Mixed Models Tutorial: Contrast Coding

Author

Reinhold Kliegl

Published

2025-08-26

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:

  1. Setup with reading and examining the data

  2. Contrasts coding

  1. Other topics

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 SMLP2025: dataset
using Statistics
using StatsBase

ProgressMeter.ijulia_behavior(:clear);

1.2 Readme for dataset("fggk21")

Number of scores: 525126

  1. Cohort: 9 levels; 2011-2019

  2. School: 515 levels

  3. Child: 108295 levels; all children are between 8.0 and 8.99 years old

  4. Sex: “Girls” (n=55,086), “Boys” (n= 53,209)

  5. age: testdate - middle of month of birthdate

  6. 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]

  7. 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 2016 S102167 C047186 8.47091 4.65116
2 S20_r Boys 2017 S100924 C025395 8.27926 4.7619
3 S20_r Boys 2014 S101990 C017054 8.20808 4.54545
4 S20_r Boys 2013 S102489 C021285 8.24641 4.87805
5 S20_r Boys 2017 S103690 C097368 8.90349 4.65116
6 S20_r Boys 2016 S102167 C047186 8.47091 4.65116
7 S20_r Boys 2013 S105594 C006815 8.0794 4.44444
8 S20_r Boys 2019 S111314 C085678 8.80219 4.08163
9 S20_r Boys 2013 S102489 C087119 8.82683 4.65116
10 S20_r Boys 2017 S104905 C080869 8.75291 4.16667
11 S20_r Boys 2014 S101291 C004636 8.03833 5.55556
12 S20_r Boys 2018 S104474 C053165 8.52567 4.54545
13 S20_r Boys 2012 S105983 C050944 8.50103 4.44444
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
4989 Run Girls 2014 S112458 C064456 8.61875 920.0
4990 Run Girls 2015 S111089 C049983 8.49829 909.0
4991 Run Girls 2016 S111764 C046178 8.4627 1051.0
4992 Run Girls 2016 S103494 C097436 8.90623 999.0
4993 Run Girls 2012 S100961 C013694 8.16701 1071.0
4994 Run Girls 2014 S113074 C026568 8.29021 729.0
4995 Run Girls 2019 S101035 C037332 8.38877 918.0
4996 Run Girls 2012 S100640 C079267 8.75017 990.0
4997 Run Girls 2017 S106616 C067636 8.64613 882.0
4998 Run Girls 2017 S111405 C085679 8.80219 1035.0
4999 Run Girls 2019 S104220 C085136 8.80219 1026.0
5000 Run Girls 2018 S103883 C081842 8.76934 981.0

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 2016 S102167 C047186 8.47091 4.65116 -0.0290897 0.264145
2 S20_r Boys 2017 S100924 C025395 8.27926 4.7619 -0.220739 0.523304
3 S20_r Boys 2014 S101990 C017054 8.20808 4.54545 -0.291923 0.016766
4 S20_r Boys 2013 S102489 C021285 8.24641 4.87805 -0.253593 0.795105
5 S20_r Boys 2017 S103690 C097368 8.90349 4.65116 0.403491 0.264145
6 S20_r Boys 2016 S102167 C047186 8.47091 4.65116 -0.0290897 0.264145
7 S20_r Boys 2013 S105594 C006815 8.0794 4.44444 -0.420602 -0.219618
8 S20_r Boys 2019 S111314 C085678 8.80219 4.08163 0.30219 -1.06867
9 S20_r Boys 2013 S102489 C087119 8.82683 4.65116 0.326831 0.264145
10 S20_r Boys 2017 S104905 C080869 8.75291 4.16667 0.252909 -0.869675
11 S20_r Boys 2014 S101291 C004636 8.03833 5.55556 -0.46167 2.38061
12 S20_r Boys 2018 S104474 C053165 8.52567 4.54545 0.0256674 0.016766
13 S20_r Boys 2012 S105983 C050944 8.50103 4.44444 0.00102669 -0.219618
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
4989 Run Girls 2014 S112458 C064456 8.61875 920.0 0.118754 -0.562856
4990 Run Girls 2015 S111089 C049983 8.49829 909.0 -0.00171116 -0.635974
4991 Run Girls 2016 S111764 C046178 8.4627 1051.0 -0.0373032 0.307914
4992 Run Girls 2016 S103494 C097436 8.90623 999.0 0.406229 -0.0377356
4993 Run Girls 2012 S100961 C013694 8.16701 1071.0 -0.332991 0.440855
4994 Run Girls 2014 S113074 C026568 8.29021 729.0 -0.209788 -1.83245
4995 Run Girls 2019 S101035 C037332 8.38877 918.0 -0.111225 -0.57615
4996 Run Girls 2012 S100640 C079267 8.75017 990.0 0.250171 -0.0975595
4997 Run Girls 2017 S106616 C067636 8.64613 882.0 0.146133 -0.815446
4998 Run Girls 2017 S111405 C085679 8.80219 1035.0 0.30219 0.20156
4999 Run Girls 2019 S104220 C085136 8.80219 1026.0 0.30219 0.141736
5000 Run Girls 2018 S103883 C081842 8.76934 981.0 0.269336 -0.157383 
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 4.59109 0.437769 0.123553 1.02447
2 BPT Boys 3.9446 0.749636 0.317866 1.02005
3 SLJ Boys 129.174 20.157 0.173194 1.06241
4 Star_r Boys 2.07515 0.293585 0.0967507 1.03158
5 Run Boys 1039.42 155.181 0.230927 1.03151
6 S20_r Girls 4.48549 0.410282 -0.123553 0.960144
7 BPT Girls 3.4774 0.640257 -0.317866 0.871216
8 SLJ Girls 122.602 17.1092 -0.173194 0.901768
9 Star_r Girls 2.02008 0.272839 -0.0967507 0.958688
10 Run Girls 969.936 137.152 -0.230927 0.911663

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) -0.0026 0.0142 -0.18 0.8571 0.7289
Test: Star_r -0.0097 0.0441 -0.22 0.8258
Test: S20_r -0.0034 0.0441 -0.08 0.9392
Test: SLJ -0.0062 0.0442 -0.14 0.8892
Test: BPT 0.0105 0.0444 0.24 0.8135
Residual 0.6822

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) -0.0169 0.0145 -1.16 0.2461 0.7272
Test: Star_r -0.0160 0.0449 -0.36 0.7215
Test: S20_r -0.0055 0.0448 -0.12 0.9019
Test: SLJ 0.0060 0.0452 0.13 0.8950
Test: BPT -0.0116 0.0456 -0.26 0.7987
a1 0.2412 0.0495 4.87 <1e-05
Test: Star_r & a1 0.1214 0.1534 0.79 0.4288
Test: S20_r & a1 0.0632 0.1546 0.41 0.6826
Test: SLJ & a1 -0.2619 0.1530 -1.71 0.0869
Test: BPT & a1 0.3509 0.1548 2.27 0.0234
Residual 0.6796

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) -0.0163 0.0142 -1.15 0.2513 0.6905
Test: Star_r -0.0137 0.0441 -0.31 0.7562
Test: S20_r -0.0049 0.0439 -0.11 0.9120
Test: SLJ 0.0046 0.0444 0.10 0.9174
Test: BPT -0.0119 0.0447 -0.27 0.7896
a1 0.2423 0.0485 4.99 <1e-06
Sex: Boys 0.1851 0.0139 13.31 <1e-39
Test: Star_r & a1 0.1240 0.1505 0.82 0.4100
Test: S20_r & a1 0.0466 0.1517 0.31 0.7588
Test: SLJ & a1 -0.2317 0.1502 -1.54 0.1227
Test: BPT & a1 0.3286 0.1518 2.17 0.0303
Test: Star_r & Sex: Boys -0.1226 0.0432 -2.84 0.0045
Test: S20_r & Sex: Boys 0.0224 0.0432 0.52 0.6047
Test: SLJ & Sex: Boys 0.0430 0.0433 0.99 0.3206
Test: BPT & Sex: Boys 0.1454 0.0434 3.35 0.0008
Residual 0.6881

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) -0.0162 0.0142 -1.14 0.2536 0.6912
Test: Star_r -0.0141 0.0441 -0.32 0.7492
Test: S20_r -0.0041 0.0439 -0.09 0.9250
Test: SLJ 0.0043 0.0444 0.10 0.9235
Test: BPT -0.0112 0.0447 -0.25 0.8026
a1 0.2417 0.0485 4.98 <1e-06
Sex: Boys 0.1892 0.0142 13.30 <1e-39
Test: Star_r & a1 0.1267 0.1506 0.84 0.4002
Test: S20_r & a1 0.0439 0.1517 0.29 0.7723
Test: SLJ & a1 -0.2330 0.1501 -1.55 0.1207
Test: BPT & a1 0.3210 0.1518 2.11 0.0345
Test: Star_r & Sex: Boys -0.1201 0.0441 -2.72 0.0064
Test: S20_r & Sex: Boys 0.0192 0.0439 0.44 0.6622
Test: SLJ & Sex: Boys 0.0410 0.0444 0.93 0.3548
Test: BPT & Sex: Boys 0.1540 0.0447 3.44 0.0006
a1 & Sex: Boys -0.0689 0.0485 -1.42 0.1559
Test: Star_r & a1 & Sex: Boys -0.0479 0.1506 -0.32 0.7503
Test: S20_r & a1 & Sex: Boys 0.0533 0.1517 0.35 0.7251
Test: SLJ & a1 & Sex: Boys 0.0387 0.1501 0.26 0.7968
Test: BPT & a1 & Sex: Boys -0.1330 0.1518 -0.88 0.3810
Residual 0.6870

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) -0.0162 0.0142 -1.14 0.2536 0.6912
Test: Star_r -0.0070 0.0220 -0.32 0.7492
Test: S20_r -0.0037 0.0127 -0.29 0.7688
Test: SLJ -0.0008 0.0091 -0.09 0.9301
Test: BPT -0.0027 0.0070 -0.39 0.6993
a1 0.2417 0.0485 4.98 <1e-06
Sex: Boys 0.1892 0.0142 13.30 <1e-39
Test: Star_r & a1 0.0634 0.0753 0.84 0.4002
Test: S20_r & a1 0.0358 0.0433 0.83 0.4090
Test: SLJ & a1 -0.0404 0.0307 -1.31 0.1890
Test: BPT & a1 0.0400 0.0241 1.66 0.0972
Test: Star_r & Sex: Boys -0.0600 0.0220 -2.72 0.0064
Test: S20_r & Sex: Boys -0.0136 0.0127 -1.07 0.2830
Test: SLJ & Sex: Boys 0.0035 0.0091 0.38 0.7043
Test: BPT & Sex: Boys 0.0329 0.0070 4.68 <1e-05
a1 & Sex: Boys -0.0689 0.0485 -1.42 0.1559
Test: Star_r & a1 & Sex: Boys -0.0240 0.0753 -0.32 0.7503
Test: S20_r & a1 & Sex: Boys 0.0098 0.0433 0.23 0.8211
Test: SLJ & a1 & Sex: Boys 0.0146 0.0307 0.47 0.6357
Test: BPT & a1 & Sex: Boys -0.0179 0.0241 -0.74 0.4586
Residual 0.6870

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) -0.0162 0.0142 -1.14 0.2536 0.6912
Test: BPT-other -0.0543 0.1405 -0.39 0.6993
Test: Star-End -0.0141 0.0441 -0.32 0.7492
Test: S20-Star -0.0041 0.0439 -0.09 0.9250
Test: SLJ-S20 0.0043 0.0444 0.10 0.9235
a1 0.2417 0.0485 4.98 <1e-06
Sex: Boys 0.1892 0.0142 13.30 <1e-39
Test: BPT-other & a1 0.7997 0.4821 1.66 0.0972
Test: Star-End & a1 0.1267 0.1506 0.84 0.4002
Test: S20-Star & a1 0.0439 0.1517 0.29 0.7723
Test: SLJ-S20 & a1 -0.2330 0.1501 -1.55 0.1207
Test: BPT-other & Sex: Boys 0.6573 0.1405 4.68 <1e-05
Test: Star-End & Sex: Boys -0.1201 0.0441 -2.72 0.0064
Test: S20-Star & Sex: Boys 0.0192 0.0439 0.44 0.6622
Test: SLJ-S20 & Sex: Boys 0.0410 0.0444 0.93 0.3548
a1 & Sex: Boys -0.0689 0.0485 -1.42 0.1559
Test: BPT-other & a1 & Sex: Boys -0.3574 0.4821 -0.74 0.4586
Test: Star-End & a1 & Sex: Boys -0.0479 0.1506 -0.32 0.7503
Test: S20-Star & a1 & Sex: Boys 0.0533 0.1517 0.35 0.7251
Test: SLJ-S20 & a1 & Sex: Boys 0.0387 0.1501 0.26 0.7968
Residual 0.6870

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) -0.0162 0.0142 -1.14 0.2536 0.6912
Test: Star-Run -0.0141 0.0441 -0.32 0.7492
Test: S20-Star -0.0041 0.0439 -0.09 0.9250
Test: SLJ-S20 0.0043 0.0444 0.10 0.9235
Test: BPT-SLJ -0.0112 0.0447 -0.25 0.8026
a1 0.2417 0.0485 4.98 <1e-06
Sex: Boys 0.1892 0.0142 13.30 <1e-39
Test: Star-Run & a1 0.1267 0.1506 0.84 0.4002
Test: S20-Star & a1 0.0439 0.1517 0.29 0.7723
Test: SLJ-S20 & a1 -0.2330 0.1501 -1.55 0.1207
Test: BPT-SLJ & a1 0.3210 0.1518 2.11 0.0345
Test: Star-Run & Sex: Boys -0.1201 0.0441 -2.72 0.0064
Test: S20-Star & Sex: Boys 0.0192 0.0439 0.44 0.6622
Test: SLJ-S20 & Sex: Boys 0.0410 0.0444 0.93 0.3548
Test: BPT-SLJ & Sex: Boys 0.1540 0.0447 3.44 0.0006
a1 & Sex: Boys -0.0689 0.0485 -1.42 0.1559
Test: Star-Run & a1 & Sex: Boys -0.0479 0.1506 -0.32 0.7503
Test: S20-Star & a1 & Sex: Boys 0.0533 0.1517 0.35 0.7251
Test: SLJ-S20 & a1 & Sex: Boys 0.0387 0.1501 0.26 0.7968
Test: BPT-SLJ & a1 & Sex: Boys -0.1330 0.1518 -0.88 0.3810
Residual 0.6870 
m_zcp_SeqD = let
  form = @formula(
    zScore ~ 1 + Test * a1 * Sex + zerocorr(1 + Test | Child)
  )
  fit(MixedModel, form, dat; contrasts=contr1b)
end
Minimizing 23    Time: 0:00:00 ( 4.39 ms/it)
   objective: 13889.62766345656


