 ms/it)
   objective: 13805.0192309058


Minimizing 138    Time: 0:00:01 ( 9.53 ms/it)
   objective: 13797.428880645884


Minimizing 149    Time: 0:00:01 ( 9.51 ms/it)
   objective: 13793.245631622543


Minimizing 160    Time: 0:00:01 ( 9.49 ms/it)
   objective: 13793.326258092055


Minimizing 171    Time: 0:00:01 ( 9.47 ms/it)
   objective: 13791.263217174266


Minimizing 182    Time: 0:00:01 ( 9.45 ms/it)
   objective: 13788.908114626933


Minimizing 193    Time: 0:00:01 ( 9.44 ms/it)
   objective: 13788.786117442503


Minimizing 204    Time: 0:00:01 ( 9.42 ms/it)
   objective: 13787.050568169436


Minimizing 215    Time: 0:00:02 ( 9.42 ms/it)
   objective: 13786.1023970063


Minimizing 226    Time: 0:00:02 ( 9.41 ms/it)
   objective: 13785.790162386087


Minimizing 237    Time: 0:00:02 ( 9.40 ms/it)
   objective: 13784.124707520914


Minimizing 248    Time: 0:00:02 ( 9.39 ms/it)
   objective: 13778.641951285657


Minimizing 259    Time: 0:00:02 ( 9.38 ms/it)
   objective: 13777.070297737813


Minimizing 270    Time: 0:00:02 ( 9.37 ms/it)
   objective: 13776.403039260029


Minimizing 281    Time: 0:00:02 ( 9.37 ms/it)
   objective: 13772.488788293114


Minimizing 292    Time: 0:00:02 ( 9.36 ms/it)
   objective: 13771.824324453883


Minimizing 303    Time: 0:00:02 ( 9.36 ms/it)
   objective: 13770.955681392079


Minimizing 314    Time: 0:00:02 ( 9.35 ms/it)
   objective: 13765.34916596756


Minimizing 325    Time: 0:00:03 ( 9.35 ms/it)
   objective: 13763.455078413099


Minimizing 336    Time: 0:00:03 ( 9.34 ms/it)
   objective: 13749.121477320257


Minimizing 347    Time: 0:00:03 ( 9.34 ms/it)
   objective: 13739.981294252444


Minimizing 358    Time: 0:00:03 ( 9.34 ms/it)
   objective: 13739.923882396564


Minimizing 369    Time: 0:00:03 ( 9.35 ms/it)
   objective: 13738.997404242265


Minimizing 380    Time: 0:00:03 ( 9.34 ms/it)
   objective: 13737.156577425929


Minimizing 391    Time: 0:00:03 ( 9.34 ms/it)
   objective: 13735.58159153853


Minimizing 402    Time: 0:00:03 ( 9.34 ms/it)
   objective: 13735.40900154875


Minimizing 413    Time: 0:00:03 ( 9.34 ms/it)
   objective: 13734.971696416067


Minimizing 424    Time: 0:00:03 ( 9.33 ms/it)
   objective: 13734.089967842148


Minimizing 435    Time: 0:00:04 ( 9.34 ms/it)
   objective: 13732.407405165608


Minimizing 446    Time: 0:00:04 ( 9.34 ms/it)
   objective: 13726.332285505709


Minimizing 457    Time: 0:00:04 ( 9.33 ms/it)
   objective: 13722.377857008483


Minimizing 468    Time: 0:00:04 ( 9.33 ms/it)
   objective: 13721.99962398152


Minimizing 479    Time: 0:00:04 ( 9.36 ms/it)
   objective: 13719.98639815268


Minimizing 490    Time: 0:00:04 ( 9.36 ms/it)
   objective: 13718.747271572433


Minimizing 501    Time: 0:00:04 ( 9.36 ms/it)
   objective: 13715.479200816426


Minimizing 512    Time: 0:00:04 ( 9.36 ms/it)
   objective: 13712.195834743769


Minimizing 523    Time: 0:00:04 ( 9.35 ms/it)
   objective: 13710.923313808147


Minimizing 534    Time: 0:00:04 ( 9.35 ms/it)
   objective: 13708.657294668534


Minimizing 545    Time: 0:00:05 ( 9.35 ms/it)
   objective: 13705.22978072302


Minimizing 556    Time: 0:00:05 ( 9.35 ms/it)
   objective: 13703.311553864667


Minimizing 567    Time: 0:00:05 ( 9.35 ms/it)
   objective: 13699.546986585694


Minimizing 578    Time: 0:00:05 ( 9.35 ms/it)
   objective: 13683.17183202612


Minimizing 589    Time: 0:00:05 ( 9.34 ms/it)
   objective: 13660.207399732324


Minimizing 600    Time: 0:00:05 ( 9.34 ms/it)
   objective: 13659.864343811256


Minimizing 611    Time: 0:00:05 ( 9.34 ms/it)
   objective: 13655.19242750496


Minimizing 622    Time: 0:00:05 ( 9.33 ms/it)
   objective: 13655.034111646724


Minimizing 633    Time: 0:00:05 ( 9.33 ms/it)
   objective: 13655.003202051528


Minimizing 644    Time: 0:00:06 ( 9.33 ms/it)
   objective: 13654.40783156328


Minimizing 655    Time: 0:00:06 ( 9.33 ms/it)
   objective: 13654.152935730279


Minimizing 666    Time: 0:00:06 ( 9.33 ms/it)
   objective: 13653.17882035164


Minimizing 677    Time: 0:00:06 ( 9.32 ms/it)
   objective: 13652.267921742314


Minimizing 688    Time: 0:00:06 ( 9.32 ms/it)
   objective: 13651.02512916104


Minimizing 699    Time: 0:00:06 ( 9.32 ms/it)
   objective: 13649.14050936279


Minimizing 710    Time: 0:00:06 ( 9.32 ms/it)
   objective: 13647.816792422294


Minimizing 721    Time: 0:00:06 ( 9.32 ms/it)
   objective: 13644.79071287853


Minimizing 734    Time: 0:00:06 ( 9.34 ms/it)
   objective: 13640.549288752067


Minimizing 747    Time: 0:00:06 ( 9.33 ms/it)
   objective: 13635.19950775979


Minimizing 758    Time: 0:00:07 ( 9.33 ms/it)
   objective: 13634.262127561204


Minimizing 769    Time: 0:00:07 ( 9.33 ms/it)
   objective: 13629.94485803778


Minimizing 780    Time: 0:00:07 ( 9.33 ms/it)
   objective: 13629.527178120647


Minimizing 791    Time: 0:00:07 ( 9.33 ms/it)
   objective: 13627.929337383597


Minimizing 802    Time: 0:00:07 ( 9.33 ms/it)
   objective: 13624.077649391103


Minimizing 813    Time: 0:00:07 ( 9.33 ms/it)
   objective: 13623.41725809133


Minimizing 824    Time: 0:00:07 ( 9.33 ms/it)
   objective: 13620.409858084706


Minimizing 835    Time: 0:00:07 ( 9.34 ms/it)
   objective: 13616.310591420566


Minimizing 846    Time: 0:00:07 ( 9.34 ms/it)
   objective: 13614.706614687319


Minimizing 857    Time: 0:00:08 ( 9.34 ms/it)
   objective: 13613.887201920603


Minimizing 868    Time: 0:00:08 ( 9.34 ms/it)
   objective: 13612.647264726838


Minimizing 879    Time: 0:00:08 ( 9.34 ms/it)
   objective: 13610.448587409388


Minimizing 890    Time: 0:00:08 ( 9.33 ms/it)
   objective: 13610.362082505315


Minimizing 901    Time: 0:00:08 ( 9.33 ms/it)
   objective: 13609.397378515081


Minimizing 912    Time: 0:00:08 ( 9.33 ms/it)
   objective: 13608.506441759702


Minimizing 923    Time: 0:00:08 ( 9.34 ms/it)
   objective: 13607.031509707216


Minimizing 934    Time: 0:00:08 ( 9.34 ms/it)
   objective: 13605.719220779923


Minimizing 945    Time: 0:00:08 ( 9.34 ms/it)
   objective: 13605.582312877268


Minimizing 956    Time: 0:00:08 ( 9.34 ms/it)
   objective: 13603.943678067415


Minimizing 967    Time: 0:00:09 ( 9.34 ms/it)
   objective: 13597.815902282804


Minimizing 978    Time: 0:00:09 ( 9.34 ms/it)
   objective: 13597.292583852817


Minimizing 989    Time: 0:00:09 ( 9.33 ms/it)
   objective: 13595.96404846554


Minimizing 1000    Time: 0:00:09 ( 9.33 ms/it)
   objective: 13595.292338935142


Minimizing 1011    Time: 0:00:09 ( 9.33 ms/it)
   objective: 13594.236949661616


Minimizing 1022    Time: 0:00:09 ( 9.33 ms/it)
   objective: 13592.511507656578


Minimizing 1033    Time: 0:00:09 ( 9.33 ms/it)
   objective: 13591.75071692538


Minimizing 1044    Time: 0:00:09 ( 9.33 ms/it)
   objective: 13589.25623106915


Minimizing 1055    Time: 0:00:09 ( 9.33 ms/it)
   objective: 13586.508852663857


Minimizing 1066    Time: 0:00:09 ( 9.32 ms/it)
   objective: 13584.25746729818


Minimizing 1077    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13571.739646570328