Minimizing 77    Time: 0:00:00 ( 6.11 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0162 0.0142 -1.14 0.2560 0.7060
Test: Star-Run -0.0114 0.0448 -0.25 0.7992 0.0000
Test: S20-Star -0.0034 0.0439 -0.08 0.9379 0.6060
Test: SLJ-S20 0.0032 0.0437 0.07 0.9421 0.3615
Test: BPT-SLJ -0.0081 0.0444 -0.18 0.8543 0.0000
a1 0.2403 0.0486 4.95 <1e-06
Sex: Boys 0.1886 0.0142 13.24 <1e-39
Test: Star-Run & a1 0.1236 0.1527 0.81 0.4182
Test: S20-Star & a1 0.0419 0.1516 0.28 0.7821
Test: SLJ-S20 & a1 -0.2448 0.1480 -1.65 0.0980
Test: BPT-SLJ & a1 0.3383 0.1507 2.24 0.0248
Test: Star-Run & Sex: Boys -0.1203 0.0448 -2.69 0.0072
Test: S20-Star & Sex: Boys 0.0199 0.0439 0.45 0.6498
Test: SLJ-S20 & Sex: Boys 0.0366 0.0437 0.84 0.4025
Test: BPT-SLJ & Sex: Boys 0.1615 0.0444 3.64 0.0003
a1 & Sex: Boys -0.0684 0.0486 -1.41 0.1588
Test: Star-Run & a1 & Sex: Boys -0.0333 0.1527 -0.22 0.8271
Test: S20-Star & a1 & Sex: Boys 0.0434 0.1516 0.29 0.7748
Test: SLJ-S20 & a1 & Sex: Boys 0.0397 0.1480 0.27 0.7883
Test: BPT-SLJ & a1 & Sex: Boys -0.1328 0.1507 -0.88 0.3784
Residual 0.5766 
m_zcp_SeqD_2 = let
  form = @formula(
    zScore ~ 1 + Test * a1 * Sex + (0 + Test | Child)
  )
  fit(MixedModel, form, dat; contrasts=contr1b)
end
Minimizing 16    Time: 0:00:00 ( 6.57 ms/it)
   objective: 14116.7458155308


Minimizing 31    Time: 0:00:00 ( 6.75 ms/it)
   objective: 14043.569355400463


Minimizing 47    Time: 0:00:00 ( 6.65 ms/it)
   objective: 13897.985845578722


Minimizing 63    Time: 0:00:00 ( 6.58 ms/it)
   objective: 13896.481841170676


Minimizing 79    Time: 0:00:00 ( 6.55 ms/it)
   objective: 13882.812238625022


Minimizing 95    Time: 0:00:00 ( 6.54 ms/it)
   objective: 13868.308491060769


Minimizing 110    Time: 0:00:00 ( 6.56 ms/it)
   objective: 13856.216831043


Minimizing 126    Time: 0:00:00 ( 6.57 ms/it)
   objective: 13853.164941178708


Minimizing 142    Time: 0:00:00 ( 6.56 ms/it)
   objective: 13845.805102268929


Minimizing 158    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13842.734309127845


Minimizing 174    Time: 0:00:01 ( 6.55 ms/it)
   objective: 13840.78520713637


Minimizing 190    Time: 0:00:01 ( 6.54 ms/it)
   objective: 13833.756866776312


Minimizing 206    Time: 0:00:01 ( 6.54 ms/it)
   objective: 13830.393563631662


Minimizing 222    Time: 0:00:01 ( 6.53 ms/it)
   objective: 13824.631679614678


Minimizing 238    Time: 0:00:01 ( 6.53 ms/it)
   objective: 13824.374358046545


Minimizing 254    Time: 0:00:01 ( 6.52 ms/it)
   objective: 13803.549656542724


Minimizing 270    Time: 0:00:01 ( 6.53 ms/it)
   objective: 13800.802611547102


Minimizing 286    Time: 0:00:01 ( 6.52 ms/it)
   objective: 13794.944369246734


Minimizing 302    Time: 0:00:01 ( 6.52 ms/it)
   objective: 13792.860063467142


Minimizing 318    Time: 0:00:02 ( 6.52 ms/it)
   objective: 13784.567109477575


Minimizing 334    Time: 0:00:02 ( 6.52 ms/it)
   objective: 13782.799721872954


Minimizing 350    Time: 0:00:02 ( 6.52 ms/it)
   objective: 13779.282258733732


Minimizing 366    Time: 0:00:02 ( 6.51 ms/it)
   objective: 13774.461964005783


Minimizing 382    Time: 0:00:02 ( 6.51 ms/it)
   objective: 13766.630330463335


Minimizing 398    Time: 0:00:02 ( 6.51 ms/it)
   objective: 13733.841139876651


Minimizing 414    Time: 0:00:02 ( 6.51 ms/it)
   objective: 13732.176800495701


Minimizing 430    Time: 0:00:02 ( 6.51 ms/it)
   objective: 13729.443597345973


Minimizing 446    Time: 0:00:02 ( 6.51 ms/it)
   objective: 13726.167717650198


Minimizing 462    Time: 0:00:03 ( 6.51 ms/it)
   objective: 13725.572325593534


Minimizing 478    Time: 0:00:03 ( 6.51 ms/it)
   objective: 13723.039152587826


Minimizing 494    Time: 0:00:03 ( 6.50 ms/it)
   objective: 13717.62162695016


Minimizing 510    Time: 0:00:03 ( 6.50 ms/it)
   objective: 13715.13931078877


Minimizing 526    Time: 0:00:03 ( 6.50 ms/it)
   objective: 13708.356585166872


Minimizing 542    Time: 0:00:03 ( 6.50 ms/it)
   objective: 13694.777981583458


Minimizing 558    Time: 0:00:03 ( 6.50 ms/it)
   objective: 13688.898790546085


Minimizing 573    Time: 0:00:03 ( 6.51 ms/it)
   objective: 13686.27758494842


Minimizing 589    Time: 0:00:03 ( 6.51 ms/it)
   objective: 13671.759287288322


Minimizing 605    Time: 0:00:03 ( 6.51 ms/it)
   objective: 13670.902792755442


Minimizing 621    Time: 0:00:04 ( 6.51 ms/it)
   objective: 13667.158331750812


Minimizing 637    Time: 0:00:04 ( 6.51 ms/it)
   objective: 13662.111361597363


Minimizing 653    Time: 0:00:04 ( 6.52 ms/it)
   objective: 13655.246433408836


Minimizing 669    Time: 0:00:04 ( 6.52 ms/it)
   objective: 13651.992156501707


Minimizing 685    Time: 0:00:04 ( 6.52 ms/it)
   objective: 13650.824462368728


Minimizing 701    Time: 0:00:04 ( 6.52 ms/it)
   objective: 13649.337580207946


Minimizing 717    Time: 0:00:04 ( 6.52 ms/it)
   objective: 13645.429653450476


Minimizing 732    Time: 0:00:04 ( 6.53 ms/it)
   objective: 13644.26818294856


Minimizing 748    Time: 0:00:04 ( 6.53 ms/it)
   objective: 13640.656918863446


Minimizing 769    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13639.146401866983


Minimizing 788    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13637.331693134052


Minimizing 804    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13633.956623446313


Minimizing 820    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13632.770588340609


Minimizing 836    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13632.205565148375


Minimizing 852    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13631.395243059138


Minimizing 868    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13629.291149339646


Minimizing 883    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13627.831599851117


Minimizing 899    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13625.846441077636


Minimizing 915    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13623.65302309161


Minimizing 931    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13623.557383161635


Minimizing 947    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13623.128384565869


Minimizing 963    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13622.321646787073


Minimizing 979    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13621.446418589141


Minimizing 995    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13619.425421758984


Minimizing 1011    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13617.366468968408


Minimizing 1027    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13616.361757619794


Minimizing 1043    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13614.54435188615


Minimizing 1059    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13611.491312014645


Minimizing 1075    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13611.454899744662


Minimizing 1091    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13610.815000298353


Minimizing 1107    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13609.788679011974


Minimizing 1123    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13607.72547836155


Minimizing 1139    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13604.620599544658


Minimizing 1155    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13602.128261322148


Minimizing 1171    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13600.145199825369


Minimizing 1186    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13599.339180499475


Minimizing 1202    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13597.959887792931


Minimizing 1218    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13597.280336155396


Minimizing 1234    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13596.836067950171


Minimizing 1250    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13596.57584214241


Minimizing 1266    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13595.826742186611


Minimizing 1282    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13595.092662790135


Minimizing 1298    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13593.205706188579


Minimizing 1314    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13592.342104882642


Minimizing 1330    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13592.262658093801


Minimizing 1346    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13591.481923871761


Minimizing 1362    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13590.728573037079


Minimizing 1378    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13589.066498728658


Minimizing 1394    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13588.520916595051


Minimizing 1410    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13585.409962250327


Minimizing 1426    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13583.894293240824


Minimizing 1442    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13582.752579221851


Minimizing 1458    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13581.99428739374


Minimizing 1474    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13581.050691408542


Minimizing 1490    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13577.336753640833


Minimizing 1506    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13577.158769046342


Minimizing 1522    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13576.30914446916


Minimizing 1538    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13576.248450316816


Minimizing 1554    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13575.667328779084


Minimizing 1570    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13575.1759693489


Minimizing 1586    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13574.634208781652


Minimizing 1602    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13572.941147576676


Minimizing 1618    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13571.876764805085


Minimizing 1634    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13566.904621937414


Minimizing 1650    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13562.557152398942


Minimizing 1666    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13561.424874334807


Minimizing 1682    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13533.651123838717


Minimizing 1698    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13528.486343916593


Minimizing 1714    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13521.5810509699


Minimizing 1730    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13519.714221460476


Minimizing 1746    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13517.047659189317


Minimizing 1762    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13513.007551764342


Minimizing 1778    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13512.81519755673


Minimizing 1794    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13511.117690996376


Minimizing 1810    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13505.702163634174


Minimizing 1826    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13505.380756840917


Minimizing 1840    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13503.603087654286


Minimizing 1856    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13501.64557361661


Minimizing 1872    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13499.091589214382


Minimizing 1888    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13494.68194983583


Minimizing 1904    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13494.028764813214


Minimizing 1920    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13491.269542913076


Minimizing 1936    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13487.570000518368


Minimizing 1952    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13479.393422361609


Minimizing 1968    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13475.648788625724


Minimizing 1984    Time: 0:00:13 ( 6.56 ms/it)
   objective: 13461.774190196826


Minimizing 2000    Time: 0:00:13 ( 6.56 ms/it)
   objective: 13460.74713055863


Minimizing 2016    Time: 0:00:13 ( 6.56 ms/it)
   objective: 13456.737822589814


Minimizing 2032    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13449.57002423724


Minimizing 2048    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13445.031321208153


Minimizing 2064    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13443.241556666297


Minimizing 2080    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13442.841953732684


Minimizing 2096    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13437.616756564195


Minimizing 2112    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13435.019418140713


Minimizing 2128    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13428.703393974778


Minimizing 2144    Time: 0:00:14 ( 6.55 ms/it)
   objective: 13427.236979761597


Minimizing 2253    Time: 0:00:14 ( 6.58 ms/it)
   objective: 13416.48875174929


Minimizing 2270    Time: 0:00:14 ( 6.58 ms/it)
   objective: 13408.810170067023


Minimizing 2286    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13405.353775735843


Minimizing 2302    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13403.203502413438


Minimizing 2318    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13399.000942895567


Minimizing 2334    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13387.15078549822


Minimizing 2350    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13381.432201972188


Minimizing 2366    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13328.769017269355


Minimizing 2382    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13328.614475366747


Minimizing 2398    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13327.582665438822


Minimizing 2414    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13327.432628917959


Minimizing 2430    Time: 0:00:15 ( 6.58 ms/it)
   objective: 13326.873067959968


Minimizing 2446    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13326.27469647622


Minimizing 2462    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13324.871800201916


Minimizing 2478    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13322.746376758703


Minimizing 2494    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13320.532960982877


Minimizing 2510    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13318.50475643776


Minimizing 2526    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13316.27353457264


Minimizing 2542    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13311.699393556133


Minimizing 2558    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13306.449809150232


Minimizing 2574    Time: 0:00:16 ( 6.57 ms/it)
   objective: 13297.432766306418


Minimizing 2590    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13295.653546536923


Minimizing 2606    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13271.351724831533


Minimizing 2622    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13269.757582574879


Minimizing 2638    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13262.405027134111


Minimizing 2654    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13259.131146436208


Minimizing 2670    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13259.073385331212


Minimizing 2686    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13259.063320648871


Minimizing 2702    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13259.064910840258


Minimizing 2718    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13259.063735522563


Minimizing 2734    Time: 0:00:17 ( 6.57 ms/it)
   objective: 13259.067624088944


Minimizing 2750    Time: 0:00:18 ( 6.57 ms/it)
   objective: 13259.0633818551


Minimizing 2766    Time: 0:00:18 ( 6.57 ms/it)
   objective: 13259.062721782131


Minimizing 2782    Time: 0:00:18 ( 6.57 ms/it)
   objective: 13259.063989790113


Minimizing 2798    Time: 0:00:18 ( 6.57 ms/it)
   objective: 13259.065344853661


Minimizing 2814    Time: 0:00:18 ( 6.57 ms/it)
   objective: 13259.070479251415


Minimizing 2830    Time: 0:00:18 ( 6.56 ms/it)
   objective: 13259.06471473648


Minimizing 2846    Time: 0:00:18 ( 6.56 ms/it)
   objective: 13259.066100848504


Minimizing 2862    Time: 0:00:18 ( 6.56 ms/it)
   objective: 13259.059627010356


Minimizing 2862    Time: 0:00:18 ( 6.56 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0166 0.0142 -1.16 0.2440
Test: Star-Run -0.0178 0.0438 -0.41 0.6840
Test: S20-Star -0.0018 0.0443 -0.04 0.9677
Test: SLJ-S20 0.0094 0.0444 0.21 0.8314
Test: BPT-SLJ -0.0146 0.0442 -0.33 0.7407
a1 0.2416 0.0486 4.97 <1e-06
Sex: Boys 0.1877 0.0142 13.17 <1e-38
Test: Star-Run & a1 0.1455 0.1482 0.98 0.3264
Test: S20-Star & a1 0.0347 0.1526 0.23 0.8202
Test: SLJ-S20 & a1 -0.2474 0.1500 -1.65 0.0991
Test: BPT-SLJ & a1 0.3326 0.1501 2.22 0.0267
Test: Star-Run & Sex: Boys -0.1169 0.0438 -2.67 0.0075
Test: S20-Star & Sex: Boys 0.0227 0.0443 0.51 0.6091
Test: SLJ-S20 & Sex: Boys 0.0353 0.0444 0.80 0.4264
Test: BPT-SLJ & Sex: Boys 0.1562 0.0442 3.53 0.0004
a1 & Sex: Boys -0.0680 0.0486 -1.40 0.1619
Test: Star-Run & a1 & Sex: Boys -0.0115 0.1482 -0.08 0.9383
Test: S20-Star & a1 & Sex: Boys 0.0382 0.1526 0.25 0.8023
Test: SLJ-S20 & a1 & Sex: Boys 0.0557 0.1500 0.37 0.7103
Test: BPT-SLJ & a1 & Sex: Boys -0.1464 0.1501 -0.98 0.3293
Test: Run 0.9715
Test: Star_r 0.9918
Test: S20_r 0.9813
Test: SLJ 0.9700
Test: BPT 0.9577
Residual 0.0000 
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 16    Time: 0:00:00 ( 6.61 ms/it)
   objective: 14116.7458155308