Minimizing 1088    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13546.464277020757


Minimizing 1099    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13545.271166853126


Minimizing 1110    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13545.041364355551


Minimizing 1121    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13543.843895622427


Minimizing 1132    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13543.388358036042


Minimizing 1143    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13543.081421600393


Minimizing 1154    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13542.519053736556


Minimizing 1165    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13541.97713521168


Minimizing 1176    Time: 0:00:10 ( 9.32 ms/it)
   objective: 13541.847497560186


Minimizing 1187    Time: 0:00:11 ( 9.32 ms/it)
   objective: 13540.823109309


Minimizing 1198    Time: 0:00:11 ( 9.32 ms/it)
   objective: 13540.287826725238


Minimizing 1209    Time: 0:00:11 ( 9.32 ms/it)
   objective: 13539.878724237074


Minimizing 1220    Time: 0:00:11 ( 9.31 ms/it)
   objective: 13539.018588035004


Minimizing 1231    Time: 0:00:11 ( 9.31 ms/it)
   objective: 13537.960954737311


Minimizing 1242    Time: 0:00:11 ( 9.31 ms/it)
   objective: 13534.875622397201


Minimizing 1253    Time: 0:00:11 ( 9.31 ms/it)
   objective: 13529.491905250965


Minimizing 1264    Time: 0:00:11 ( 9.31 ms/it)
   objective: 13525.687650043983


Minimizing 1275    Time: 0:00:11 ( 9.31 ms/it)
   objective: 13524.804357565983


Minimizing 1286    Time: 0:00:11 ( 9.31 ms/it)
   objective: 13516.005321631994


Minimizing 1297    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13512.98234541963


Minimizing 1308    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13512.310835921104


Minimizing 1319    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13509.247707178496


Minimizing 1330    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13505.564022640101


Minimizing 1341    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13502.071713042504


Minimizing 1352    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13501.448098562905


Minimizing 1364    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13500.970017423053


Minimizing 1375    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13500.596435636267


Minimizing 1386    Time: 0:00:12 ( 9.31 ms/it)
   objective: 13499.978638050248


Minimizing 1397    Time: 0:00:13 ( 9.31 ms/it)
   objective: 13498.183503368957


Minimizing 1408    Time: 0:00:13 ( 9.31 ms/it)
   objective: 13497.799180655304


Minimizing 1419    Time: 0:00:13 ( 9.31 ms/it)
   objective: 13497.003770955227


Minimizing 1430    Time: 0:00:13 ( 9.31 ms/it)
   objective: 13495.095210999105


Minimizing 1441    Time: 0:00:13 ( 9.31 ms/it)
   objective: 13493.230339812682


Minimizing 1452    Time: 0:00:13 ( 9.31 ms/it)
   objective: 13493.091361178624


Minimizing 1463    Time: 0:00:13 ( 9.31 ms/it)
   objective: 13492.420457924818


Minimizing 1474    Time: 0:00:13 ( 9.31 ms/it)
   objective: 13492.140554938975


Minimizing 1485    Time: 0:00:13 ( 9.30 ms/it)
   objective: 13491.557618991967


Minimizing 1496    Time: 0:00:13 ( 9.30 ms/it)
   objective: 13490.871922885897


Minimizing 1507    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13488.61751922559


Minimizing 1518    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13485.501435160098


Minimizing 1529    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13485.31584992395


Minimizing 1540    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13485.264074539416


Minimizing 1551    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13484.562398820039


Minimizing 1562    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13484.209564830191


Minimizing 1573    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13483.963362897193


Minimizing 1584    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13483.357820137739


Minimizing 1595    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13482.86805629592


Minimizing 1606    Time: 0:00:14 ( 9.30 ms/it)
   objective: 13482.555679248137


Minimizing 1617    Time: 0:00:15 ( 9.30 ms/it)
   objective: 13481.486892191577


Minimizing 1628    Time: 0:00:15 ( 9.30 ms/it)
   objective: 13478.793233583026


Minimizing 1639    Time: 0:00:15 ( 9.30 ms/it)
   objective: 13478.418094819848


Minimizing 1650    Time: 0:00:15 ( 9.30 ms/it)
   objective: 13478.406068604469


Minimizing 1661    Time: 0:00:15 ( 9.29 ms/it)
   objective: 13478.406610715843


Minimizing 1672    Time: 0:00:15 ( 9.29 ms/it)
   objective: 13478.407184899435


Minimizing 1683    Time: 0:00:15 ( 9.29 ms/it)
   objective: 13478.40638167184


Minimizing 1694    Time: 0:00:15 ( 9.29 ms/it)
   objective: 13478.405999328912


Minimizing 1705    Time: 0:00:15 ( 9.29 ms/it)
   objective: 13478.405957738112


Minimizing 1716    Time: 0:00:15 ( 9.29 ms/it)
   objective: 13478.405832735327


Minimizing 1727    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.405620885751


Minimizing 1738    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.405804492431


Minimizing 1749    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.405540314721


Minimizing 1760    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.40550328471


Minimizing 1771    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.405720455528


Minimizing 1782    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.405940372395


Minimizing 1793    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.406162485742


Minimizing 1804    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.405918924065


Minimizing 1815    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.405628996115


Minimizing 1826    Time: 0:00:16 ( 9.29 ms/it)
   objective: 13478.405804701644


Minimizing 1837    Time: 0:00:17 ( 9.29 ms/it)
   objective: 13478.40553981559


Minimizing 1845    Time: 0:00:17 ( 9.29 ms/it)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0185	0.0143	-1.29	0.1970	0.7211
Test: c5.1	0.0247	0.0304	0.81	0.4173	0.7948
Test: c234.15	0.0015	0.0311	0.05	0.9612	0.5734
Test: c12.34	0.0013	0.0313	0.04	0.9664	0.6719
Test: c3.4	-0.0108	0.0315	-0.34	0.7320	0.8671
a1	0.3418	0.0490	6.97	<1e-11
Sex: Boys	0.1834	0.0143	12.78	<1e-36
Test: c5.1 & a1	-0.3354	0.1024	-3.27	0.0011
Test: c234.15 & a1	-0.1049	0.1061	-0.99	0.3227
Test: c12.34 & a1	0.0387	0.1087	0.36	0.7217
Test: c3.4 & a1	0.2262	0.1078	2.10	0.0358
Test: c5.1 & Sex: Boys	-0.1387	0.0304	-4.55	<1e-05
Test: c234.15 & Sex: Boys	0.1236	0.0311	3.98	<1e-04
Test: c12.34 & Sex: Boys	0.0134	0.0313	0.43	0.6685
Test: c3.4 & Sex: Boys	-0.0374	0.0315	-1.19	0.2350
a1 & Sex: Boys	-0.0792	0.0490	-1.61	0.1063
Test: c5.1 & a1 & Sex: Boys	-0.1529	0.1024	-1.49	0.1355
Test: c234.15 & a1 & Sex: Boys	0.1594	0.1061	1.50	0.1329
Test: c12.34 & a1 & Sex: Boys	0.0854	0.1087	0.79	0.4320
Test: c3.4 & a1 & Sex: Boys	0.0254	0.1078	0.24	0.8139
Residual	0.0001

VarCorr(m_cpx_1_PC_2)

	Column	Variance	Std.Dev	Corr.
Child	(Intercept)	0.51992273	0.72105667
	Test: c5.1	0.63174299	0.79482261	+0.36
	Test: c234.15	0.32873160	0.57335120	+0.02	-0.39
	Test: c12.34	0.45151101	0.67194569	+0.23	-0.20	-0.30
	Test: c3.4	0.75182697	0.86707956	-0.08	-0.10	+0.76	-0.50
Residual		0.00000000	0.00006224

m_cpx_1_PC_2.PCA

(Child = 
Principal components based on correlation matrix
 (Intercept)     1.0     .      .      .     .
 Test: c5.1      0.36   1.0     .      .     .
 Test: c234.15   0.02  -0.39   1.0     .     .
 Test: c12.34    0.23  -0.2   -0.3    1.0    .
 Test: c3.4     -0.08  -0.1    0.76  -0.5   1.0

Normalized cumulative variances:
[0.43, 0.6953, 0.9071, 0.9708, 1.0]

Component loadings
                  PC1    PC2    PC3    PC4    PC5
 (Intercept)    -0.19   0.5    0.71   0.39   0.24
 Test: c5.1     -0.24   0.75  -0.22  -0.45  -0.37
 Test: c234.15   0.59  -0.02   0.4    0.02  -0.7
 Test: c12.34   -0.42  -0.39   0.52  -0.63  -0.06
 Test: c3.4      0.61   0.2    0.11  -0.5    0.57,)

f_zcp_1 = @formula(zScore ~ 1 + Test*a1*Sex + zerocorr(1 + Test | Child))
m_zcp_1_PC_2 = fit(MixedModel, f_zcp_1, dat; contrasts=contr4b)