Minimizing 31    Time: 0:00:00 ( 6.81 ms/it)
   objective: 14043.569355400463


Minimizing 47    Time: 0:00:00 ( 6.70 ms/it)
   objective: 13897.985845578722


Minimizing 63    Time: 0:00:00 ( 6.66 ms/it)
   objective: 13896.481841170676


Minimizing 79    Time: 0:00:00 ( 6.64 ms/it)
   objective: 13882.812238625022


Minimizing 95    Time: 0:00:00 ( 6.64 ms/it)
   objective: 13868.308491060769


Minimizing 111    Time: 0:00:00 ( 6.62 ms/it)
   objective: 13856.739431610815


Minimizing 127    Time: 0:00:00 ( 6.61 ms/it)
   objective: 13852.14791273751


Minimizing 143    Time: 0:00:00 ( 6.59 ms/it)
   objective: 13845.805001157916


Minimizing 159    Time: 0:00:01 ( 6.58 ms/it)
   objective: 13843.819711733297


Minimizing 175    Time: 0:00:01 ( 6.58 ms/it)
   objective: 13840.23639331013


Minimizing 191    Time: 0:00:01 ( 6.57 ms/it)
   objective: 13833.776091198652


Minimizing 207    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13829.942665437417


Minimizing 223    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13823.258314387029


Minimizing 239    Time: 0:00:01 ( 6.57 ms/it)
   objective: 13809.709259858191


Minimizing 255    Time: 0:00:01 ( 6.57 ms/it)
   objective: 13803.486460168398


Minimizing 271    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13800.501183587226


Minimizing 287    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13794.161669625919


Minimizing 303    Time: 0:00:01 ( 6.57 ms/it)
   objective: 13792.695803370583


Minimizing 318    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13784.567109477575


Minimizing 334    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13782.799721872954


Minimizing 350    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13779.282258733732


Minimizing 366    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13774.461964005783


Minimizing 382    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13766.630330463335


Minimizing 397    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13734.120824573016


Minimizing 413    Time: 0:00:02 ( 6.58 ms/it)
   objective: 13732.540909137257


Minimizing 429    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13729.891077317476


Minimizing 445    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13726.054077916444


Minimizing 461    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13725.69165992094


Minimizing 477    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13723.285135524093


Minimizing 493    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13717.538031649518


Minimizing 509    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13715.41974771964


Minimizing 525    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13708.777984993056


Minimizing 541    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13695.18774206312


Minimizing 557    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13688.096130274076


Minimizing 573    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13686.27758494842


Minimizing 589    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13671.759287288322


Minimizing 605    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13670.902792755442


Minimizing 621    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13667.158331750812


Minimizing 637    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13662.111361597363


Minimizing 653    Time: 0:00:04 ( 6.55 ms/it)
   objective: 13655.246433408836


Minimizing 669    Time: 0:00:04 ( 6.55 ms/it)
   objective: 13651.992156501707


Minimizing 685    Time: 0:00:04 ( 6.55 ms/it)
   objective: 13650.824462368728


Minimizing 701    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13649.337580207946


Minimizing 717    Time: 0:00:04 ( 6.55 ms/it)
   objective: 13645.429653450476


Minimizing 733    Time: 0:00:04 ( 6.55 ms/it)
   objective: 13644.218099447608


Minimizing 749    Time: 0:00:04 ( 6.55 ms/it)
   objective: 13642.73723224604


Minimizing 765    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13639.855585064637


Minimizing 781    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13638.06992580252


Minimizing 797    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13636.05565790592


Minimizing 813    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13632.789797857557


Minimizing 829    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13632.441473355306


Minimizing 845    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13631.973018590244


Minimizing 861    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13630.147871125482


Minimizing 877    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13627.985394563271


Minimizing 893    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13626.817698358827


Minimizing 909    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13623.908041995572


Minimizing 925    Time: 0:00:06 ( 6.55 ms/it)
   objective: 13623.576579589579


Minimizing 941    Time: 0:00:06 ( 6.55 ms/it)
   objective: 13623.251415522245


Minimizing 957    Time: 0:00:06 ( 6.54 ms/it)
   objective: 13622.483244824056


Minimizing 973    Time: 0:00:06 ( 6.54 ms/it)
   objective: 13621.911113823553


Minimizing 989    Time: 0:00:06 ( 6.54 ms/it)
   objective: 13619.9917890844


Minimizing 1005    Time: 0:00:06 ( 6.54 ms/it)
   objective: 13617.831455519176


Minimizing 1019    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13617.226600902293


Minimizing 1033    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13616.135192219816


Minimizing 1048    Time: 0:00:06 ( 6.58 ms/it)
   objective: 13613.029884016432


Minimizing 1063    Time: 0:00:06 ( 6.58 ms/it)
   objective: 13611.487848660043


Minimizing 1078    Time: 0:00:07 ( 6.59 ms/it)
   objective: 13611.301462611576


Minimizing 1093    Time: 0:00:07 ( 6.59 ms/it)
   objective: 13610.616382970518


Minimizing 1108    Time: 0:00:07 ( 6.59 ms/it)
   objective: 13609.742442965187


Minimizing 1124    Time: 0:00:07 ( 6.59 ms/it)
   objective: 13607.510395411584


Minimizing 1139    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13604.620599544658


Minimizing 1154    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13601.136962719625


Minimizing 1170    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13600.155245215312


Minimizing 1186    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13599.339180499475


Minimizing 1202    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13597.959887792931


Minimizing 1218    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13597.280336155396


Minimizing 1234    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13596.836067950171


Minimizing 1250    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13596.57584214241


Minimizing 1266    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13595.826742186611


Minimizing 1282    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13595.092662790135


Minimizing 1297    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13593.529960579348


Minimizing 1312    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13592.341347366404


Minimizing 1327    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13592.322267765405


Minimizing 1343    Time: 0:00:08 ( 6.62 ms/it)
   objective: 13591.489080693798


Minimizing 1358    Time: 0:00:08 ( 6.62 ms/it)
   objective: 13591.177908094374


Minimizing 1373    Time: 0:00:09 ( 6.62 ms/it)
   objective: 13589.742067887477


Minimizing 1389    Time: 0:00:09 ( 6.62 ms/it)
   objective: 13588.747114832433


Minimizing 1404    Time: 0:00:09 ( 6.62 ms/it)
   objective: 13586.006535146647


Minimizing 1419    Time: 0:00:09 ( 6.62 ms/it)
   objective: 13585.241976574878


Minimizing 1435    Time: 0:00:09 ( 6.62 ms/it)
   objective: 13582.774103312804


Minimizing 1450    Time: 0:00:09 ( 6.62 ms/it)
   objective: 13582.717404402647


Minimizing 1466    Time: 0:00:09 ( 6.62 ms/it)
   objective: 13581.225921105928


Minimizing 1481    Time: 0:00:09 ( 6.62 ms/it)
   objective: 13580.584367774201


Minimizing 1497    Time: 0:00:09 ( 6.63 ms/it)
   objective: 13577.203572975632


Minimizing 1513    Time: 0:00:10 ( 6.63 ms/it)
   objective: 13577.108037032558


Minimizing 1529    Time: 0:00:10 ( 6.63 ms/it)
   objective: 13576.276350782464


Minimizing 1544    Time: 0:00:10 ( 6.63 ms/it)
   objective: 13576.055788906204


Minimizing 1560    Time: 0:00:10 ( 6.63 ms/it)
   objective: 13575.510289604194


Minimizing 1575    Time: 0:00:10 ( 6.63 ms/it)
   objective: 13575.115806777467


Minimizing 1590    Time: 0:00:10 ( 6.63 ms/it)
   objective: 13574.44756114253


Minimizing 1606    Time: 0:00:10 ( 6.63 ms/it)
   objective: 13572.640333194038


Minimizing 1622    Time: 0:00:10 ( 6.63 ms/it)
   objective: 13573.374209071364


Minimizing 1636    Time: 0:00:10 ( 6.64 ms/it)
   objective: 13566.902595545645


Minimizing 1651    Time: 0:00:10 ( 6.64 ms/it)
   objective: 13561.82202590839


Minimizing 1666    Time: 0:00:11 ( 6.64 ms/it)
   objective: 13561.424874334807


Minimizing 1681    Time: 0:00:11 ( 6.64 ms/it)
   objective: 13533.72066329715


Minimizing 1696    Time: 0:00:11 ( 6.64 ms/it)
   objective: 13529.066961550532


Minimizing 1712    Time: 0:00:11 ( 6.64 ms/it)
   objective: 13522.91028815502


Minimizing 1727    Time: 0:00:11 ( 6.65 ms/it)
   objective: 13519.847762429752


Minimizing 1742    Time: 0:00:11 ( 6.65 ms/it)
   objective: 13518.004932221476


Minimizing 1758    Time: 0:00:11 ( 6.65 ms/it)
   objective: 13513.467223801541


Minimizing 1774    Time: 0:00:11 ( 6.64 ms/it)
   objective: 13512.846434701729


Minimizing 1790    Time: 0:00:11 ( 6.64 ms/it)
   objective: 13511.513653346941


Minimizing 1806    Time: 0:00:11 ( 6.64 ms/it)
   objective: 13509.77847312126


Minimizing 1822    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13505.464042862768


Minimizing 1838    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13503.728345892312


Minimizing 1854    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13501.724356483268


Minimizing 1870    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13499.721431695434


Minimizing 1886    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13496.550838814415


Minimizing 1901    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13494.220257354653


Minimizing 1917    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13492.093138254066


Minimizing 1933    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13488.958466226533


Minimizing 1949    Time: 0:00:12 ( 6.64 ms/it)
   objective: 13484.151278498888


Minimizing 1965    Time: 0:00:13 ( 6.64 ms/it)
   objective: 13475.873834917104


Minimizing 1981    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13465.985289014316


Minimizing 1997    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13461.002051226395


Minimizing 2013    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13457.015232755919


Minimizing 2029    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13449.656337664186


Minimizing 2045    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13445.330997745856


Minimizing 2061    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13444.093304064954


Minimizing 2077    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13442.881951126808


Minimizing 2093    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13439.436207315273


Minimizing 2109    Time: 0:00:13 ( 6.63 ms/it)
   objective: 13435.14135538139


Minimizing 2125    Time: 0:00:14 ( 6.63 ms/it)
   objective: 13431.284997991082


Minimizing 2141    Time: 0:00:14 ( 6.63 ms/it)
   objective: 13427.253279189172


Minimizing 2157    Time: 0:00:14 ( 6.63 ms/it)
   objective: 13427.010955426187


Minimizing 2173    Time: 0:00:14 ( 6.63 ms/it)
   objective: 13425.262361348243


Minimizing 2189    Time: 0:00:14 ( 6.62 ms/it)
   objective: 13423.458183424518


Minimizing 2204    Time: 0:00:14 ( 6.63 ms/it)
   objective: 13421.99598929868


Minimizing 2220    Time: 0:00:14 ( 6.63 ms/it)
   objective: 13419.089999828357


Minimizing 2236    Time: 0:00:14 ( 6.62 ms/it)
   objective: 13418.19193420031


Minimizing 2252    Time: 0:00:14 ( 6.62 ms/it)
   objective: 13416.49023359461


Minimizing 2268    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13411.579898217009


Minimizing 2284    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13405.36989336941


Minimizing 2300    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13403.05101259578


Minimizing 2315    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13400.398572395192


Minimizing 2331    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13388.47299335552


Minimizing 2347    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13385.114705747284


Minimizing 2363    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13328.797077860669


Minimizing 2379    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13328.640406026345


Minimizing 2395    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13327.987391182221


Minimizing 2411    Time: 0:00:15 ( 6.62 ms/it)
   objective: 13327.450559661142


Minimizing 2427    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13326.961843263736


Minimizing 2443    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13326.41732778697


Minimizing 2459    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13325.327099828603


Minimizing 2475    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13323.211953392907


Minimizing 2491    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13321.275625986891


Minimizing 2506    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13318.593866926662


Minimizing 2522    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13317.07165441505


Minimizing 2538    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13313.057265986165


Minimizing 2554    Time: 0:00:16 ( 6.62 ms/it)
   objective: 13308.1774400781


Minimizing 2570    Time: 0:00:17 ( 6.62 ms/it)
   objective: 13303.239424415777


Minimizing 2586    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13295.31499296338


Minimizing 2602    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13272.542404332955


Minimizing 2618    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13270.437462930044


Minimizing 2634    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13265.643737527193


Minimizing 2650    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13259.282482709023


Minimizing 2666    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13259.074368702743


Minimizing 2682    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13259.06314561807


Minimizing 2698    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13259.066898249104


Minimizing 2714    Time: 0:00:17 ( 6.61 ms/it)
   objective: 13259.064529716052


Minimizing 2730    Time: 0:00:18 ( 6.61 ms/it)
   objective: 13259.061999110592


Minimizing 2746    Time: 0:00:18 ( 6.61 ms/it)
   objective: 13259.064573392825


Minimizing 2762    Time: 0:00:18 ( 6.61 ms/it)
   objective: 13259.063417673067


Minimizing 2778    Time: 0:00:18 ( 6.61 ms/it)
   objective: 13259.06657092835


Minimizing 2794    Time: 0:00:18 ( 6.61 ms/it)
   objective: 13259.067945979012


Minimizing 2810    Time: 0:00:18 ( 6.60 ms/it)
   objective: 13259.061208424479


Minimizing 2826    Time: 0:00:18 ( 6.60 ms/it)
   objective: 13259.062869325426


Minimizing 2845    Time: 0:00:18 ( 6.61 ms/it)
   objective: 13259.062977757843


Minimizing 2862    Time: 0:00:18 ( 6.61 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0166 0.0142 -1.16 0.2440
Test: Star-Run -0.0178 0.0438 -0.41 0.6840
Test: S20-Star -0.0018 0.0443 -0.04 0.9677
Test: SLJ-S20 0.0094 0.0444 0.21 0.8314
Test: BPT-SLJ -0.0146 0.0442 -0.33 0.7407
a1 0.2416 0.0486 4.97 <1e-06
Sex: Boys 0.1877 0.0142 13.17 <1e-38
Test: Star-Run & a1 0.1455 0.1482 0.98 0.3264
Test: S20-Star & a1 0.0347 0.1526 0.23 0.8202
Test: SLJ-S20 & a1 -0.2474 0.1500 -1.65 0.0991
Test: BPT-SLJ & a1 0.3326 0.1501 2.22 0.0267
Test: Star-Run & Sex: Boys -0.1169 0.0438 -2.67 0.0075
Test: S20-Star & Sex: Boys 0.0227 0.0443 0.51 0.6091
Test: SLJ-S20 & Sex: Boys 0.0353 0.0444 0.80 0.4264
Test: BPT-SLJ & Sex: Boys 0.1562 0.0442 3.53 0.0004
a1 & Sex: Boys -0.0680 0.0486 -1.40 0.1619
Test: Star-Run & a1 & Sex: Boys -0.0115 0.1482 -0.08 0.9383
Test: S20-Star & a1 & Sex: Boys 0.0382 0.1526 0.25 0.8023
Test: SLJ-S20 & a1 & Sex: Boys 0.0557 0.1500 0.37 0.7103
Test: BPT-SLJ & a1 & Sex: Boys -0.1464 0.1501 -0.98 0.3293
Test: Run 0.9715
Test: Star_r 0.9918
Test: S20_r 0.9813
Test: SLJ 0.9700
Test: BPT 0.9577
Residual 0.0000 
VarCorr(m_cpx_0_SeqDiff)
Column Variance Std.Dev Corr.
Child Test: Run 0.94379854 0.97149295
Test: Star_r 0.98370206 0.99181755 +0.81
Test: S20_r 0.96291617 0.98128292 +0.61 +0.39
Test: SLJ 0.94094326 0.97002230 +0.37 +0.74 +0.50
Test: BPT 0.91716658 0.95768814 +0.42 +0.46 +0.45 +0.52
Residual 0.00000000 0.00000908 
m_cpx_0_SeqDiff.PCA
(Child = 
Principal components based on correlation matrix
 Test: Run     1.0    .     .     .     .
 Test: Star_r  0.81  1.0    .     .     .
 Test: S20_r   0.61  0.39  1.0    .     .
 Test: SLJ     0.37  0.74  0.5   1.0    .
 Test: BPT     0.42  0.46  0.45  0.52  1.0

Normalized cumulative variances:
[0.6253, 0.7669, 0.9006, 1.0, 1.0]

Component loadings
                 PC1    PC2    PC3    PC4    PC5
 Test: Run     -0.47   0.62  -0.05   0.29   0.56
 Test: Star_r  -0.5    0.21   0.53   0.07  -0.65
 Test: S20_r   -0.42   0.1   -0.72  -0.47  -0.29
 Test: SLJ     -0.45  -0.45   0.36  -0.52   0.43
 Test: BPT     -0.4   -0.59  -0.26   0.65  -0.03,)
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 16    Time: 0:00:00 ( 6.61 ms/it)
   objective: 14024.558243037623


Minimizing 31    Time: 0:00:00 ( 6.83 ms/it)
   objective: 13915.948215417342


Minimizing 47    Time: 0:00:00 ( 6.71 ms/it)
   objective: 13877.257179521142


Minimizing 63    Time: 0:00:00 ( 6.65 ms/it)
   objective: 13871.931185514724


Minimizing 79    Time: 0:00:00 ( 6.61 ms/it)
   objective: 13862.953072247416


Minimizing 95    Time: 0:00:00 ( 6.59 ms/it)
   objective: 13854.173206469535


Minimizing 111    Time: 0:00:00 ( 6.57 ms/it)
   objective: 13837.320124087199


Minimizing 127    Time: 0:00:00 ( 6.57 ms/it)
   objective: 13832.20968233436


Minimizing 143    Time: 0:00:00 ( 6.58 ms/it)
   objective: 13828.556192927808


Minimizing 159    Time: 0:00:01 ( 6.57 ms/it)
   objective: 13825.852370922938


Minimizing 175    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13821.133564064898


Minimizing 191    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13806.509675586445


Minimizing 207    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13804.449442993577


Minimizing 223    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13801.294378115583


Minimizing 239    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13798.800869264378


Minimizing 255    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13797.000408904


Minimizing 271    Time: 0:00:01 ( 6.55 ms/it)
   objective: 13795.117164234882


Minimizing 286    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13793.827190945598


Minimizing 302    Time: 0:00:01 ( 6.56 ms/it)
   objective: 13791.584480999833


Minimizing 318    Time: 0:00:02 ( 6.56 ms/it)
   objective: 13790.963186636487


Minimizing 334    Time: 0:00:02 ( 6.56 ms/it)
   objective: 13789.106191070805


Minimizing 350    Time: 0:00:02 ( 6.55 ms/it)
   objective: 13782.670979638668


Minimizing 366    Time: 0:00:02 ( 6.55 ms/it)
   objective: 13781.107635353907


Minimizing 382    Time: 0:00:02 ( 6.55 ms/it)
   objective: 13772.583609056965


Minimizing 398    Time: 0:00:02 ( 6.55 ms/it)
   objective: 13769.265378517734


Minimizing 414    Time: 0:00:02 ( 6.55 ms/it)
   objective: 13764.254401589189


Minimizing 430    Time: 0:00:02 ( 6.54 ms/it)
   objective: 13755.88061577621


Minimizing 445    Time: 0:00:02 ( 6.55 ms/it)
   objective: 13749.076416979053


Minimizing 461    Time: 0:00:03 ( 6.55 ms/it)
   objective: 13736.084657340049


Minimizing 477    Time: 0:00:03 ( 6.55 ms/it)
   objective: 13735.605141907366


Minimizing 493    Time: 0:00:03 ( 6.55 ms/it)
   objective: 13722.182736292216


Minimizing 509    Time: 0:00:03 ( 6.54 ms/it)
   objective: 13720.947572350506


Minimizing 525    Time: 0:00:03 ( 6.54 ms/it)
   objective: 13714.73639764959


Minimizing 541    Time: 0:00:03 ( 6.54 ms/it)
   objective: 13717.178190534363


Minimizing 557    Time: 0:00:03 ( 6.54 ms/it)
   objective: 13705.803160449417


Minimizing 573    Time: 0:00:03 ( 6.54 ms/it)
   objective: 13703.956567800684


Minimizing 589    Time: 0:00:03 ( 6.54 ms/it)
   objective: 13702.93467410042


Minimizing 605    Time: 0:00:03 ( 6.54 ms/it)
   objective: 13701.704192425783


Minimizing 621    Time: 0:00:04 ( 6.54 ms/it)
   objective: 13699.966595706232


Minimizing 641    Time: 0:00:04 ( 6.57 ms/it)
   objective: 13698.975160195034


Minimizing 659    Time: 0:00:04 ( 6.57 ms/it)
   objective: 13696.141951849557


Minimizing 675    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13693.626994120477


Minimizing 691    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13691.871806827581


Minimizing 707    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13689.891530383447


Minimizing 723    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13688.363633724293


Minimizing 739    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13683.284570364904


Minimizing 754    Time: 0:00:04 ( 6.57 ms/it)
   objective: 13681.0705216053


Minimizing 770    Time: 0:00:05 ( 6.57 ms/it)
   objective: 13679.903126294186


Minimizing 786    Time: 0:00:05 ( 6.57 ms/it)
   objective: 13674.883291867322


Minimizing 802    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13658.92780179892


Minimizing 818    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13646.740233417935


Minimizing 834    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13640.362359749313


Minimizing 850    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13638.696415076156


Minimizing 866    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13635.913537689536


Minimizing 882    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13630.88690406843


Minimizing 898    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13628.20405232774


Minimizing 914    Time: 0:00:05 ( 6.56 ms/it)
   objective: 13625.471607423307


Minimizing 929    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13623.78156089138


Minimizing 945    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13617.622265423423


Minimizing 961    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13608.785884690282


Minimizing 977    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13585.444727583279


Minimizing 993    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13580.96408365394


Minimizing 1009    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13576.908081912807


Minimizing 1025    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13573.70683793092


Minimizing 1041    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13571.9296067127


Minimizing 1057    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13554.537683911629


Minimizing 1073    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13527.89676696773


Minimizing 1089    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13523.190939778164


Minimizing 1105    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13519.199551799808


Minimizing 1121    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13514.573237604513


Minimizing 1137    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13507.61177230761


Minimizing 1153    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13500.622588278668


Minimizing 1169    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13494.263849269017


Minimizing 1185    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13491.51116275655


Minimizing 1201    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13484.52712073455


Minimizing 1217    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13481.406017715897


Minimizing 1233    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13472.080776719587


Minimizing 1249    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13469.04207047115


Minimizing 1265    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13461.78672180543


Minimizing 1281    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13458.541483119465


Minimizing 1297    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13457.292832907297


Minimizing 1313    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13454.532378658274


Minimizing 1329    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13452.290678362624


Minimizing 1345    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13451.603026268727


Minimizing 1361    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13446.406356352963


Minimizing 1377    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13445.699387924047


Minimizing 1393    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13444.409082090264


Minimizing 1409    Time: 0:00:09 ( 6.55 ms/it)
   objective: 13442.72052518808


Minimizing 1425    Time: 0:00:09 ( 6.55 ms/it)
   objective: 13441.275311606893


Minimizing 1441    Time: 0:00:09 ( 6.55 ms/it)
   objective: 13440.234372241961


Minimizing 1457    Time: 0:00:09 ( 6.55 ms/it)
   objective: 13437.882868199682


Minimizing 1473    Time: 0:00:09 ( 6.55 ms/it)
   objective: 13426.905119774005


Minimizing 1489    Time: 0:00:09 ( 6.55 ms/it)
   objective: 13423.891296106478


Minimizing 1505    Time: 0:00:09 ( 6.55 ms/it)
   objective: 13421.41746812682


Minimizing 1521    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13417.092996040155


Minimizing 1537    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13411.049659963624


Minimizing 1553    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13404.569491855538


Minimizing 1569    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13399.322754648863


Minimizing 1585    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13391.571067453595


Minimizing 1601    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13382.899084861507


Minimizing 1617    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13379.595233508982


Minimizing 1633    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13376.60811478272


Minimizing 1649    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13357.407736054229


Minimizing 1665    Time: 0:00:10 ( 6.55 ms/it)
   objective: 13350.073609406958


Minimizing 1681    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13346.582271882202


Minimizing 1697    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13341.482862755438


Minimizing 1713    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13337.759640964316


Minimizing 1729    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13332.684771979097


Minimizing 1745    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13324.145290416054


Minimizing 1761    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13319.431042862314


Minimizing 1777    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13302.925678203188


Minimizing 1793    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13292.976061560985


Minimizing 1809    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13290.458857674937


Minimizing 1825    Time: 0:00:11 ( 6.55 ms/it)
   objective: 13288.367563831605


Minimizing 1841    Time: 0:00:12 ( 6.55 ms/it)
   objective: 13285.497953876285


Minimizing 1857    Time: 0:00:12 ( 6.55 ms/it)
   objective: 13282.558462812362


Minimizing 1873    Time: 0:00:12 ( 6.55 ms/it)
   objective: 13278.350148607133


Minimizing 1889    Time: 0:00:12 ( 6.55 ms/it)
   objective: 13278.189757136497


Minimizing 1905    Time: 0:00:12 ( 6.55 ms/it)
   objective: 13278.18815103991


Minimizing 1923    Time: 0:00:12 ( 6.55 ms/it)
   objective: 13278.180165141675


Minimizing 1941    Time: 0:00:12 ( 6.55 ms/it)
   objective: 13278.181746707065


Minimizing 1957    Time: 0:00:12 ( 6.55 ms/it)
   objective: 13278.18832114838


Minimizing 1972    Time: 0:00:12 ( 6.56 ms/it)
   objective: 13278.178930102978


Minimizing 1988    Time: 0:00:13 ( 6.56 ms/it)
   objective: 13278.179739609157


Minimizing 2004    Time: 0:00:13 ( 6.56 ms/it)
   objective: 13278.173073527054


Minimizing 2020    Time: 0:00:13 ( 6.56 ms/it)
   objective: 13278.183411821825


Minimizing 2036    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13278.184381466795


Minimizing 2052    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13278.174891056668


Minimizing 2068    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13278.17623105603


Minimizing 2084    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13278.18566650385


Minimizing 2100    Time: 0:00:13 ( 6.55 ms/it)
   objective: 13278.1731961459


Minimizing 2111    Time: 0:00:13 ( 6.55 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0158 0.0142 -1.11 0.2671 0.7264
Test: Star-Run -0.0092 0.0445 -0.21 0.8366 0.8468
Test: S20-Star -0.0032 0.0445 -0.07 0.9432 0.9514
Test: SLJ-S20 0.0164 0.0442 0.37 0.7099 0.7017
Test: BPT-SLJ -0.0216 0.0441 -0.49 0.6243 0.9598
a1 0.2411 0.0485 4.97 <1e-06
Sex: Boys 0.1873 0.0142 13.18 <1e-38
Test: Star-Run & a1 0.1139 0.1516 0.75 0.4524
Test: S20-Star & a1 0.0352 0.1535 0.23 0.8186
Test: SLJ-S20 & a1 -0.2592 0.1494 -1.73 0.0828
Test: BPT-SLJ & a1 0.3482 0.1495 2.33 0.0199
Test: Star-Run & Sex: Boys -0.1196 0.0445 -2.69 0.0072
Test: S20-Star & Sex: Boys 0.0161 0.0445 0.36 0.7183
Test: SLJ-S20 & Sex: Boys 0.0378 0.0442 0.86 0.3923
Test: BPT-SLJ & Sex: Boys 0.1598 0.0441 3.63 0.0003
a1 & Sex: Boys -0.0661 0.0485 -1.36 0.1730
Test: Star-Run & a1 & Sex: Boys -0.0569 0.1516 -0.38 0.7073
Test: S20-Star & a1 & Sex: Boys 0.0511 0.1535 0.33 0.7393
Test: SLJ-S20 & a1 & Sex: Boys 0.0794 0.1494 0.53 0.5950
Test: BPT-SLJ & a1 & Sex: Boys -0.1636 0.1495 -1.09 0.2739
Residual 0.0000 
m_cpx_1_SeqDiff.PCA
(Child = 
Principal components based on correlation matrix
 (Intercept)      1.0     .      .      .      .
 Test: Star-Run   0.43   1.0     .      .      .
 Test: S20-Star  -0.13  -0.11   1.0     .      .
 Test: SLJ-S20   -0.0    0.7   -0.62   1.0     .
 Test: BPT-SLJ   -0.13  -0.62  -0.02  -0.28   1.0