Minimizing 17    Time: 0:00:00 ( 5.95 ms/it)
   objective: 13835.865576073087


Minimizing 34    Time: 0:00:00 ( 6.09 ms/it)
   objective: 13822.961224737712


Minimizing 51    Time: 0:00:00 ( 6.13 ms/it)
   objective: 13766.415614525606


Minimizing 67    Time: 0:00:00 ( 6.17 ms/it)
   objective: 13761.902235438532


Minimizing 83    Time: 0:00:00 ( 6.19 ms/it)
   objective: 13758.34711335586


Minimizing 99    Time: 0:00:00 ( 6.21 ms/it)
   objective: 13753.15817574061


Minimizing 116    Time: 0:00:00 ( 6.22 ms/it)
   objective: 13748.490856818726


Minimizing 133    Time: 0:00:00 ( 6.21 ms/it)
   objective: 13738.375946845925


Minimizing 150    Time: 0:00:00 ( 6.19 ms/it)
   objective: 13692.590024841054


Minimizing 167    Time: 0:00:01 ( 6.16 ms/it)
   objective: 13685.559973132902


Minimizing 185    Time: 0:00:01 ( 6.13 ms/it)
   objective: 13683.578850896865


Minimizing 203    Time: 0:00:01 ( 6.11 ms/it)
   objective: 13679.78366939749


Minimizing 221    Time: 0:00:01 ( 6.09 ms/it)
   objective: 13675.714216755834


Minimizing 239    Time: 0:00:01 ( 6.07 ms/it)
   objective: 13672.358710905602


Minimizing 260    Time: 0:00:01 ( 6.13 ms/it)
   objective: 13667.893771095369


Minimizing 280    Time: 0:00:01 ( 6.11 ms/it)
   objective: 13660.090004641599


Minimizing 298    Time: 0:00:01 ( 6.10 ms/it)
   objective: 13643.076456753573


Minimizing 315    Time: 0:00:01 ( 6.10 ms/it)
   objective: 13641.315588143676


Minimizing 332    Time: 0:00:02 ( 6.09 ms/it)
   objective: 13639.899997376138


Minimizing 349    Time: 0:00:02 ( 6.08 ms/it)
   objective: 13637.040540561553


Minimizing 366    Time: 0:00:02 ( 6.08 ms/it)
   objective: 13609.164600395547


Minimizing 384    Time: 0:00:02 ( 6.07 ms/it)
   objective: 13567.29202503719


Minimizing 402    Time: 0:00:02 ( 6.06 ms/it)
   objective: 13564.899787835115


Minimizing 419    Time: 0:00:02 ( 6.05 ms/it)
   objective: 13560.887106210306


Minimizing 436    Time: 0:00:02 ( 6.05 ms/it)
   objective: 13559.279278206348


Minimizing 454    Time: 0:00:02 ( 6.04 ms/it)
   objective: 13552.560324728387


Minimizing 472    Time: 0:00:02 ( 6.04 ms/it)
   objective: 13546.92231171143


Minimizing 489    Time: 0:00:02 ( 6.04 ms/it)
   objective: 13539.081366875165


Minimizing 506    Time: 0:00:03 ( 6.04 ms/it)
   objective: 13536.211455915836


Minimizing 524    Time: 0:00:03 ( 6.03 ms/it)
   objective: 13532.542230582869


Minimizing 542    Time: 0:00:03 ( 6.03 ms/it)
   objective: 13528.32681571941


Minimizing 560    Time: 0:00:03 ( 6.02 ms/it)
   objective: 13523.959200304002


Minimizing 578    Time: 0:00:03 ( 6.02 ms/it)
   objective: 13497.11374308812


Minimizing 594    Time: 0:00:03 ( 6.05 ms/it)
   objective: 13488.46525596558


Minimizing 611    Time: 0:00:03 ( 6.04 ms/it)
   objective: 13481.588419334861


Minimizing 628    Time: 0:00:03 ( 6.04 ms/it)
   objective: 13472.88242500188


Minimizing 646    Time: 0:00:03 ( 6.04 ms/it)
   objective: 13470.710024890635


Minimizing 664    Time: 0:00:04 ( 6.03 ms/it)
   objective: 13469.465805216794


Minimizing 682    Time: 0:00:04 ( 6.03 ms/it)
   objective: 13465.943988824787


Minimizing 700    Time: 0:00:04 ( 6.02 ms/it)
   objective: 13464.166566562548


Minimizing 718    Time: 0:00:04 ( 6.02 ms/it)
   objective: 13446.187408461978


Minimizing 736    Time: 0:00:04 ( 6.01 ms/it)
   objective: 13402.107912238818


Minimizing 754    Time: 0:00:04 ( 6.01 ms/it)
   objective: 13381.503198226099


Minimizing 771    Time: 0:00:04 ( 6.01 ms/it)
   objective: 13350.781376452767


Minimizing 788    Time: 0:00:04 ( 6.04 ms/it)
   objective: 13346.865512885823


Minimizing 803    Time: 0:00:04 ( 6.05 ms/it)
   objective: 13347.077746908006


Minimizing 820    Time: 0:00:04 ( 6.05 ms/it)
   objective: 13347.124252066671


Minimizing 837    Time: 0:00:05 ( 6.05 ms/it)
   objective: 13346.637101374377


Minimizing 855    Time: 0:00:05 ( 6.04 ms/it)
   objective: 13346.936288345794


Minimizing 872    Time: 0:00:05 ( 6.04 ms/it)
   objective: 13346.57827407583


Minimizing 884    Time: 0:00:05 ( 6.04 ms/it)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0188	0.0143	-1.32	0.1873	0.5900
Test: c5.1	0.0224	0.0309	0.72	0.4687	0.6962
Test: c234.15	-0.0013	0.0322	-0.04	0.9668	1.0042
Test: c12.34	0.0002	0.0315	0.01	0.9940	0.8102
Test: c3.4	-0.0128	0.0312	-0.41	0.6811	0.8967
a1	0.3381	0.0487	6.94	<1e-11
Sex: Boys	0.1840	0.0143	12.90	<1e-37
Test: c5.1 & a1	-0.3233	0.1039	-3.11	0.0019
Test: c234.15 & a1	-0.0648	0.1097	-0.59	0.5547
Test: c12.34 & a1	0.0499	0.1092	0.46	0.6475
Test: c3.4 & a1	0.2108	0.1065	1.98	0.0479
Test: c5.1 & Sex: Boys	-0.1362	0.0309	-4.41	<1e-04
Test: c234.15 & Sex: Boys	0.1280	0.0322	3.98	<1e-04
Test: c12.34 & Sex: Boys	0.0081	0.0315	0.26	0.7964
Test: c3.4 & Sex: Boys	-0.0320	0.0312	-1.02	0.3055
a1 & Sex: Boys	-0.0781	0.0487	-1.60	0.1090
Test: c5.1 & a1 & Sex: Boys	-0.1602	0.1039	-1.54	0.1232
Test: c234.15 & a1 & Sex: Boys	0.1459	0.1097	1.33	0.1837
Test: c12.34 & a1 & Sex: Boys	0.0961	0.1092	0.88	0.3789
Test: c3.4 & a1 & Sex: Boys	0.0173	0.1065	0.16	0.8709
Residual	0.0000

VarCorr(m_zcp_1_PC_2)

	Column	Variance	Std.Dev	Corr.
Child	(Intercept)	0.34809468	0.58999549
	Test: c5.1	0.48475857	0.69624606	.
	Test: c234.15	1.00841580	1.00419909	.	.
	Test: c12.34	0.65642237	0.81019897	.	.	.
	Test: c3.4	0.80403986	0.89668270	.	.	.	.
Residual		0.00000000	0.00000110

MixedModels.likelihoodratiotest(m_zcp_1_PC_2, m_cpx_1_PC_2)

	model-dof	deviance	χ²	χ²-dof	P(>χ²)
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + zerocorr(1 + Test \| Child)	26	13346
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test \| Child)	36	13478	-132	10	NaN

3 Other topics

3.1 Contrasts are re-parameterizations of the same model

The choice of contrast does not affect the model objective, in other words, they all yield the same goodness of fit. It does not matter whether a contrast is orthogonal or not.

[
  objective(m_ovi_SeqDiff),
  objective(m_ovi_Helmert),
  objective(m_ovi_Hypo),
]

3-element Vector{Float64}:
 13854.10319061622
 13854.103190616239
 13854.103190616255

3.2 VCs and CPs depend on contrast coding

Trivially, the meaning of a contrast depends on its definition. Consequently, the contrast specification has a big effect on the random-effect structure. As an illustration, we refit the LMMs with variance components (VCs) and correlation parameters (CPs) for Child-related contrasts of Test. Unfortunately, it is not easy, actually rather quite difficult, to grasp the meaning of correlations of contrast-based effects; they represent two-way interactions.

begin
  f_Child = @formula zScore ~
    1 + Test * a1 * Sex + (1 + Test | Child)
  m_Child_SDC = fit(MixedModel, f_Child, dat; contrasts=contr1)
  m_Child_HeC = fit(MixedModel, f_Child, dat; contrasts=contr2)
  m_Child_HyC = fit(MixedModel, f_Child, dat; contrasts=contr3)
  m_Child_PCA = fit(MixedModel, f_Child, dat; contrasts=contr4)
end