Normalized cumulative variances:
[0.466, 0.7189, 0.909, 0.9976, 1.0]

Component loadings
                   PC1    PC2    PC3    PC4    PC5
 (Intercept)     -0.26   0.35   0.85  -0.06   0.3
 Test: Star-Run  -0.59   0.27  -0.05   0.42  -0.63
 Test: S20-Star   0.32   0.67  -0.27   0.5    0.35
 Test: SLJ-S20   -0.55  -0.39  -0.2    0.36   0.61
 Test: BPT-SLJ    0.42  -0.44   0.41   0.66  -0.17,)

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 16    Time: 0:00:00 ( 6.61 ms/it)
   objective: 13915.240595604904


Minimizing 31    Time: 0:00:00 ( 6.81 ms/it)
   objective: 13901.2610708842


Minimizing 47    Time: 0:00:00 ( 6.71 ms/it)
   objective: 13882.779207309211


Minimizing 63    Time: 0:00:00 ( 6.66 ms/it)
   objective: 13875.48977801441


Minimizing 79    Time: 0:00:00 ( 6.63 ms/it)
   objective: 13861.603842398083


Minimizing 95    Time: 0:00:00 ( 6.62 ms/it)
   objective: 13854.685546419272


Minimizing 110    Time: 0:00:00 ( 6.63 ms/it)
   objective: 13843.242744506319


Minimizing 126    Time: 0:00:00 ( 6.62 ms/it)
   objective: 13833.145724604985


Minimizing 142    Time: 0:00:00 ( 6.61 ms/it)
   objective: 13826.513686837128


Minimizing 158    Time: 0:00:01 ( 6.60 ms/it)
   objective: 13816.211659851391


Minimizing 177    Time: 0:00:01 ( 6.67 ms/it)
   objective: 13809.633599860217


Minimizing 195    Time: 0:00:01 ( 6.66 ms/it)
   objective: 13797.269382974924


Minimizing 211    Time: 0:00:01 ( 6.65 ms/it)
   objective: 13791.132368769764


Minimizing 227    Time: 0:00:01 ( 6.64 ms/it)
   objective: 13788.557885637721


Minimizing 243    Time: 0:00:01 ( 6.63 ms/it)
   objective: 13786.761692447039


Minimizing 259    Time: 0:00:01 ( 6.63 ms/it)
   objective: 13784.002136966146


Minimizing 275    Time: 0:00:01 ( 6.62 ms/it)
   objective: 13781.959027316962


Minimizing 291    Time: 0:00:01 ( 6.62 ms/it)
   objective: 13780.093851313417


Minimizing 307    Time: 0:00:02 ( 6.61 ms/it)
   objective: 13774.72796710736


Minimizing 323    Time: 0:00:02 ( 6.61 ms/it)
   objective: 13770.479974038908


Minimizing 339    Time: 0:00:02 ( 6.60 ms/it)
   objective: 13769.628429450615


Minimizing 355    Time: 0:00:02 ( 6.60 ms/it)
   objective: 13766.711903591158


Minimizing 371    Time: 0:00:02 ( 6.60 ms/it)
   objective: 13763.02457501715


Minimizing 387    Time: 0:00:02 ( 6.59 ms/it)
   objective: 13759.437627234372


Minimizing 403    Time: 0:00:02 ( 6.59 ms/it)
   objective: 13758.08318601533


Minimizing 419    Time: 0:00:02 ( 6.60 ms/it)
   objective: 13752.601208800836


Minimizing 435    Time: 0:00:02 ( 6.59 ms/it)
   objective: 13750.874794292275


Minimizing 451    Time: 0:00:02 ( 6.59 ms/it)
   objective: 13739.822754271274


Minimizing 467    Time: 0:00:03 ( 6.58 ms/it)
   objective: 13738.142399479548


Minimizing 483    Time: 0:00:03 ( 6.58 ms/it)
   objective: 13729.258117087404


Minimizing 499    Time: 0:00:03 ( 6.58 ms/it)
   objective: 13724.346639791373


Minimizing 515    Time: 0:00:03 ( 6.58 ms/it)
   objective: 13718.415415252854


Minimizing 531    Time: 0:00:03 ( 6.58 ms/it)
   objective: 13698.80923404434


Minimizing 547    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13693.403875639277


Minimizing 563    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13684.857999341191


Minimizing 579    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13681.580526791058


Minimizing 595    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13675.900114955522


Minimizing 611    Time: 0:00:04 ( 6.57 ms/it)
   objective: 13672.443635316518


Minimizing 627    Time: 0:00:04 ( 6.57 ms/it)
   objective: 13658.664743721674


Minimizing 643    Time: 0:00:04 ( 6.57 ms/it)
   objective: 13655.59908292511


Minimizing 659    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13643.166975401567


Minimizing 675    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13635.78512604427


Minimizing 691    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13625.364116215671


Minimizing 705    Time: 0:00:04 ( 6.58 ms/it)
   objective: 13616.159211065737


Minimizing 720    Time: 0:00:04 ( 6.58 ms/it)
   objective: 13606.630383077209


Minimizing 736    Time: 0:00:04 ( 6.58 ms/it)
   objective: 13604.174554560901


Minimizing 751    Time: 0:00:04 ( 6.59 ms/it)
   objective: 13599.574566713876


Minimizing 766    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13594.663735536764


Minimizing 782    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13592.887280516581


Minimizing 798    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13590.452986119388


Minimizing 814    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13587.01977710041


Minimizing 830    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13569.100813444093


Minimizing 846    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13566.878086174802


Minimizing 862    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13562.13901796619


Minimizing 878    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13558.714449284467


Minimizing 894    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13550.770880820717


Minimizing 910    Time: 0:00:05 ( 6.59 ms/it)
   objective: 13537.97808556843


Minimizing 925    Time: 0:00:06 ( 6.59 ms/it)
   objective: 13496.25847766258


Minimizing 940    Time: 0:00:06 ( 6.60 ms/it)
   objective: 13494.973072353896


Minimizing 956    Time: 0:00:06 ( 6.60 ms/it)
   objective: 13491.023134189512


Minimizing 972    Time: 0:00:06 ( 6.60 ms/it)
   objective: 13489.525638457235


Minimizing 988    Time: 0:00:06 ( 6.60 ms/it)
   objective: 13483.180195156558


Minimizing 1004    Time: 0:00:06 ( 6.60 ms/it)
   objective: 13481.7025010352


Minimizing 1019    Time: 0:00:06 ( 6.60 ms/it)
   objective: 13476.153625433471


Minimizing 1035    Time: 0:00:06 ( 6.60 ms/it)
   objective: 13467.095454632748


Minimizing 1051    Time: 0:00:06 ( 6.60 ms/it)
   objective: 13454.551450449377


Minimizing 1067    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13448.659531897982


Minimizing 1081    Time: 0:00:07 ( 6.61 ms/it)
   objective: 13421.36416824552


Minimizing 1097    Time: 0:00:07 ( 6.61 ms/it)
   objective: 13380.78073546871


Minimizing 1113    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13368.883311132071


Minimizing 1129    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13363.191809952812


Minimizing 1145    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13356.926336915683


Minimizing 1161    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13352.435179886408


Minimizing 1177    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13345.273433542185


Minimizing 1193    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13338.980105523733


Minimizing 1209    Time: 0:00:07 ( 6.60 ms/it)
   objective: 13324.853474906355


Minimizing 1225    Time: 0:00:08 ( 6.60 ms/it)
   objective: 13292.148558424873


Minimizing 1241    Time: 0:00:08 ( 6.60 ms/it)
   objective: 13268.575188404488


Minimizing 1257    Time: 0:00:08 ( 6.60 ms/it)
   objective: 13267.280565280278


Minimizing 1276    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13266.988751589583


Minimizing 1294    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13266.970667752234


Minimizing 1310    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13266.975103265111


Minimizing 1325    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13266.962394788075


Minimizing 1341    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13266.977501428322


Minimizing 1357    Time: 0:00:08 ( 6.61 ms/it)
   objective: 13266.974156104552


Minimizing 1373    Time: 0:00:09 ( 6.61 ms/it)
   objective: 13266.969451325262


Minimizing 1389    Time: 0:00:09 ( 6.61 ms/it)
   objective: 13266.98424285547


Minimizing 1405    Time: 0:00:09 ( 6.61 ms/it)
   objective: 13266.963216553399


Minimizing 1421    Time: 0:00:09 ( 6.60 ms/it)
   objective: 13266.985979586621


Minimizing 1437    Time: 0:00:09 ( 6.60 ms/it)
   objective: 13267.002117841563


Minimizing 1453    Time: 0:00:09 ( 6.60 ms/it)
   objective: 13266.970917325772


Minimizing 1469    Time: 0:00:09 ( 6.60 ms/it)
   objective: 13266.963319169314


Minimizing 1485    Time: 0:00:09 ( 6.60 ms/it)
   objective: 13266.969422047812


Minimizing 1493    Time: 0:00:09 ( 6.60 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0167 0.0142 -1.18 0.2388 0.6317
Test: c5.1 -0.0222 0.0439 -0.51 0.6135 1.4354
Test: c234.15 -0.0110 0.1704 -0.06 0.9487 0.3056
Test: c2.34 0.0053 0.0775 0.07 0.9454 1.5786
Test: c3.4 -0.0033 0.0450 -0.07 0.9408 1.6105
a1 0.2486 0.0484 5.14 <1e-06
Sex: Boys 0.1882 0.0142 13.27 <1e-39
Test: c5.1 & a1 0.2475 0.1489 1.66 0.0965
Test: c234.15 & a1 -0.2309 0.5804 -0.40 0.6907
Test: c2.34 & a1 0.0994 0.2681 0.37 0.7110
Test: c3.4 & a1 0.2373 0.1522 1.56 0.1191
Test: c5.1 & Sex: Boys 0.0913 0.0439 2.08 0.0377
Test: c234.15 & Sex: Boys -0.8431 0.1704 -4.95 <1e-06
Test: c2.34 & Sex: Boys -0.0770 0.0775 -0.99 0.3201
Test: c3.4 & Sex: Boys -0.0410 0.0450 -0.91 0.3619
a1 & Sex: Boys -0.0644 0.0484 -1.33 0.1832
Test: c5.1 & a1 & Sex: Boys -0.0996 0.1489 -0.67 0.5035
Test: c234.15 & a1 & Sex: Boys 0.3286 0.5804 0.57 0.5713
Test: c2.34 & a1 & Sex: Boys -0.1146 0.2681 -0.43 0.6691
Test: c3.4 & a1 & Sex: Boys -0.0447 0.1522 -0.29 0.7691
Residual 0.0000 
VarCorr(m_cpx_1_PC)
Column Variance Std.Dev Corr.
Child (Intercept) 0.3990042 0.6316678
Test: c5.1 2.0602684 1.4353635 -0.08
Test: c234.15 0.0933852 0.3055900 -0.18 -0.84
Test: c2.34 2.4920554 1.5786245 +0.49 +0.42 -0.84
Test: c3.4 2.5937623 1.6105161 -0.02 -0.07 +0.01 -0.04
Residual 0.0000000 0.0000084 
m_cpx_1_PC.PCA
(Child = 
Principal components based on correlation matrix
 (Intercept)     1.0     .      .      .      .
 Test: c5.1     -0.08   1.0     .      .      .
 Test: c234.15  -0.18  -0.84   1.0     .      .
 Test: c2.34     0.49   0.42  -0.84   1.0     .
 Test: c3.4     -0.02  -0.07   0.01  -0.04   1.0

Normalized cumulative variances:
[0.5009, 0.7367, 0.9365, 1.0, 1.0]

Component loadings
                  PC1    PC2    PC3    PC4    PC5
 (Intercept)    -0.24   0.81  -0.04   0.53  -0.07
 Test: c5.1     -0.49  -0.49   0.01   0.58   0.42
 Test: c234.15   0.62   0.17  -0.07   0.12   0.76
 Test: c2.34    -0.56   0.28   0.02  -0.6    0.49
 Test: c3.4      0.04   0.04   1.0    0.03   0.04,)

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 16    Time: 0:00:00 ( 6.66 ms/it)
   objective: 13921.43551440495


Minimizing 31    Time: 0:00:00 ( 6.86 ms/it)
   objective: 13920.843622966713


Minimizing 47    Time: 0:00:00 ( 6.74 ms/it)
   objective: 13871.039734904336


Minimizing 63    Time: 0:00:00 ( 6.68 ms/it)
   objective: 13859.470688289364


Minimizing 79    Time: 0:00:00 ( 6.64 ms/it)
   objective: 13848.425462430034


Minimizing 95    Time: 0:00:00 ( 6.62 ms/it)
   objective: 13832.448029606727


Minimizing 111    Time: 0:00:00 ( 6.61 ms/it)
   objective: 13813.062176737752


Minimizing 127    Time: 0:00:00 ( 6.60 ms/it)
   objective: 13779.859791058234


Minimizing 143    Time: 0:00:00 ( 6.59 ms/it)
   objective: 13777.5478506683


Minimizing 158    Time: 0:00:01 ( 6.61 ms/it)
   objective: 13763.504904783413


Minimizing 174    Time: 0:00:01 ( 6.61 ms/it)
   objective: 13758.36151477789


Minimizing 190    Time: 0:00:01 ( 6.61 ms/it)
   objective: 13753.032364250099


Minimizing 206    Time: 0:00:01 ( 6.60 ms/it)
   objective: 13746.304410685198


Minimizing 222    Time: 0:00:01 ( 6.60 ms/it)
   objective: 13717.460080879267


Minimizing 238    Time: 0:00:01 ( 6.59 ms/it)
   objective: 13712.984081493472


Minimizing 254    Time: 0:00:01 ( 6.59 ms/it)
   objective: 13708.619557971768


Minimizing 270    Time: 0:00:01 ( 6.58 ms/it)
   objective: 13705.643108210366


Minimizing 286    Time: 0:00:01 ( 6.58 ms/it)
   objective: 13700.455750019148


Minimizing 302    Time: 0:00:01 ( 6.58 ms/it)
   objective: 13699.242698204343


Minimizing 318    Time: 0:00:02 ( 6.58 ms/it)
   objective: 13694.61041406247


Minimizing 334    Time: 0:00:02 ( 6.58 ms/it)
   objective: 13691.657626223201


Minimizing 350    Time: 0:00:02 ( 6.58 ms/it)
   objective: 13690.20665115047


Minimizing 366    Time: 0:00:02 ( 6.58 ms/it)
   objective: 13687.166564696654


Minimizing 382    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13686.30180547437