Minimizing 12    Time: 0:00:00 ( 9.01 ms/it)
   objective: 14000.964427255823


Minimizing 22    Time: 0:00:00 ( 9.54 ms/it)
   objective: 13891.169931774632


Minimizing 33    Time: 0:00:00 ( 9.63 ms/it)
   objective: 13854.397284105919


Minimizing 44    Time: 0:00:00 ( 9.63 ms/it)
   objective: 13839.312054141385


Minimizing 54    Time: 0:00:00 ( 9.71 ms/it)
   objective: 13837.390219818128


Minimizing 65    Time: 0:00:00 ( 9.71 ms/it)
   objective: 13832.870356555626


Minimizing 76    Time: 0:00:00 ( 9.70 ms/it)
   objective: 13826.546137930354


Minimizing 87    Time: 0:00:00 ( 9.70 ms/it)
   objective: 13826.007015585048


Minimizing 98    Time: 0:00:00 ( 9.68 ms/it)
   objective: 13824.58496134066


Minimizing 109    Time: 0:00:01 ( 9.66 ms/it)
   objective: 13823.288576739527


Minimizing 120    Time: 0:00:01 ( 9.64 ms/it)
   objective: 13822.666253666197


Minimizing 134    Time: 0:00:01 ( 9.78 ms/it)
   objective: 13823.09390654049


Minimizing 147    Time: 0:00:01 ( 9.82 ms/it)
   objective: 13820.966641306815


Minimizing 158    Time: 0:00:01 ( 9.78 ms/it)
   objective: 13815.759473180517


Minimizing 169    Time: 0:00:01 ( 9.75 ms/it)
   objective: 13814.508484889162


Minimizing 180    Time: 0:00:01 ( 9.72 ms/it)
   objective: 13808.395778391674


Minimizing 191    Time: 0:00:01 ( 9.70 ms/it)
   objective: 13806.607241240512


Minimizing 202    Time: 0:00:01 ( 9.68 ms/it)
   objective: 13805.918141616752


Minimizing 213    Time: 0:00:02 ( 9.66 ms/it)
   objective: 13803.91044943107


Minimizing 224    Time: 0:00:02 ( 9.64 ms/it)
   objective: 13803.267043218582


Minimizing 235    Time: 0:00:02 ( 9.63 ms/it)
   objective: 13801.39836162128


Minimizing 246    Time: 0:00:02 ( 9.61 ms/it)
   objective: 13801.24128089299


Minimizing 257    Time: 0:00:02 ( 9.63 ms/it)
   objective: 13799.679733203517


Minimizing 268    Time: 0:00:02 ( 9.63 ms/it)
   objective: 13797.286802930663


Minimizing 278    Time: 0:00:02 ( 9.71 ms/it)
   objective: 13792.66794398438


Minimizing 289    Time: 0:00:02 ( 9.71 ms/it)
   objective: 13791.911175696878


Minimizing 300    Time: 0:00:02 ( 9.70 ms/it)
   objective: 13790.986675462656


Minimizing 311    Time: 0:00:03 ( 9.70 ms/it)
   objective: 13789.608083221196


Minimizing 322    Time: 0:00:03 ( 9.69 ms/it)
   objective: 13788.536210827606


Minimizing 333    Time: 0:00:03 ( 9.69 ms/it)
   objective: 13786.969707286242


Minimizing 344    Time: 0:00:03 ( 9.70 ms/it)
   objective: 13784.275925359845


Minimizing 354    Time: 0:00:03 ( 9.72 ms/it)
   objective: 13780.21732440179


Minimizing 365    Time: 0:00:03 ( 9.72 ms/it)
   objective: 13779.553746840982


Minimizing 376    Time: 0:00:03 ( 9.71 ms/it)
   objective: 13778.339499643775


Minimizing 387    Time: 0:00:03 ( 9.70 ms/it)
   objective: 13777.542781149623


Minimizing 398    Time: 0:00:03 ( 9.69 ms/it)
   objective: 13777.109219652757


Minimizing 409    Time: 0:00:03 ( 9.68 ms/it)
   objective: 13775.96680734041


Minimizing 420    Time: 0:00:04 ( 9.67 ms/it)
   objective: 13774.91256414129


Minimizing 431    Time: 0:00:04 ( 9.66 ms/it)
   objective: 13766.938671991476


Minimizing 442    Time: 0:00:04 ( 9.65 ms/it)
   objective: 13762.812867086805


Minimizing 453    Time: 0:00:04 ( 9.65 ms/it)
   objective: 13744.906806367742


Minimizing 464    Time: 0:00:04 ( 9.65 ms/it)
   objective: 13743.303586267248


Minimizing 475    Time: 0:00:04 ( 9.65 ms/it)
   objective: 13743.035950418096


Minimizing 486    Time: 0:00:04 ( 9.65 ms/it)
   objective: 13740.418697602783


Minimizing 497    Time: 0:00:04 ( 9.64 ms/it)
   objective: 13738.896880601316


Minimizing 508    Time: 0:00:04 ( 9.64 ms/it)
   objective: 13738.714403810545


Minimizing 519    Time: 0:00:05 ( 9.63 ms/it)
   objective: 13738.348994168533


Minimizing 530    Time: 0:00:05 ( 9.63 ms/it)
   objective: 13736.07841985484


Minimizing 541    Time: 0:00:05 ( 9.62 ms/it)
   objective: 13730.930124022001


Minimizing 552    Time: 0:00:05 ( 9.62 ms/it)
   objective: 13730.222576082877


Minimizing 563    Time: 0:00:05 ( 9.62 ms/it)
   objective: 13729.339607921793


Minimizing 574    Time: 0:00:05 ( 9.62 ms/it)
   objective: 13728.219029647844


Minimizing 585    Time: 0:00:05 ( 9.62 ms/it)
   objective: 13726.255443405309


Minimizing 596    Time: 0:00:05 ( 9.62 ms/it)
   objective: 13725.170022920065


Minimizing 607    Time: 0:00:05 ( 9.61 ms/it)
   objective: 13725.078323887796


Minimizing 618    Time: 0:00:05 ( 9.62 ms/it)
   objective: 13724.27942353571


Minimizing 628    Time: 0:00:06 ( 9.62 ms/it)
   objective: 13724.144329345821


Minimizing 639    Time: 0:00:06 ( 9.62 ms/it)
   objective: 13723.984183599827


Minimizing 650    Time: 0:00:06 ( 9.62 ms/it)
   objective: 13721.648559866178


Minimizing 661    Time: 0:00:06 ( 9.62 ms/it)
   objective: 13720.685898060205


Minimizing 672    Time: 0:00:06 ( 9.64 ms/it)
   objective: 13720.448656966335


Minimizing 682    Time: 0:00:06 ( 9.65 ms/it)
   objective: 13719.459816209433


Minimizing 693    Time: 0:00:06 ( 9.65 ms/it)
   objective: 13719.148752187702


Minimizing 704    Time: 0:00:06 ( 9.64 ms/it)
   objective: 13718.437254795685


Minimizing 715    Time: 0:00:06 ( 9.64 ms/it)
   objective: 13716.10300674407


Minimizing 726    Time: 0:00:06 ( 9.63 ms/it)
   objective: 13709.994406853202


Minimizing 737    Time: 0:00:07 ( 9.63 ms/it)
   objective: 13701.046030508052


Minimizing 748    Time: 0:00:07 ( 9.63 ms/it)
   objective: 13696.883519440802


Minimizing 759    Time: 0:00:07 ( 9.63 ms/it)
   objective: 13695.52493540723


Minimizing 770    Time: 0:00:07 ( 9.63 ms/it)
   objective: 13694.39161719961


Minimizing 781    Time: 0:00:07 ( 9.63 ms/it)
   objective: 13693.56041571957


Minimizing 792    Time: 0:00:07 ( 9.62 ms/it)
   objective: 13692.934506845042


Minimizing 803    Time: 0:00:07 ( 9.62 ms/it)
   objective: 13691.972149965899


Minimizing 814    Time: 0:00:07 ( 9.62 ms/it)
   objective: 13686.883824072811


Minimizing 825    Time: 0:00:07 ( 9.61 ms/it)
   objective: 13686.141489506765


Minimizing 838    Time: 0:00:08 ( 9.63 ms/it)
   objective: 13684.082681605647


Minimizing 851    Time: 0:00:08 ( 9.63 ms/it)
   objective: 13682.494113929206


Minimizing 862    Time: 0:00:08 ( 9.62 ms/it)
   objective: 13681.078099969833


Minimizing 873    Time: 0:00:08 ( 9.62 ms/it)
   objective: 13678.63464407821


Minimizing 884    Time: 0:00:08 ( 9.62 ms/it)
   objective: 13677.590519511785


Minimizing 895    Time: 0:00:08 ( 9.63 ms/it)
   objective: 13676.748677622392


Minimizing 906    Time: 0:00:08 ( 9.63 ms/it)
   objective: 13668.40051484466


Minimizing 917    Time: 0:00:08 ( 9.63 ms/it)
   objective: 13665.508462870392


Minimizing 928    Time: 0:00:08 ( 9.63 ms/it)
   objective: 13664.866266214172


Minimizing 939    Time: 0:00:09 ( 9.62 ms/it)
   objective: 13655.480068932164


Minimizing 950    Time: 0:00:09 ( 9.62 ms/it)
   objective: 13654.533353769417


Minimizing 961    Time: 0:00:09 ( 9.62 ms/it)
   objective: 13654.380020536984


Minimizing 972    Time: 0:00:09 ( 9.61 ms/it)
   objective: 13653.404496112998


Minimizing 983    Time: 0:00:09 ( 9.61 ms/it)
   objective: 13652.786772269268


Minimizing 994    Time: 0:00:09 ( 9.61 ms/it)
   objective: 13650.66943430117


Minimizing 1005    Time: 0:00:09 ( 9.60 ms/it)
   objective: 13649.93706538975


Minimizing 1016    Time: 0:00:09 ( 9.60 ms/it)
   objective: 13648.688953074095


Minimizing 1027    Time: 0:00:09 ( 9.60 ms/it)
   objective: 13648.62756321377


Minimizing 1038    Time: 0:00:09 ( 9.59 ms/it)
   objective: 13647.893937268207


Minimizing 1049    Time: 0:00:10 ( 9.59 ms/it)
   objective: 13645.647322050048


Minimizing 1060    Time: 0:00:10 ( 9.59 ms/it)
   objective: 13643.897024092272


Minimizing 1071    Time: 0:00:10 ( 9.59 ms/it)
   objective: 13642.911542990943


Minimizing 1082    Time: 0:00:10 ( 9.58 ms/it)
   objective: 13636.704952025786


Minimizing 1093    Time: 0:00:10 ( 9.58 ms/it)
   objective: 13636.722863542105


Minimizing 1104    Time: 0:00:10 ( 9.59 ms/it)
   objective: 13636.65236837147


Minimizing 1115    Time: 0:00:10 ( 9.58 ms/it)
   objective: 13636.206008298657


Minimizing 1126    Time: 0:00:10 ( 9.58 ms/it)
   objective: 13635.725697273701


Minimizing 1137    Time: 0:00:10 ( 9.58 ms/it)
   objective: 13635.449930515184


Minimizing 1148    Time: 0:00:10 ( 9.57 ms/it)
   objective: 13635.17219640372


Minimizing 1159    Time: 0:00:11 ( 9.57 ms/it)
   objective: 13634.571596852016


Minimizing 1170    Time: 0:00:11 ( 9.57 ms/it)
   objective: 13633.879309288714


Minimizing 1181    Time: 0:00:11 ( 9.57 ms/it)
   objective: 13633.262655853425


Minimizing 1192    Time: 0:00:11 ( 9.56 ms/it)
   objective: 13632.147023224396


Minimizing 1203    Time: 0:00:11 ( 9.56 ms/it)
   objective: 13631.65731715077


Minimizing 1214    Time: 0:00:11 ( 9.56 ms/it)
   objective: 13631.28339076323


Minimizing 1225    Time: 0:00:11 ( 9.56 ms/it)
   objective: 13631.012007484474


Minimizing 1236    Time: 0:00:11 ( 9.55 ms/it)
   objective: 13630.238894947608


Minimizing 1247    Time: 0:00:11 ( 9.55 ms/it)
   objective: 13627.105662962349


Minimizing 1258    Time: 0:00:12 ( 9.55 ms/it)
   objective: 13626.811638999752


Minimizing 1269    Time: 0:00:12 ( 9.55 ms/it)
   objective: 13626.678498267436


Minimizing 1280    Time: 0:00:12 ( 9.55 ms/it)
   objective: 13625.757739833956


Minimizing 1291    Time: 0:00:12 ( 9.54 ms/it)
   objective: 13624.713793294053


Minimizing 1302    Time: 0:00:12 ( 9.54 ms/it)
   objective: 13624.685942752309


Minimizing 1313    Time: 0:00:12 ( 9.54 ms/it)
   objective: 13624.537003445002


Minimizing 1324    Time: 0:00:12 ( 9.54 ms/it)
   objective: 13624.020166989969


Minimizing 1335    Time: 0:00:12 ( 9.54 ms/it)
   objective: 13623.424506125644


Minimizing 1346    Time: 0:00:12 ( 9.54 ms/it)
   objective: 13622.673365967843


Minimizing 1357    Time: 0:00:12 ( 9.54 ms/it)
   objective: 13621.624890218249


Minimizing 1368    Time: 0:00:13 ( 9.53 ms/it)
   objective: 13621.216627529473


Minimizing 1379    Time: 0:00:13 ( 9.53 ms/it)
   objective: 13620.089695188253


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Minimizing 1862    Time: 0:00:17 ( 9.52 ms/it)
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Minimizing 1873    Time: 0:00:17 ( 9.52 ms/it)
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Minimizing 1884    Time: 0:00:17 ( 9.52 ms/it)
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Minimizing 1895    Time: 0:00:18 ( 9.51 ms/it)
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Minimizing 1906    Time: 0:00:18 ( 9.51 ms/it)
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Minimizing 1917    Time: 0:00:18 ( 9.51 ms/it)
   objective: 13553.912390049205


Minimizing 1928    Time: 0:00:18 ( 9.51 ms/it)
   objective: 13546.820105137318


Minimizing 1939    Time: 0:00:18 ( 9.51 ms/it)
   objective: 13545.318788515768


Minimizing 1950    Time: 0:00:18 ( 9.51 ms/it)
   objective: 13545.086731361298


Minimizing 1961    Time: 0:00:18 ( 9.51 ms/it)
   objective: 13544.244219688524


Minimizing 1972    Time: 0:00:18 ( 9.51 ms/it)
   objective: 13543.006505770318


Minimizing 1983    Time: 0:00:18 ( 9.51 ms/it)
   objective: 13542.344190079413


Minimizing 1994    Time: 0:00:18 ( 9.50 ms/it)
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Minimizing 2005    Time: 0:00:19 ( 9.50 ms/it)
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Minimizing 2016    Time: 0:00:19 ( 9.50 ms/it)
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Minimizing 2214    Time: 0:00:21 ( 9.49 ms/it)
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Minimizing 958    Time: 0:00:09 ( 9.42 ms/it)
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Minimizing 969    Time: 0:00:09 ( 9.42 ms/it)
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Minimizing 991    Time: 0:00:09 ( 9.43 ms/it)
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Minimizing 1024    Time: 0:00:09 ( 9.43 ms/it)
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Minimizing 1057    Time: 0:00:09 ( 9.44 ms/it)
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Minimizing 1067    Time: 0:00:10 ( 9.45 ms/it)
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Minimizing 1086    Time: 0:00:10 ( 9.48 ms/it)
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Minimizing 1130    Time: 0:00:10 ( 9.48 ms/it)
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Minimizing 1163    Time: 0:00:11 ( 9.48 ms/it)
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Minimizing 1174    Time: 0:00:11 ( 9.47 ms/it)
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Minimizing 1229    Time: 0:00:11 ( 9.47 ms/it)
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Minimizing 1240    Time: 0:00:11 ( 9.47 ms/it)
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Minimizing 1262    Time: 0:00:11 ( 9.47 ms/it)
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Minimizing 1273    Time: 0:00:12 ( 9.47 ms/it)
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Minimizing 1284    Time: 0:00:12 ( 9.47 ms/it)
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Minimizing 1590    Time: 0:00:15 ( 9.49 ms/it)
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Minimizing 1601    Time: 0:00:15 ( 9.48 ms/it)
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Minimizing 1634    Time: 0:00:15 ( 9.48 ms/it)
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Minimizing 1645    Time: 0:00:15 ( 9.48 ms/it)
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Minimizing 1656    Time: 0:00:15 ( 9.48 ms/it)
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Minimizing 1678    Time: 0:00:15 ( 9.48 ms/it)
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Minimizing 1689    Time: 0:00:16 ( 9.48 ms/it)
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Minimizing 1712    Time: 0:00:16 ( 9.48 ms/it)
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Minimizing 1734    Time: 0:00:16 ( 9.48 ms/it)
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Minimizing 1767    Time: 0:00:16 ( 9.49 ms/it)
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Minimizing 1789    Time: 0:00:16 ( 9.49 ms/it)
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Minimizing 1800    Time: 0:00:17 ( 9.48 ms/it)
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Minimizing 1811    Time: 0:00:17 ( 9.48 ms/it)
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Minimizing 1822    Time: 0:00:17 ( 9.48 ms/it)
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Minimizing 1855    Time: 0:00:17 ( 9.48 ms/it)
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Minimizing 1866    Time: 0:00:17 ( 9.48 ms/it)
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Minimizing 1877    Time: 0:00:17 ( 9.48 ms/it)
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Minimizing 1888    Time: 0:00:17 ( 9.48 ms/it)
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Minimizing 1899    Time: 0:00:17 ( 9.48 ms/it)
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Minimizing 1910    Time: 0:00:18 ( 9.48 ms/it)
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Minimizing 1921    Time: 0:00:18 ( 9.48 ms/it)
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Minimizing 1932    Time: 0:00:18 ( 9.48 ms/it)
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Minimizing 1943    Time: 0:00:18 ( 9.47 ms/it)
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Minimizing 1954    Time: 0:00:18 ( 9.48 ms/it)
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Minimizing 1965    Time: 0:00:18 ( 9.48 ms/it)
   objective: 13609.658851767868