Minimizing 398    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13684.579121732546


Minimizing 414    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13682.872410355223


Minimizing 430    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13680.708805226972


Minimizing 446    Time: 0:00:02 ( 6.57 ms/it)
   objective: 13674.153299331072


Minimizing 461    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13670.151857500128


Minimizing 477    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13667.145645546148


Minimizing 493    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13663.520035940299


Minimizing 509    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13658.850355692775


Minimizing 525    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13643.675131394506


Minimizing 541    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13624.556319542156


Minimizing 557    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13621.984369756436


Minimizing 573    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13616.769527898665


Minimizing 589    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13613.604646937049


Minimizing 605    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13608.188194215232


Minimizing 621    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13607.608849249315


Minimizing 637    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13604.49074911487


Minimizing 653    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13601.912264326456


Minimizing 669    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13600.02141365967


Minimizing 685    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13597.222883906004


Minimizing 705    Time: 0:00:04 ( 6.58 ms/it)
   objective: 13587.769630153794


Minimizing 723    Time: 0:00:04 ( 6.58 ms/it)
   objective: 13586.27778231557


Minimizing 739    Time: 0:00:04 ( 6.58 ms/it)
   objective: 13584.169116719298


Minimizing 755    Time: 0:00:04 ( 6.58 ms/it)
   objective: 13581.653447947625


Minimizing 771    Time: 0:00:05 ( 6.58 ms/it)
   objective: 13579.834602990733


Minimizing 787    Time: 0:00:05 ( 6.58 ms/it)
   objective: 13575.439448297482


Minimizing 803    Time: 0:00:05 ( 6.58 ms/it)
   objective: 13570.932969556947


Minimizing 819    Time: 0:00:05 ( 6.57 ms/it)
   objective: 13567.640940635014


Minimizing 835    Time: 0:00:05 ( 6.57 ms/it)
   objective: 13564.489816688401


Minimizing 851    Time: 0:00:05 ( 6.57 ms/it)
   objective: 13560.853875182831


Minimizing 867    Time: 0:00:05 ( 6.57 ms/it)
   objective: 13520.825680189679


Minimizing 883    Time: 0:00:05 ( 6.57 ms/it)
   objective: 13518.850061519814


Minimizing 899    Time: 0:00:05 ( 6.57 ms/it)
   objective: 13517.269195273155


Minimizing 915    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13516.430627354719


Minimizing 931    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13513.883647627801


Minimizing 947    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13505.791108443264


Minimizing 963    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13505.00568022269


Minimizing 979    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13502.315458340927


Minimizing 995    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13500.627025802423


Minimizing 1011    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13500.104540279819


Minimizing 1027    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13498.178127483356


Minimizing 1043    Time: 0:00:06 ( 6.57 ms/it)
   objective: 13493.701735301132


Minimizing 1059    Time: 0:00:06 ( 6.56 ms/it)
   objective: 13492.278802631132


Minimizing 1074    Time: 0:00:07 ( 6.57 ms/it)
   objective: 13482.970157811185


Minimizing 1090    Time: 0:00:07 ( 6.57 ms/it)
   objective: 13476.947784709548


Minimizing 1106    Time: 0:00:07 ( 6.57 ms/it)
   objective: 13466.386063351747


Minimizing 1122    Time: 0:00:07 ( 6.57 ms/it)
   objective: 13458.415492462846


Minimizing 1138    Time: 0:00:07 ( 6.57 ms/it)
   objective: 13450.780722928801


Minimizing 1154    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13440.379786016041


Minimizing 1170    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13431.289630795465


Minimizing 1186    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13428.973918054733


Minimizing 1202    Time: 0:00:07 ( 6.56 ms/it)
   objective: 13422.662984842987


Minimizing 1218    Time: 0:00:07 ( 6.57 ms/it)
   objective: 13422.444168317495


Minimizing 1234    Time: 0:00:08 ( 6.57 ms/it)
   objective: 13420.507251331102


Minimizing 1250    Time: 0:00:08 ( 6.57 ms/it)
   objective: 13415.048622263683


Minimizing 1266    Time: 0:00:08 ( 6.57 ms/it)
   objective: 13409.129562885239


Minimizing 1282    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13406.690165216205


Minimizing 1298    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13405.86573509431


Minimizing 1314    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13404.570733207525


Minimizing 1330    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13402.098773822683


Minimizing 1346    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13399.784685674298


Minimizing 1362    Time: 0:00:08 ( 6.56 ms/it)
   objective: 13390.97913085502


Minimizing 1377    Time: 0:00:09 ( 6.57 ms/it)
   objective: 13380.089644974272


Minimizing 1393    Time: 0:00:09 ( 6.57 ms/it)
   objective: 13376.849914188148


Minimizing 1409    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13371.330925826769


Minimizing 1425    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13367.484505545232


Minimizing 1441    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13354.469359037132


Minimizing 1457    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13347.594722777416


Minimizing 1473    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13339.558614350404


Minimizing 1489    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13336.89158730804


Minimizing 1505    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13332.343048099472


Minimizing 1521    Time: 0:00:09 ( 6.56 ms/it)
   objective: 13324.349093492172


Minimizing 1537    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.90822364467


Minimizing 1553    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.88080147843


Minimizing 1569    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.879325609276


Minimizing 1585    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.881172399342


Minimizing 1601    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.879624014327


Minimizing 1617    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.879522661111


Minimizing 1633    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.879632177996


Minimizing 1649    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.880098213122


Minimizing 1665    Time: 0:00:10 ( 6.56 ms/it)
   objective: 13320.879474627538


Minimizing 1681    Time: 0:00:11 ( 6.56 ms/it)
   objective: 13320.881165020648


Minimizing 1697    Time: 0:00:11 ( 6.56 ms/it)
   objective: 13320.880015840055


Minimizing 1713    Time: 0:00:11 ( 6.56 ms/it)
   objective: 13320.880078694201


Minimizing 1729    Time: 0:00:11 ( 6.56 ms/it)
   objective: 13320.880476034727


Minimizing 1745    Time: 0:00:11 ( 6.56 ms/it)
   objective: 13320.879580248205


Minimizing 1761    Time: 0:00:11 ( 6.56 ms/it)
   objective: 13320.881365118606


Minimizing 1777    Time: 0:00:11 ( 6.56 ms/it)
   objective: 13320.879976541313


Minimizing 1790    Time: 0:00:11 ( 6.56 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0144 0.0144 -1.01 0.3146 0.7253
Test: c5.1 0.0209 0.0306 0.68 0.4950 0.3923
Test: c234.15 -0.0012 0.0313 -0.04 0.9684 0.7637
Test: c12.34 -0.0008 0.0315 -0.03 0.9797 0.9263
Test: c3.4 -0.0124 0.0316 -0.39 0.6956 0.7116
a1 0.2318 0.0490 4.73 <1e-05
Sex: Boys 0.1784 0.0144 12.43 <1e-34
Test: c5.1 & a1 -0.1769 0.1043 -1.70 0.0899
Test: c234.15 & a1 -0.0029 0.1065 -0.03 0.9782
Test: c12.34 & a1 0.0292 0.1084 0.27 0.7879
Test: c3.4 & a1 0.2023 0.1068 1.89 0.0581
Test: c5.1 & Sex: Boys -0.1011 0.0306 -3.30 0.0010
Test: c234.15 & Sex: Boys 0.1362 0.0313 4.35 <1e-04
Test: c12.34 & Sex: Boys 0.0028 0.0315 0.09 0.9293
Test: c3.4 & Sex: Boys -0.0081 0.0316 -0.26 0.7980
a1 & Sex: Boys -0.0573 0.0490 -1.17 0.2422
Test: c5.1 & a1 & Sex: Boys 0.0844 0.1043 0.81 0.4183
Test: c234.15 & a1 & Sex: Boys -0.0375 0.1065 -0.35 0.7248
Test: c12.34 & a1 & Sex: Boys -0.0608 0.1084 -0.56 0.5747
Test: c3.4 & a1 & Sex: Boys -0.0591 0.1068 -0.55 0.5799
Residual 0.0000 
VarCorr(m_cpx_1_PC_2)
Column Variance Std.Dev Corr.
Child (Intercept) 0.52601572 0.72526941
Test: c5.1 0.15393288 0.39234280 -0.20
Test: c234.15 0.58326052 0.76371495 -0.21 -0.32
Test: c12.34 0.85802592 0.92629688 +0.07 +0.45 +0.60
Test: c3.4 0.50641636 0.71162937 +0.29 -0.41 +0.63 +0.35
Residual 0.00000000 0.00002960 
m_cpx_1_PC_2.PCA
(Child = 
Principal components based on correlation matrix
 (Intercept)     1.0     .      .      .      .
 Test: c5.1     -0.2    1.0     .      .      .
 Test: c234.15  -0.21  -0.32   1.0     .      .
 Test: c12.34    0.07   0.45   0.6    1.0     .
 Test: c3.4      0.29  -0.41   0.63   0.35   1.0

Normalized cumulative variances:
[0.4238, 0.7287, 0.945, 1.0, 1.0]

Component loadings
                  PC1    PC2    PC3    PC4    PC5
 (Intercept)    -0.11  -0.34  -0.85   0.28   0.28
 Test: c5.1      0.24   0.7   -0.28  -0.37   0.48
 Test: c234.15  -0.62   0.13   0.34   0.35   0.6
 Test: c12.34   -0.43   0.57  -0.28   0.27  -0.58
 Test: c3.4     -0.6   -0.2   -0.11  -0.76  -0.06,)
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 26    Time: 0:00:00 ( 3.93 ms/it)
   objective: 13863.942199954854


Minimizing 51    Time: 0:00:00 ( 4.02 ms/it)
   objective: 13761.69293351192


Minimizing 75    Time: 0:00:00 ( 4.07 ms/it)
   objective: 13752.395415749725


Minimizing 100    Time: 0:00:00 ( 4.08 ms/it)
   objective: 13745.066978473176


Minimizing 125    Time: 0:00:00 ( 4.09 ms/it)
   objective: 13737.218585011658


Minimizing 149    Time: 0:00:00 ( 4.13 ms/it)
   objective: 13724.399921428005


Minimizing 173    Time: 0:00:00 ( 4.14 ms/it)
   objective: 13711.00182468658


Minimizing 198    Time: 0:00:00 ( 4.13 ms/it)
   objective: 13703.04681131908


Minimizing 227    Time: 0:00:00 ( 4.22 ms/it)
   objective: 13620.709468424284


Minimizing 255    Time: 0:00:01 ( 4.21 ms/it)
   objective: 13498.033230549656


Minimizing 279    Time: 0:00:01 ( 4.21 ms/it)
   objective: 13461.183299382275


Minimizing 303    Time: 0:00:01 ( 4.27 ms/it)
   objective: 13457.548327078272


Minimizing 327    Time: 0:00:01 ( 4.26 ms/it)
   objective: 13403.592735014827


Minimizing 351    Time: 0:00:01 ( 4.26 ms/it)
   objective: 13389.08575648228


Minimizing 375    Time: 0:00:01 ( 4.26 ms/it)
   objective: 13356.42322159301


Minimizing 399    Time: 0:00:01 ( 4.26 ms/it)
   objective: 13285.828201352502


Minimizing 423    Time: 0:00:01 ( 4.26 ms/it)
   objective: 13246.893980164517


Minimizing 447    Time: 0:00:01 ( 4.25 ms/it)
   objective: 13195.558933612207


Minimizing 472    Time: 0:00:02 ( 4.25 ms/it)
   objective: 13195.097049299351


Minimizing 496    Time: 0:00:02 ( 4.25 ms/it)
   objective: 13194.865349842963


Minimizing 520    Time: 0:00:02 ( 4.25 ms/it)
   objective: 13195.030043339022


Minimizing 544    Time: 0:00:02 ( 4.24 ms/it)
   objective: 13195.100200224479


Minimizing 555    Time: 0:00:02 ( 4.24 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0166 0.0144 -1.15 0.2492 0.7781
Test: c5.1 0.0168 0.0311 0.54 0.5895 0.6302
Test: c234.15 0.0085 0.0309 0.27 0.7833 0.5146
Test: c12.34 0.0079 0.0315 0.25 0.8013 0.7797
Test: c3.4 -0.0013 0.0319 -0.04 0.9665 0.6755
a1 0.2329 0.0491 4.75 <1e-05
Sex: Boys 0.1796 0.0144 12.48 <1e-35
Test: c5.1 & a1 -0.1842 0.1059 -1.74 0.0821
Test: c234.15 & a1 -0.0219 0.1054 -0.21 0.8353
Test: c12.34 & a1 0.0046 0.1082 0.04 0.9659
Test: c3.4 & a1 0.1881 0.1079 1.74 0.0812
Test: c5.1 & Sex: Boys -0.1044 0.0311 -3.36 0.0008
Test: c234.15 & Sex: Boys 0.1368 0.0309 4.42 <1e-05
Test: c12.34 & Sex: Boys -0.0014 0.0315 -0.05 0.9635
Test: c3.4 & Sex: Boys -0.0058 0.0319 -0.18 0.8555
a1 & Sex: Boys -0.0635 0.0491 -1.29 0.1956
Test: c5.1 & a1 & Sex: Boys 0.0776 0.1059 0.73 0.4639
Test: c234.15 & a1 & Sex: Boys -0.0199 0.1054 -0.19 0.8503
Test: c12.34 & a1 & Sex: Boys -0.0394 0.1082 -0.36 0.7158
Test: c3.4 & a1 & Sex: Boys -0.0394 0.1079 -0.37 0.7150
Residual 0.0000 
VarCorr(m_zcp_1_PC_2)
Column Variance Std.Dev Corr.
Child (Intercept) 0.60547940 0.77812557
Test: c5.1 0.39709666 0.63015606 .
Test: c234.15 0.26480014 0.51458735 . .
Test: c12.34 0.60793734 0.77970337 . . .
Test: c3.4 0.45629400 0.67549537 . . . .
Residual 0.00000000 0.00000256 
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 13195
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test | Child) 36 13321 -126 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}:
 13894.118610304453
 13894.118610304398
 13894.118610304453

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 16    Time: 0:00:00 ( 6.39 ms/it)
   objective: 14024.558243037627


Minimizing 31    Time: 0:00:00 ( 6.57 ms/it)
   objective: 13915.948215417344


Minimizing 47    Time: 0:00:00 ( 6.48 ms/it)
   objective: 13877.2571795236


Minimizing 63    Time: 0:00:00 ( 6.44 ms/it)
   objective: 13871.931185502679


Minimizing 79    Time: 0:00:00 ( 6.43 ms/it)
   objective: 13862.95307325783


Minimizing 95    Time: 0:00:00 ( 6.41 ms/it)
   objective: 13854.1732012448


Minimizing 111    Time: 0:00:00 ( 6.39 ms/it)
   objective: 13837.320693328513


Minimizing 127    Time: 0:00:00 ( 6.38 ms/it)
   objective: 13832.207679361563


Minimizing 143    Time: 0:00:00 ( 6.39 ms/it)
   objective: 13828.552333888663


Minimizing 159    Time: 0:00:01 ( 6.39 ms/it)
   objective: 13824.797370092063


Minimizing 175    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13823.722322845928


Minimizing 191    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13813.86503478977


Minimizing 207    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13811.542396756515


Minimizing 223    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13806.656039182286


Minimizing 239    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13802.470063817


Minimizing 255    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13799.696858718513


Minimizing 271    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13793.22600269393


Minimizing 287    Time: 0:00:01 ( 6.37 ms/it)
   objective: 13791.360142521338


Minimizing 303    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13785.617904307657


Minimizing 319    Time: 0:00:02 ( 6.37 ms/it)
   objective: 13784.724127018997


Minimizing 335    Time: 0:00:02 ( 6.37 ms/it)
   objective: 13779.914753018566


Minimizing 351    Time: 0:00:02 ( 6.37 ms/it)
   objective: 13776.771115535772


Minimizing 367    Time: 0:00:02 ( 6.37 ms/it)
   objective: 13775.236958657


Minimizing 383    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13773.823083842477


Minimizing 399    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13769.555645664905


Minimizing 415    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13767.657585847954


Minimizing 431    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13763.115314225517


Minimizing 447    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13761.084036320492


Minimizing 463    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13745.223851999173


Minimizing 479    Time: 0:00:03 ( 6.36 ms/it)
   objective: 13736.776933582538


Minimizing 498    Time: 0:00:03 ( 6.39 ms/it)
   objective: 13720.067174123695


Minimizing 517    Time: 0:00:03 ( 6.39 ms/it)
   objective: 13717.859309245345


Minimizing 533    Time: 0:00:03 ( 6.38 ms/it)
   objective: 13714.351802396533


Minimizing 549    Time: 0:00:03 ( 6.38 ms/it)
   objective: 13712.602113297631


Minimizing 565    Time: 0:00:03 ( 6.38 ms/it)
   objective: 13699.334538298837


Minimizing 581    Time: 0:00:03 ( 6.38 ms/it)
   objective: 13696.996267898623


Minimizing 597    Time: 0:00:03 ( 6.38 ms/it)
   objective: 13690.05894999664


Minimizing 613    Time: 0:00:03 ( 6.38 ms/it)
   objective: 13687.518793316416


Minimizing 629    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13675.475206401195


Minimizing 645    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13670.091820171649


Minimizing 661    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13657.457369935997


Minimizing 677    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13651.716670597514


Minimizing 693    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13651.025460674577


Minimizing 709    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13647.26266432917


Minimizing 725    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13644.823454838915


Minimizing 741    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13635.699072239753


Minimizing 757    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13629.666872666327


Minimizing 773    Time: 0:00:04 ( 6.38 ms/it)
   objective: 13629.375890118914


Minimizing 789    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13628.692351083002


Minimizing 805    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13628.319302742348


Minimizing 821    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13626.361140216279


Minimizing 837    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13623.008695264107


Minimizing 853    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13617.400109170965


Minimizing 869    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13613.663073273456


Minimizing 885    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13609.916328872496


Minimizing 901    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13608.834860018156


Minimizing 917    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13602.7859695769


Minimizing 933    Time: 0:00:05 ( 6.38 ms/it)
   objective: 13597.565184495099


Minimizing 949    Time: 0:00:06 ( 6.39 ms/it)
   objective: 13584.915592507154


Minimizing 965    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13582.23590409325


Minimizing 981    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13576.922355479612


Minimizing 997    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13573.060237543912


Minimizing 1013    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13571.398063053086


Minimizing 1029    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13566.565865302124


Minimizing 1045    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13535.546226988568


Minimizing 1061    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13534.307266120297


Minimizing 1077    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13529.631382846099


Minimizing 1093    Time: 0:00:06 ( 6.38 ms/it)
   objective: 13523.708856594312


Minimizing 1109    Time: 0:00:07 ( 6.38 ms/it)
   objective: 13514.77522175468


Minimizing 1126    Time: 0:00:07 ( 6.38 ms/it)
   objective: 13503.186915003593


Minimizing 1143    Time: 0:00:07 ( 6.38 ms/it)
   objective: 13495.228025304852


Minimizing 1160    Time: 0:00:07 ( 6.37 ms/it)
   objective: 13446.345354273028


Minimizing 1177    Time: 0:00:07 ( 6.37 ms/it)
   objective: 13436.6885475296


Minimizing 1193    Time: 0:00:07 ( 6.37 ms/it)
   objective: 13434.830776767238


Minimizing 1209    Time: 0:00:07 ( 6.37 ms/it)
   objective: 13427.511381655335


Minimizing 1226    Time: 0:00:07 ( 6.37 ms/it)
   objective: 13421.862559771762


Minimizing 1242    Time: 0:00:07 ( 6.37 ms/it)
   objective: 13418.911101801408


Minimizing 1259    Time: 0:00:08 ( 6.37 ms/it)
   objective: 13414.435328409018


Minimizing 1276    Time: 0:00:08 ( 6.36 ms/it)
   objective: 13394.089528775454


Minimizing 1292    Time: 0:00:08 ( 6.36 ms/it)
   objective: 13379.598825058376


Minimizing 1308    Time: 0:00:08 ( 6.36 ms/it)
   objective: 13376.591083028092


Minimizing 1324    Time: 0:00:08 ( 6.37 ms/it)
   objective: 13374.71591742993


Minimizing 1340    Time: 0:00:08 ( 6.37 ms/it)
   objective: 13366.796750679248


Minimizing 1356    Time: 0:00:08 ( 6.37 ms/it)
   objective: 13365.179809390014


Minimizing 1372    Time: 0:00:08 ( 6.38 ms/it)
   objective: 13353.773157806776


Minimizing 1388    Time: 0:00:08 ( 6.38 ms/it)
   objective: 13333.938910918587


Minimizing 1403    Time: 0:00:08 ( 6.38 ms/it)
   objective: 13319.294209757674


Minimizing 1419    Time: 0:00:09 ( 6.38 ms/it)
   objective: 13317.41858234645


Minimizing 1435    Time: 0:00:09 ( 6.39 ms/it)
   objective: 13312.828381163097


Minimizing 1451    Time: 0:00:09 ( 6.39 ms/it)
   objective: 13310.836219912147


Minimizing 1467    Time: 0:00:09 ( 6.39 ms/it)
   objective: 13309.054575924543


Minimizing 1483    Time: 0:00:09 ( 6.39 ms/it)
   objective: 13306.865248224058


Minimizing 1499    Time: 0:00:09 ( 6.40 ms/it)
   objective: 13305.215232933784


Minimizing 1514    Time: 0:00:09 ( 6.40 ms/it)
   objective: 13299.553365366417


Minimizing 1530    Time: 0:00:09 ( 6.40 ms/it)
   objective: 13296.790284851697


Minimizing 1545    Time: 0:00:09 ( 6.40 ms/it)
   objective: 13296.78788397368


Minimizing 1560    Time: 0:00:09 ( 6.41 ms/it)
   objective: 13296.785061730101


Minimizing 1576    Time: 0:00:10 ( 6.41 ms/it)
   objective: 13296.783153816577


Minimizing 1594    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13296.781447914109


Minimizing 1611    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13296.782950950277


Minimizing 1627    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13296.782910797134


Minimizing 1643    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13296.783202184262


Minimizing 1659    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13296.78509994717


Minimizing 1675    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13296.78057243659


Minimizing 1691    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13296.783018803922


Minimizing 1706    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13296.783330228252


Minimizing 1722    Time: 0:00:11 ( 6.44 ms/it)
   objective: 13296.784891956151


Minimizing 1738    Time: 0:00:11 ( 6.44 ms/it)
   objective: 13296.78210905855


Minimizing 1754    Time: 0:00:11 ( 6.44 ms/it)
   objective: 13296.783361140115


Minimizing 1770    Time: 0:00:11 ( 6.44 ms/it)
   objective: 13296.781965071801


Minimizing 1774    Time: 0:00:11 ( 6.44 ms/it)

Minimizing 16    Time: 0:00:00 ( 6.68 ms/it)
   objective: 14807.603275825582


Minimizing 31    Time: 0:00:00 ( 6.89 ms/it)
   objective: 14262.557005884515


Minimizing 46    Time: 0:00:00 ( 6.83 ms/it)
   objective: 13879.750168608787


Minimizing 62    Time: 0:00:00 ( 6.79 ms/it)
   objective: 13869.759477796786


Minimizing 78    Time: 0:00:00 ( 6.75 ms/it)
   objective: 13848.902033187655


Minimizing 94    Time: 0:00:00 ( 6.73 ms/it)
   objective: 13835.334363970858


Minimizing 110    Time: 0:00:00 ( 6.71 ms/it)
   objective: 13829.90305911952


Minimizing 128    Time: 0:00:00 ( 6.80 ms/it)
   objective: 13826.121895231701


Minimizing 145    Time: 0:00:00 ( 6.77 ms/it)
   objective: 13824.16434049827


Minimizing 161    Time: 0:00:01 ( 6.75 ms/it)
   objective: 13813.343536773455


Minimizing 177    Time: 0:00:01 ( 6.74 ms/it)
   objective: 13792.408044504573


Minimizing 193    Time: 0:00:01 ( 6.73 ms/it)
   objective: 13788.764576158539


Minimizing 208    Time: 0:00:01 ( 6.74 ms/it)
   objective: 13787.572029820749


Minimizing 224    Time: 0:00:01 ( 6.73 ms/it)
   objective: 13782.534641306163


Minimizing 240    Time: 0:00:01 ( 6.73 ms/it)
   objective: 13777.499440581227


Minimizing 256    Time: 0:00:01 ( 6.72 ms/it)
   objective: 13773.018322227363


Minimizing 272    Time: 0:00:01 ( 6.71 ms/it)
   objective: 13771.012164980963


Minimizing 288    Time: 0:00:01 ( 6.71 ms/it)
   objective: 13770.410886084399


Minimizing 304    Time: 0:00:02 ( 6.70 ms/it)
   objective: 13768.344061628757


Minimizing 320    Time: 0:00:02 ( 6.70 ms/it)
   objective: 13767.596344875912


Minimizing 334    Time: 0:00:02 ( 6.74 ms/it)
   objective: 13766.265552848155


Minimizing 349    Time: 0:00:02 ( 6.75 ms/it)
   objective: 13765.471147323551


Minimizing 364    Time: 0:00:02 ( 6.76 ms/it)
   objective: 13762.203359480012


Minimizing 380    Time: 0:00:02 ( 6.75 ms/it)
   objective: 13749.075516125866


Minimizing 396    Time: 0:00:02 ( 6.75 ms/it)
   objective: 13748.716707112326


Minimizing 412    Time: 0:00:02 ( 6.74 ms/it)
   objective: 13744.763645868705


Minimizing 428    Time: 0:00:02 ( 6.74 ms/it)
   objective: 13742.749135402057


Minimizing 444    Time: 0:00:02 ( 6.73 ms/it)
   objective: 13739.177775282467


Minimizing 459    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13734.417611450852


Minimizing 475    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13731.351588977574


Minimizing 491    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13724.269470845331


Minimizing 506    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13710.103685661878


Minimizing 522    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13709.62995804218


Minimizing 537    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13704.46458103833


Minimizing 553    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13702.075833895124


Minimizing 569    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13698.58693095628


Minimizing 585    Time: 0:00:03 ( 6.73 ms/it)
   objective: 13697.407033619496


Minimizing 601    Time: 0:00:04 ( 6.72 ms/it)
   objective: 13691.974710126218


Minimizing 617    Time: 0:00:04 ( 6.72 ms/it)
   objective: 13690.077784845678


Minimizing 633    Time: 0:00:04 ( 6.72 ms/it)
   objective: 13687.085092685073


Minimizing 648    Time: 0:00:04 ( 6.72 ms/it)
   objective: 13684.65263507289


Minimizing 663    Time: 0:00:04 ( 6.72 ms/it)
   objective: 13680.800895020711


Minimizing 679    Time: 0:00:04 ( 6.72 ms/it)
   objective: 13671.937454092884


Minimizing 695    Time: 0:00:04 ( 6.72 ms/it)
   objective: 13630.462505068586


Minimizing 711    Time: 0:00:04 ( 6.71 ms/it)
   objective: 13627.561506775026


Minimizing 727    Time: 0:00:04 ( 6.71 ms/it)
   objective: 13619.883796837603


Minimizing 743    Time: 0:00:04 ( 6.71 ms/it)
   objective: 13617.791380269991


Minimizing 759    Time: 0:00:05 ( 6.71 ms/it)
   objective: 13616.24793334306


Minimizing 775    Time: 0:00:05 ( 6.71 ms/it)
   objective: 13614.542458552598


Minimizing 791    Time: 0:00:05 ( 6.71 ms/it)
   objective: 13613.804187097667


Minimizing 806    Time: 0:00:05 ( 6.71 ms/it)
   objective: 13613.464160500138


Minimizing 822    Time: 0:00:05 ( 6.70 ms/it)
   objective: 13612.13484303101


Minimizing 838    Time: 0:00:05 ( 6.70 ms/it)
   objective: 13610.621419163355


Minimizing 854    Time: 0:00:05 ( 6.70 ms/it)
   objective: 13609.293700882146


Minimizing 870    Time: 0:00:05 ( 6.70 ms/it)
   objective: 13605.168275824173


Minimizing 886    Time: 0:00:05 ( 6.70 ms/it)
   objective: 13603.42348455629


Minimizing 902    Time: 0:00:06 ( 6.70 ms/it)
   objective: 13600.32191712712


Minimizing 918    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13599.699872598896


Minimizing 934    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13598.32716002503


Minimizing 949    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13596.91911521244


Minimizing 965    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13595.258102410306


Minimizing 981    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13593.083763873474


Minimizing 997    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13589.61504586527


Minimizing 1013    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13587.974999808954


Minimizing 1029    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13584.325077976435