Minimizing 1976    Time: 0:00:18 ( 9.48 ms/it)
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Minimizing 1987    Time: 0:00:18 ( 9.48 ms/it)
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Minimizing 1998    Time: 0:00:18 ( 9.48 ms/it)
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Minimizing 2009    Time: 0:00:19 ( 9.48 ms/it)
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Minimizing 2020    Time: 0:00:19 ( 9.48 ms/it)
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Minimizing 1524    Time: 0:00:14 ( 9.52 ms/it)
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Minimizing 1634    Time: 0:00:15 ( 9.50 ms/it)
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Minimizing 1645    Time: 0:00:15 ( 9.50 ms/it)
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Minimizing 1656    Time: 0:00:15 ( 9.50 ms/it)
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Minimizing 1689    Time: 0:00:16 ( 9.50 ms/it)
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Minimizing 1755    Time: 0:00:16 ( 9.49 ms/it)
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Minimizing 1843    Time: 0:00:17 ( 9.49 ms/it)
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Minimizing 1854    Time: 0:00:17 ( 9.49 ms/it)
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Minimizing 1865    Time: 0:00:17 ( 9.49 ms/it)
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Minimizing 1876    Time: 0:00:17 ( 9.49 ms/it)
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Minimizing 1886    Time: 0:00:17 ( 9.50 ms/it)
   objective: 13518.663502011215


Minimizing 1897    Time: 0:00:18 ( 9.50 ms/it)
   objective: 13514.120031016093


Minimizing 1908    Time: 0:00:18 ( 9.50 ms/it)
   objective: 13512.915429735396


Minimizing 1919    Time: 0:00:18 ( 9.50 ms/it)
   objective: 13512.674592357987


Minimizing 1930    Time: 0:00:18 ( 9.50 ms/it)
   objective: 13510.639924956908


Minimizing 1941    Time: 0:00:18 ( 9.50 ms/it)
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Minimizing 1952    Time: 0:00:18 ( 9.50 ms/it)
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Minimizing 1963    Time: 0:00:18 ( 9.49 ms/it)
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Minimizing 1974    Time: 0:00:18 ( 9.49 ms/it)
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Minimizing 1985    Time: 0:00:18 ( 9.49 ms/it)
   objective: 13503.821503813539


Minimizing 2045    Time: 0:00:19 ( 9.57 ms/it)
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Minimizing 704    Time: 0:00:06 ( 9.42 ms/it)
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Minimizing 737    Time: 0:00:06 ( 9.41 ms/it)
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Minimizing 759    Time: 0:00:07 ( 9.43 ms/it)
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   objective: 13638.058481927044


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   objective: 13637.796987733993


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   objective: 13635.685779809835


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   objective: 13633.347303756134


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   objective: 13632.702064456491


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   objective: 13627.281480270372


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   objective: 13613.747051119586


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   objective: 13591.265000421241


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   objective: 13586.230627047531


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   objective: 13584.610001137931


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   objective: 13579.082783567414


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   objective: 13578.476462061968


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   objective: 13576.54688872263


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   objective: 13567.668063536497


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   objective: 13566.545547342212


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   objective: 13566.139043061201


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   objective: 13564.197434434325


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   objective: 13560.337870931064


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   objective: 13557.796564425284


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   objective: 13549.841716035065


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   objective: 13548.997911166065


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   objective: 13548.177892406093


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   objective: 13545.26628431787


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   objective: 13543.115718455243


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   objective: 13542.580301190857


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   objective: 13540.47894128345


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   objective: 13530.070929235066


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   objective: 13526.808248378642


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   objective: 13526.085374604518


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   objective: 13523.2881579167


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   objective: 13522.384821100262


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   objective: 13518.677444321278


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   objective: 13514.10705380667


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   objective: 13511.550966512048


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   objective: 13436.046194367358


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   objective: 13436.044431755028


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   objective: 13436.045080855285


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	Est.	SE	z	p	σ_Child
(Intercept)	-0.0201	0.0142	-1.41	0.1578	0.7704
Test: c5.1	-0.0349	0.0426	-0.82	0.4118	1.1136
Test: c234.15	0.0063	0.1669	0.04	0.9697	0.7795
Test: c2.34	-0.0011	0.0769	-0.01	0.9882	1.3053
Test: c3.4	-0.0009	0.0448	-0.02	0.9833	1.2942
a1	0.3534	0.0486	7.27	<1e-12
Sex: Boys	0.1916	0.0142	13.46	<1e-40
Test: c5.1 & a1	0.4738	0.1430	3.31	0.0009
Test: c234.15 & a1	-0.2440	0.5658	-0.43	0.6663
Test: c2.34 & a1	0.4090	0.2682	1.52	0.1273
Test: c3.4 & a1	0.2684	0.1537	1.75	0.0808
Test: c5.1 & Sex: Boys	0.1384	0.0426	3.25	0.0012
Test: c234.15 & Sex: Boys	-0.7903	0.1669	-4.74	<1e-05
Test: c2.34 & Sex: Boys	-0.0223	0.0769	-0.29	0.7720
Test: c3.4 & Sex: Boys	-0.0832	0.0448	-1.86	0.0631
a1 & Sex: Boys	-0.0694	0.0486	-1.43	0.1535
Test: c5.1 & a1 & Sex: Boys	0.1003	0.1430	0.70	0.4831
Test: c234.15 & a1 & Sex: Boys	-1.2668	0.5658	-2.24	0.0252
Test: c2.34 & a1 & Sex: Boys	0.1666	0.2682	0.62	0.5345
Test: c3.4 & a1 & Sex: Boys	0.0048	0.1537	0.03	0.9749
Residual	0.0000

VarCorr(m_Child_SDC)

	Column	Variance	Std.Dev	Corr.
Child	(Intercept)	0.50089248	0.70773758
	Test: Star_r	0.59880213	0.77382306	+0.03
	Test: S20_r	1.31453563	1.14653200	-0.18	-0.77
	Test: SLJ	0.98819620	0.99408058	+0.07	+0.97	-0.78
	Test: BPT	1.57363692	1.25444686	-0.22	-0.36	-0.17	-0.22
Residual		0.00000000	0.00003541

VarCorr(m_Child_HeC)

	Column	Variance	Std.Dev	Corr.
Child	(Intercept)	0.35824173	0.59853298
	Test: Star_r	0.11547245	0.33981238	-0.22
	Test: S20_r	0.16587384	0.40727613	-0.33	-0.77
	Test: SLJ	0.04819977	0.21954445	-0.06	+0.72	-0.35
	Test: BPT	0.05465325	0.23378035	-0.35	+0.03	+0.13	-0.20
Residual		0.00000000	0.00006373

VarCorr(m_Child_HyC)

	Column	Variance	Std.Dev	Corr.
Child	(Intercept)	0.46499053	0.68190214
	Test: BPT-other	1.37712944	1.17351159	+0.88
	Test: Star-End	1.09761146	1.04766954	-0.15	+0.32
	Test: S20-Star	2.12748747	1.45859092	-0.04	-0.34	-0.80
	Test: SLJ-S20	1.91189494	1.38271289	-0.02	+0.11	+0.46	-0.57
Residual		0.00000000	0.00000692

VarCorr(m_Child_PCA)

	Column	Variance	Std.Dev	Corr.
Child	(Intercept)	0.59345437	0.77035990
	Test: c5.1	1.24016299	1.11362605	-0.11
	Test: c234.15	0.60757415	0.77947043	+0.24	-0.47
	Test: c2.34	1.70391375	1.30534047	+0.26	-0.11	+0.85
	Test: c3.4	1.67495660	1.29420114	-0.14	-0.11	-0.72	-0.69
Residual		0.00000000	0.00001476

The CPs for the various contrasts are in line with expectations. For the SDC we observe substantial negative CPs between neighboring contrasts. For the orthogonal HeC, all CPs are small; they are uncorrelated. HyC contains some of the SDC contrasts and we observe again the negative CPs. The (roughly) PCA-based contrasts are small with one exception; there is a sizeable CP of +.41 between GM and the core of adjusted physical fitness (c234.15).

Do these differences in CPs imply that we can move to zcpLMMs when we have orthogonal contrasts? We pursue this question with by refitting the four LMMs with zerocorr() and compare the goodness of fit.

begin
  f_Child0 = @formula zScore ~
    1 + Test * a1 * Sex + zerocorr(1 + Test | Child)
  m_Child_SDC0 = fit(MixedModel, f_Child0, dat; contrasts=contr1)
  m_Child_HeC0 = fit(MixedModel, f_Child0, dat; contrasts=contr2)
  m_Child_HyC0 = fit(MixedModel, f_Child0, dat; contrasts=contr3)
  m_Child_PCA0 = fit(MixedModel, f_Child0, dat; contrasts=contr4)
end

Minimizing 16    Time: 0:00:00 ( 6.48 ms/it)
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Minimizing 53    Time: 0:00:00 ( 5.85 ms/it)
   objective: 13769.531339865413


Minimizing 70    Time: 0:00:00 ( 5.87 ms/it)
   objective: 13764.040309345592


Minimizing 87    Time: 0:00:00 ( 5.88 ms/it)
   objective: 13716.41984484435


Minimizing 105    Time: 0:00:00 ( 5.88 ms/it)
   objective: 13709.92845558625


Minimizing 121    Time: 0:00:00 ( 6.18 ms/it)
   objective: 13707.081794535596


Minimizing 133    Time: 0:00:00 ( 6.42 ms/it)
   objective: 13706.478661960537


Minimizing 146    Time: 0:00:00 ( 6.53 ms/it)
   objective: 13705.317922182232


Minimizing 163    Time: 0:00:01 ( 6.50 ms/it)
   objective: 13701.965462211927


Minimizing 180    Time: 0:00:01 ( 6.45 ms/it)
   objective: 13699.568573596553


Minimizing 197    Time: 0:00:01 ( 6.53 ms/it)
   objective: 13698.84532012331


Minimizing 211    Time: 0:00:01 ( 6.57 ms/it)
   objective: 13689.723699316404


Minimizing 225    Time: 0:00:01 ( 6.66 ms/it)
   objective: 13681.91337829551


Minimizing 240    Time: 0:00:01 ( 6.68 ms/it)
   objective: 13660.455031529993


Minimizing 253    Time: 0:00:01 ( 6.75 ms/it)
   objective: 13652.870999844781


Minimizing 269    Time: 0:00:01 ( 6.73 ms/it)
   objective: 13630.880003717859


Minimizing 286    Time: 0:00:01 ( 6.69 ms/it)
   objective: 13620.095897442581


Minimizing 303    Time: 0:00:02 ( 6.66 ms/it)
   objective: 13568.949687499437


Minimizing 320    Time: 0:00:02 ( 6.71 ms/it)
   objective: 13561.623032311923


Minimizing 335    Time: 0:00:02 ( 6.73 ms/it)
   objective: 13560.746961866476


Minimizing 351    Time: 0:00:02 ( 6.74 ms/it)
   objective: 13560.442894829466


Minimizing 368    Time: 0:00:02 ( 6.72 ms/it)
   objective: 13558.771275972918


Minimizing 385    Time: 0:00:02 ( 6.69 ms/it)
   objective: 13549.46599115293


Minimizing 400    Time: 0:00:02 ( 6.75 ms/it)
   objective: 13546.963239475052


Minimizing 412    Time: 0:00:02 ( 6.81 ms/it)
   objective: 13540.53775233333


Minimizing 427    Time: 0:00:02 ( 6.81 ms/it)
   objective: 13539.451463509351


Minimizing 442    Time: 0:00:03 ( 6.88 ms/it)
   objective: 13538.94404207157


Minimizing 456    Time: 0:00:03 ( 6.90 ms/it)
   objective: 13538.533393575824


Minimizing 472    Time: 0:00:03 ( 6.89 ms/it)
   objective: 13537.714700873563


Minimizing 488    Time: 0:00:03 ( 6.88 ms/it)
   objective: 13535.79186120721


Minimizing 504    Time: 0:00:03 ( 6.87 ms/it)
   objective: 13533.53519242545


Minimizing 520    Time: 0:00:03 ( 6.86 ms/it)
   objective: 13531.045598248966


Minimizing 537    Time: 0:00:03 ( 6.83 ms/it)
   objective: 13502.643477476144


Minimizing 554    Time: 0:00:03 ( 6.81 ms/it)
   objective: 13490.036496344139


Minimizing 571    Time: 0:00:03 ( 6.78 ms/it)
   objective: 13456.849734484073


Minimizing 588    Time: 0:00:03 ( 6.80 ms/it)
   objective: 13446.23853680784


Minimizing 604    Time: 0:00:04 ( 6.79 ms/it)
   objective: 13436.442966024115


Minimizing 620    Time: 0:00:04 ( 6.78 ms/it)
   objective: 13433.565879008718


Minimizing 637    Time: 0:00:04 ( 6.76 ms/it)
   objective: 13429.560679404924


Minimizing 654    Time: 0:00:04 ( 6.74 ms/it)
   objective: 13426.16476715682


Minimizing 670    Time: 0:00:04 ( 6.74 ms/it)
   objective: 13425.95463605941


Minimizing 687    Time: 0:00:04 ( 6.72 ms/it)
   objective: 13425.971274855983


Minimizing 704    Time: 0:00:04 ( 6.70 ms/it)
   objective: 13425.934639823448


Minimizing 721    Time: 0:00:04 ( 6.69 ms/it)
   objective: 13425.947318870196


Minimizing 738    Time: 0:00:04 ( 6.67 ms/it)
   objective: 13425.938420972321


Minimizing 754    Time: 0:00:05 ( 6.67 ms/it)
   objective: 13425.947303135865


Minimizing 765    Time: 0:00:05 ( 6.67 ms/it)

	Est.	SE	z	p	σ_Child
(Intercept)	-0.0201	0.0142	-1.41	0.1573	0.7194
Test: c5.1	-0.0340	0.0432	-0.79	0.4310	1.2273
Test: c234.15	0.0287	0.1683	0.17	0.8644	0.0905
Test: c2.34	-0.0151	0.0777	-0.19	0.8462	2.0300
Test: c3.4	-0.0090	0.0449	-0.20	0.8419	1.1606
a1	0.3533	0.0484	7.30	<1e-12
Sex: Boys	0.1917	0.0142	13.51	<1e-40
Test: c5.1 & a1	0.4551	0.1451	3.14	0.0017
Test: c234.15 & a1	-0.3260	0.5711	-0.57	0.5682
Test: c2.34 & a1	0.3401	0.2693	1.26	0.2066
Test: c3.4 & a1	0.2475	0.1539	1.61	0.1079
Test: c5.1 & Sex: Boys	0.1344	0.0432	3.11	0.0018
Test: c234.15 & Sex: Boys	-0.8046	0.1683	-4.78	<1e-05
Test: c2.34 & Sex: Boys	-0.0393	0.0777	-0.51	0.6126
Test: c3.4 & Sex: Boys	-0.0850	0.0449	-1.89	0.0585
a1 & Sex: Boys	-0.0687	0.0484	-1.42	0.1559
Test: c5.1 & a1 & Sex: Boys	0.1135	0.1451	0.78	0.4340
Test: c234.15 & a1 & Sex: Boys	-1.1448	0.5711	-2.00	0.0450
Test: c2.34 & a1 & Sex: Boys	0.1482	0.2693	0.55	0.5820
Test: c3.4 & a1 & Sex: Boys	-0.0236	0.1539	-0.15	0.8779
Residual	0.0000

MixedModels.likelihoodratiotest(m_Child_SDC0, m_Child_SDC)

	model-dof	deviance	χ²	χ²-dof	P(>χ²)
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + zerocorr(1 + Test \| Child)	26	13849
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test \| Child)	36	13458	391	10	<1e-77

MixedModels.likelihoodratiotest(m_Child_HeC0, m_Child_HeC)

	model-dof	deviance	χ²	χ²-dof	P(>χ²)
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + zerocorr(1 + Test \| Child)	26	13377
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test \| Child)	36	13482	-105	10	NaN

MixedModels.likelihoodratiotest(m_Child_HyC0, m_Child_HyC)

	model-dof	deviance	χ²	χ²-dof	P(>χ²)
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + zerocorr(1 + Test \| Child)	26	13427
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test \| Child)	36	13428	-1	10	NaN

MixedModels.likelihoodratiotest(m_Child_PCA0, m_Child_PCA)

	model-dof	deviance	χ²	χ²-dof	P(>χ²)
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + zerocorr(1 + Test \| Child)	26	13426
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test \| Child)	36	13436	-10	10	NaN

Obviously, we can not drop CPs from any of the LMMs. The full LMMs all have the same objective, but we can compare the goodness-of-fit statistics of zcpLMMs more directly.

begin
  zcpLMM = ["SDC0", "HeC0", "HyC0", "PCA0"]
  mods = [m_Child_SDC0, m_Child_HeC0, m_Child_HyC0, m_Child_PCA0]
  gof_summary = sort!(
    DataFrame(;
      zcpLMM=zcpLMM,
      dof=dof.(mods),
      deviance=deviance.(mods),
      AIC=aic.(mods),
      BIC=bic.(mods),
    ),
    :deviance,
  )
end

4×5 DataFrame

Row	zcpLMM	dof	deviance	AIC	BIC
	String	Int64	Float64	Float64	Float64
1	HeC0	26	13377.2	13429.2	13598.6
2	PCA0	26	13425.9	13477.9	13647.4
3	HyC0	26	13426.7	13478.7	13648.1
4	SDC0	26	13849.3	13901.3	14070.8

The best fit was obtained for the PCA-based zcpLMM. Somewhat surprisingly the second best fit was obtained for the SDC. The relatively poor performance of HeC-based zcpLMM is puzzling to me. I thought it might be related to imbalance in design in the present data, but this does not appear to be the case. The same comparison of SequentialDifferenceCoding and Helmert Coding also showed a worse fit for the zcp-HeC LMM than the zcp-SDC LMM.

3.3 VCs and CPs depend on random factor

VCs and CPs resulting from a set of test contrasts can also be estimated for the random factor School. Of course, these VCs and CPs may look different from the ones we just estimated for Child.

The effect of age (i.e., developmental gain) varies within School. Therefore, we also include its VCs and CPs in this model; the school-related VC for Sex was not significant.

f_School = @formula zScore ~
  1 + Test * a1 * Sex + (1 + Test + a1 | School);
m_School_SeqDiff = fit(MixedModel, f_School, dat; contrasts=contr1);
m_School_Helmert = fit(MixedModel, f_School, dat; contrasts=contr2);
m_School_Hypo = fit(MixedModel, f_School, dat; contrasts=contr3);
m_School_PCA = fit(MixedModel, f_School, dat; contrasts=contr4);

Minimizing 104    Time: 0:00:00 ( 0.97 ms/it)
   objective: 13819.74723597413


Minimizing 209    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.654519624797


Minimizing 316    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.50544165633


Minimizing 423    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13808.471596497504


Minimizing 530    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13808.455500856595


Minimizing 637    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13808.44362399357


Minimizing 743    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.441285905257


Minimizing 845    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.439668419018


Minimizing 952    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.439130467106


Minimizing 1058    Time: 0:00:01 ( 0.96 ms/it)
   objective: 13808.43892086393


Minimizing 1122    Time: 0:00:01 ( 0.96 ms/it)

Minimizing 104    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13854.442415144315


Minimizing 211    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13813.829874747807


Minimizing 318    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13809.355775758644


Minimizing 425    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13808.767393799635


Minimizing 532    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13808.635572898338


Minimizing 639    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13808.56609927732


Minimizing 746    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.559386160661


Minimizing 842    Time: 0:00:00 ( 0.97 ms/it)
   objective: 13808.550907909086


Minimizing 943    Time: 0:00:00 ( 0.98 ms/it)
   objective: 13808.54890535289


Minimizing 1045    Time: 0:00:01 ( 0.98 ms/it)
   objective: 13808.548594183534


Minimizing 1130    Time: 0:00:01 ( 0.98 ms/it)

Minimizing 103    Time: 0:00:00 ( 0.97 ms/it)
   objective: 13820.6544025035


Minimizing 205    Time: 0:00:00 ( 1.00 ms/it)
   objective: 13811.170608157483


Minimizing 311    Time: 0:00:00 ( 0.98 ms/it)
   objective: 13808.760164856307


Minimizing 418    Time: 0:00:00 ( 0.97 ms/it)
   objective: 13808.49018673968


Minimizing 525    Time: 0:00:00 ( 0.97 ms/it)
   objective: 13808.468434189059


Minimizing 632    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.462713406785


Minimizing 739    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.451949499191


Minimizing 846    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13808.442352036687


Minimizing 953    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13808.44089083063


Minimizing 1060    Time: 0:00:01 ( 0.95 ms/it)
   objective: 13808.440539158832


Minimizing 1167    Time: 0:00:01 ( 0.95 ms/it)
   objective: 13808.440256970303


Minimizing 1273    Time: 0:00:01 ( 0.96 ms/it)
   objective: 13808.439738257059


Minimizing 1376    Time: 0:00:01 ( 0.96 ms/it)
   objective: 13808.43925808307


Minimizing 1479    Time: 0:00:01 ( 0.97 ms/it)
   objective: 13808.439024656294


Minimizing 1585    Time: 0:00:01 ( 0.97 ms/it)
   objective: 13808.438937334235


Minimizing 1618    Time: 0:00:01 ( 0.97 ms/it)

Minimizing 104    Time: 0:00:00 ( 0.97 ms/it)
   objective: 13818.33191108724


Minimizing 211    Time: 0:00:00 ( 0.96 ms/it)
   objective: 13809.74426939401


Minimizing 318    Time: 0:00:00 ( 0.95 ms/it)
   objective: 13808.894883475572


Minimizing 425    Time: 0:00:00 ( 0.97 ms/it)
   objective: 13808.61618574267


Minimizing 522    Time: 0:00:00 ( 0.99 ms/it)
   objective: 13808.533863677725


Minimizing 617    Time: 0:00:00 ( 1.03 ms/it)
   objective: 13808.507211853701


Minimizing 723    Time: 0:00:00 ( 1.01 ms/it)
   objective: 13808.48541380144


Minimizing 830    Time: 0:00:00 ( 1.01 ms/it)
   objective: 13808.461219849352


Minimizing 937    Time: 0:00:00 ( 1.00 ms/it)
   objective: 13808.45429144295


Minimizing 1044    Time: 0:00:01 ( 0.99 ms/it)
   objective: 13808.446731110056


Minimizing 1151    Time: 0:00:01 ( 0.99 ms/it)
   objective: 13808.442550856755


Minimizing 1258    Time: 0:00:01 ( 0.98 ms/it)
   objective: 13808.440923616721


Minimizing 1365    Time: 0:00:01 ( 0.98 ms/it)
   objective: 13808.440146620134


Minimizing 1469    Time: 0:00:01 ( 0.98 ms/it)
   objective: 13808.439616706793


Minimizing 1568    Time: 0:00:01 ( 1.00 ms/it)
   objective: 13808.439387802759


Minimizing 1670    Time: 0:00:01 ( 1.00 ms/it)
   objective: 13808.439190609708


Minimizing 1777    Time: 0:00:01 ( 1.00 ms/it)
   objective: 13808.439014804027


Minimizing 1874    Time: 0:00:01 ( 0.99 ms/it)

VarCorr(m_School_SeqDiff)

	Column	Variance	Std.Dev	Corr.
School	(Intercept)	0.035376	0.188084
	Test: Star_r	0.108135	0.328840	-0.07
	Test: S20_r	0.149026	0.386039	+0.02	-0.73
	Test: SLJ	0.125389	0.354102	-0.09	+0.11	-0.61
	Test: BPT	0.077581	0.278533	-0.63	-0.50	+0.38	-0.32
	a1	0.069828	0.264250	+0.46	-0.41	+0.30	-0.10	-0.24
Residual		0.853736	0.923978

VarCorr(m_School_Helmert)

	Column	Variance	Std.Dev	Corr.
School	(Intercept)	0.0352304	0.1876977
	Test: Star_r	0.0271345	0.1647255	-0.08
	Test: S20_r	0.0093444	0.0966664	-0.02	-0.40
	Test: SLJ	0.0037451	0.0611972	-0.14	-0.15	-0.30
	Test: BPT	0.0032415	0.0569338	-0.71	-0.58	+0.02	+0.36
	a1	0.0675144	0.2598354	+0.49	-0.35	+0.21	-0.02	-0.18
Residual		0.8540123	0.9241279

VarCorr(m_School_Hypo)

	Column	Variance	Std.Dev	Corr.
School	(Intercept)	0.035374	0.188079
	Test: BPT-other	1.302376	1.141217	-0.70
	Test: Star-End	0.108175	0.328900	-0.07	-0.58
	Test: S20-Star	0.148956	0.385949	+0.02	+0.27	-0.72
	Test: SLJ-S20	0.125359	0.354060	-0.09	+0.23	+0.11	-0.61
	a1	0.069798	0.264193	+0.46	-0.24	-0.41	+0.30	-0.10
Residual		0.853756	0.923989

VarCorr(m_School_PCA)

	Column	Variance	Std.Dev	Corr.
School	(Intercept)	0.035375	0.188083
	Test: c5.1	0.061618	0.248230	-0.89
	Test: c234.15	1.871660	1.368086	+0.36	-0.53
	Test: c2.34	0.386611	0.621780	+0.02	-0.33	+0.48
	Test: c3.4	0.125340	0.354034	+0.09	-0.26	+0.15	-0.19
	a1	0.069784	0.264166	+0.46	-0.48	-0.04	-0.32	+0.10
Residual		0.853740	0.923981

We compare again how much of the fit resides in the CPs.

begin
  f_School0 = @formula zScore ~
    1 + Test * a1 * Sex + zerocorr(1 + Test + a1 | School)
  m_School_SDC0 = fit(MixedModel, f_School0, dat; contrasts=contr1)
  m_School_HeC0 = fit(MixedModel, f_School0, dat; contrasts=contr2)
  m_School_HyC0 = fit(MixedModel, f_School0, dat; contrasts=contr3)
  m_School_PCA0 = fit(MixedModel, f_School0, dat; contrasts=contr4)
  #
  zcpLMM2 = ["SDC0", "HeC0", "HyC0", "PCA0"]
  mods2 = [
    m_School_SDC0, m_School_HeC0, m_School_HyC0, m_School_PCA0
  ]
  gof_summary2 = sort!(
    DataFrame(;
      zcpLMM=zcpLMM2,
      dof=dof.(mods2),
      deviance=deviance.(mods2),
      AIC=aic.(mods2),
      BIC=bic.(mods2),
    ),
    :deviance,
  )
end

Minimizing 149    Time: 0:00:00 ( 0.69 ms/it)
   objective: 13836.37228205819


Minimizing 212    Time: 0:00:00 ( 0.79 ms/it)

Minimizing 152    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13828.173896540273


Minimizing 289    Time: 0:00:00 ( 0.66 ms/it)

4×5 DataFrame

Row	zcpLMM	dof	deviance	AIC	BIC
	String	Int64	Float64	Float64	Float64
1	PCA0	27	13828.0	13882.0	14058.0
2	HeC0	27	13829.9	13883.9	14059.9
3	SDC0	27	13836.1	13890.1	14066.1
4	HyC0	27	13836.4	13890.4	14066.3

For the random factor School the Helmert contrast, followed by PCA-based contrasts have least information in the CPs; SDC has the largest contribution from CPs. Interesting.

4 That’s it

That’s it for this tutorial. It is time to try your own contrast coding. You can use these data; there are many alternatives to set up hypotheses for the five tests. Of course and even better, code up some contrasts for data of your own.

Have fun!

Fühner, T., Granacher, U., Golle, K., & Kliegl, R. (2021). Age and sex effects in physical fitness components of 108,295 third graders including 515 primary schools and 9 cohorts. Scientific Reports, 11(1). https://doi.org/10.1038/s41598-021-97000-4

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