Minimizing 1045    Time: 0:00:06 ( 6.69 ms/it)
   objective: 13582.869069628636


Minimizing 1061    Time: 0:00:07 ( 6.68 ms/it)
   objective: 13581.029243647601


Minimizing 1077    Time: 0:00:07 ( 6.68 ms/it)
   objective: 13578.322703028018


Minimizing 1093    Time: 0:00:07 ( 6.68 ms/it)
   objective: 13575.773062690016


Minimizing 1108    Time: 0:00:07 ( 6.68 ms/it)
   objective: 13574.894143832782


Minimizing 1126    Time: 0:00:07 ( 6.69 ms/it)
   objective: 13569.86561235055


Minimizing 1143    Time: 0:00:07 ( 6.69 ms/it)
   objective: 13564.980774708747


Minimizing 1159    Time: 0:00:07 ( 6.69 ms/it)
   objective: 13563.236221730083


Minimizing 1175    Time: 0:00:07 ( 6.69 ms/it)
   objective: 13560.874615316861


Minimizing 1191    Time: 0:00:07 ( 6.68 ms/it)
   objective: 13560.317022416966


Minimizing 1207    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13558.317119586907


Minimizing 1223    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13554.410823158541


Minimizing 1238    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13554.107581597025


Minimizing 1253    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13553.660973708611


Minimizing 1269    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13551.367581924656


Minimizing 1285    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13550.099011987302


Minimizing 1301    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13547.697445913975


Minimizing 1317    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13546.378030205196


Minimizing 1333    Time: 0:00:08 ( 6.68 ms/it)
   objective: 13543.187819870822


Minimizing 1348    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13542.292442085221


Minimizing 1364    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13540.349621896406


Minimizing 1380    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13538.828435581592


Minimizing 1395    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13538.231814498104


Minimizing 1410    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13537.585810588076


Minimizing 1426    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13536.877783234282


Minimizing 1442    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13533.215992550213


Minimizing 1458    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13530.371254252066


Minimizing 1474    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13529.686256915353


Minimizing 1490    Time: 0:00:09 ( 6.68 ms/it)
   objective: 13528.51435692345


Minimizing 1506    Time: 0:00:10 ( 6.68 ms/it)
   objective: 13527.538985214393


Minimizing 1522    Time: 0:00:10 ( 6.67 ms/it)
   objective: 13523.905558270519


Minimizing 1538    Time: 0:00:10 ( 6.67 ms/it)
   objective: 13522.473576141085


Minimizing 1553    Time: 0:00:10 ( 6.68 ms/it)
   objective: 13515.027442596736


Minimizing 1569    Time: 0:00:10 ( 6.67 ms/it)
   objective: 13510.061541122319


Minimizing 1585    Time: 0:00:10 ( 6.67 ms/it)
   objective: 13499.996886648543


Minimizing 1601    Time: 0:00:10 ( 6.67 ms/it)
   objective: 13499.923684314526


Minimizing 1617    Time: 0:00:10 ( 6.67 ms/it)
   objective: 13498.93438043246


Minimizing 1633    Time: 0:00:10 ( 6.67 ms/it)
   objective: 13497.341327737224


Minimizing 1649    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13496.226363553527


Minimizing 1665    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13491.303423442587


Minimizing 1681    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13488.678218346562


Minimizing 1696    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13487.41715201523


Minimizing 1711    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13486.019718144744


Minimizing 1727    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13484.856725303602


Minimizing 1743    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13483.29250045729


Minimizing 1759    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13479.111672278115


Minimizing 1775    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13478.744692601409


Minimizing 1791    Time: 0:00:11 ( 6.67 ms/it)
   objective: 13475.864127254594


Minimizing 1807    Time: 0:00:12 ( 6.67 ms/it)
   objective: 13474.677711870354


Minimizing 1823    Time: 0:00:12 ( 6.67 ms/it)
   objective: 13473.085695548893


Minimizing 1839    Time: 0:00:12 ( 6.67 ms/it)
   objective: 13468.386241500666


Minimizing 1854    Time: 0:00:12 ( 6.67 ms/it)
   objective: 13465.820302772343


Minimizing 1870    Time: 0:00:12 ( 6.67 ms/it)
   objective: 13465.083330767055


Minimizing 1886    Time: 0:00:12 ( 6.67 ms/it)
   objective: 13464.019025790818


Minimizing 1902    Time: 0:00:12 ( 6.67 ms/it)
   objective: 13462.33212245191


Minimizing 1918    Time: 0:00:12 ( 6.67 ms/it)
   objective: 13460.426859645013


Minimizing 1934    Time: 0:00:12 ( 6.66 ms/it)
   objective: 13457.892234361061


Minimizing 1950    Time: 0:00:12 ( 6.66 ms/it)
   objective: 13457.451770438667


Minimizing 1966    Time: 0:00:13 ( 6.66 ms/it)
   objective: 13456.731483453994


Minimizing 1982    Time: 0:00:13 ( 6.66 ms/it)
   objective: 13456.084004479708


Minimizing 1998    Time: 0:00:13 ( 6.66 ms/it)
   objective: 13453.687305515086


Minimizing 2013    Time: 0:00:13 ( 6.67 ms/it)
   objective: 13453.128979025343


Minimizing 2029    Time: 0:00:13 ( 6.67 ms/it)
   objective: 13452.705509380998


Minimizing 2045    Time: 0:00:13 ( 6.67 ms/it)
   objective: 13452.25918679886


Minimizing 2061    Time: 0:00:13 ( 6.66 ms/it)
   objective: 13451.277309825993


Minimizing 2077    Time: 0:00:13 ( 6.66 ms/it)
   objective: 13450.693586001595


Minimizing 2093    Time: 0:00:13 ( 6.66 ms/it)
   objective: 13449.095722953032


Minimizing 2109    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13447.891120692628


Minimizing 2125    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13447.63764571563


Minimizing 2141    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13446.327670517945


Minimizing 2157    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13445.375625971297


Minimizing 2173    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13443.904504620485


Minimizing 2189    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13441.175422388085


Minimizing 2205    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13441.107549173073


Minimizing 2221    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13440.501439977772


Minimizing 2237    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13440.093077055732


Minimizing 2253    Time: 0:00:14 ( 6.66 ms/it)
   objective: 13439.377797416004


Minimizing 2269    Time: 0:00:15 ( 6.66 ms/it)
   objective: 13438.462673647067


Minimizing 2285    Time: 0:00:15 ( 6.66 ms/it)
   objective: 13433.609432931567


Minimizing 2301    Time: 0:00:15 ( 6.65 ms/it)
   objective: 13433.323878602663


Minimizing 2316    Time: 0:00:15 ( 6.66 ms/it)
   objective: 13432.757031241563


Minimizing 2332    Time: 0:00:15 ( 6.65 ms/it)
   objective: 13432.368617130618


Minimizing 2348    Time: 0:00:15 ( 6.65 ms/it)
   objective: 13432.258422656116


Minimizing 2364    Time: 0:00:15 ( 6.65 ms/it)
   objective: 13431.968191481516


Minimizing 2380    Time: 0:00:15 ( 6.65 ms/it)
   objective: 13430.832547579179


Minimizing 2396    Time: 0:00:15 ( 6.65 ms/it)
   objective: 13429.859316305374


Minimizing 2412    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13429.173779089382


Minimizing 2428    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13428.623133854082


Minimizing 2444    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13428.31660666698


Minimizing 2459    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13427.103759607286


Minimizing 2475    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13426.211386577546


Minimizing 2491    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13425.870507634841


Minimizing 2507    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13425.583011742041


Minimizing 2523    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13424.729539188542


Minimizing 2539    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13424.186082032276


Minimizing 2555    Time: 0:00:16 ( 6.65 ms/it)
   objective: 13423.094824510146


Minimizing 2571    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13421.292489419648


Minimizing 2587    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13420.863577681332


Minimizing 2603    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13419.729966004496


Minimizing 2619    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13418.63942832184


Minimizing 2635    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13416.38345621439


Minimizing 2651    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13415.551074532923


Minimizing 2667    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13412.925108896263


Minimizing 2683    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13405.402823966971


Minimizing 2699    Time: 0:00:17 ( 6.65 ms/it)
   objective: 13402.698957166707


Minimizing 2715    Time: 0:00:18 ( 6.65 ms/it)
   objective: 13388.087265237671


Minimizing 2731    Time: 0:00:18 ( 6.65 ms/it)
   objective: 13386.225835797377


Minimizing 2747    Time: 0:00:18 ( 6.65 ms/it)
   objective: 13384.804043222626


Minimizing 2762    Time: 0:00:18 ( 6.65 ms/it)
   objective: 13381.238694121523


Minimizing 2778    Time: 0:00:18 ( 6.65 ms/it)
   objective: 13380.880241687919


Minimizing 2794    Time: 0:00:18 ( 6.64 ms/it)
   objective: 13378.833764209572


Minimizing 2810    Time: 0:00:18 ( 6.64 ms/it)
   objective: 13378.055287779687


Minimizing 2826    Time: 0:00:18 ( 6.64 ms/it)
   objective: 13375.457714728414


Minimizing 2842    Time: 0:00:18 ( 6.64 ms/it)
   objective: 13374.764572601227


Minimizing 2858    Time: 0:00:18 ( 6.64 ms/it)
   objective: 13373.651620981444


Minimizing 2874    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13372.172693249828


Minimizing 2890    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13370.327777574508


Minimizing 2906    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13367.309286184565


Minimizing 2921    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13367.078935432699


Minimizing 2937    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13366.949622710381


Minimizing 2953    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13366.649080178962


Minimizing 2969    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13366.375063483822


Minimizing 2985    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13365.464302544715


Minimizing 3001    Time: 0:00:19 ( 6.64 ms/it)
   objective: 13364.803243559829


Minimizing 3017    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13361.178953974813


Minimizing 3033    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13359.576451915214


Minimizing 3049    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13359.216573082944


Minimizing 3065    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13358.761399092473


Minimizing 3081    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13358.061196257942


Minimizing 3097    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13356.897484808695


Minimizing 3113    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13355.04862132488


Minimizing 3129    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13353.932367344984


Minimizing 3145    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13351.035008940278


Minimizing 3161    Time: 0:00:20 ( 6.64 ms/it)
   objective: 13350.157565613597


Minimizing 3177    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13349.812435059095


Minimizing 3193    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13349.239432862596


Minimizing 3209    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13347.734724604132


Minimizing 3224    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13344.913675979406


Minimizing 3240    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13344.639506577281


Minimizing 3256    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13343.422223156493


Minimizing 3272    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13342.515359520912


Minimizing 3288    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13338.591677399745


Minimizing 3304    Time: 0:00:21 ( 6.63 ms/it)
   objective: 13334.932809179736


Minimizing 3320    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.913121029997


Minimizing 3336    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.912656475266


Minimizing 3352    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.913537589891


Minimizing 3368    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.912572955101


Minimizing 3384    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.91295381941


Minimizing 3400    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.913191675136


Minimizing 3416    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.91319549545


Minimizing 3432    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.913220285976


Minimizing 3447    Time: 0:00:22 ( 6.63 ms/it)
   objective: 13334.913221402792


Minimizing 3462    Time: 0:00:22 ( 6.64 ms/it)
   objective: 13334.913195161862


Minimizing 3478    Time: 0:00:23 ( 6.64 ms/it)
   objective: 13334.91331523002


Minimizing 3494    Time: 0:00:23 ( 6.64 ms/it)
   objective: 13334.912868848682


Minimizing 3510    Time: 0:00:23 ( 6.63 ms/it)
   objective: 13334.913298739295


Minimizing 3513    Time: 0:00:23 ( 6.64 ms/it)

Minimizing 16    Time: 0:00:00 ( 6.70 ms/it)
   objective: 13987.37169675876


Minimizing 31    Time: 0:00:00 ( 6.89 ms/it)
   objective: 13902.493629140423


Minimizing 47    Time: 0:00:00 ( 6.78 ms/it)
   objective: 13873.092810903749


Minimizing 63    Time: 0:00:00 ( 6.73 ms/it)
   objective: 13860.519115676441


Minimizing 79    Time: 0:00:00 ( 6.70 ms/it)
   objective: 13857.695515067742


Minimizing 95    Time: 0:00:00 ( 6.68 ms/it)
   objective: 13853.623329882732


Minimizing 111    Time: 0:00:00 ( 6.67 ms/it)
   objective: 13851.972078252636


Minimizing 127    Time: 0:00:00 ( 6.67 ms/it)
   objective: 13844.344391540424


Minimizing 143    Time: 0:00:00 ( 6.66 ms/it)
   objective: 13841.798207330434


Minimizing 158    Time: 0:00:01 ( 6.67 ms/it)
   objective: 13833.662140988634


Minimizing 174    Time: 0:00:01 ( 6.67 ms/it)
   objective: 13830.55839553144


Minimizing 190    Time: 0:00:01 ( 6.66 ms/it)
   objective: 13826.779158137699


Minimizing 206    Time: 0:00:01 ( 6.66 ms/it)
   objective: 13825.77804538878


Minimizing 222    Time: 0:00:01 ( 6.65 ms/it)
   objective: 13823.640428841905


Minimizing 238    Time: 0:00:01 ( 6.65 ms/it)
   objective: 13821.710694922309


Minimizing 254    Time: 0:00:01 ( 6.65 ms/it)
   objective: 13819.311230499456


Minimizing 270    Time: 0:00:01 ( 6.65 ms/it)
   objective: 13813.416224457056


Minimizing 285    Time: 0:00:01 ( 6.65 ms/it)
   objective: 13811.31827515125


Minimizing 300    Time: 0:00:01 ( 6.66 ms/it)
   objective: 13800.800202811197


Minimizing 315    Time: 0:00:02 ( 6.68 ms/it)
   objective: 13797.689864427462


Minimizing 330    Time: 0:00:02 ( 6.73 ms/it)
   objective: 13793.758234651697


Minimizing 347    Time: 0:00:02 ( 6.70 ms/it)
   objective: 13790.886654189726


Minimizing 363    Time: 0:00:02 ( 6.68 ms/it)
   objective: 13785.848500384684


Minimizing 379    Time: 0:00:02 ( 6.66 ms/it)
   objective: 13775.814002871311


Minimizing 395    Time: 0:00:02 ( 6.65 ms/it)
   objective: 13774.078152783462


Minimizing 411    Time: 0:00:02 ( 6.64 ms/it)
   objective: 13763.786209835614


Minimizing 427    Time: 0:00:02 ( 6.63 ms/it)
   objective: 13753.528992206573


Minimizing 443    Time: 0:00:02 ( 6.62 ms/it)
   objective: 13752.209135885738


Minimizing 459    Time: 0:00:03 ( 6.61 ms/it)
   objective: 13748.540525206567


Minimizing 475    Time: 0:00:03 ( 6.60 ms/it)
   objective: 13744.710087512798


Minimizing 491    Time: 0:00:03 ( 6.59 ms/it)
   objective: 13743.174821874163


Minimizing 507    Time: 0:00:03 ( 6.59 ms/it)
   objective: 13732.678885464884


Minimizing 523    Time: 0:00:03 ( 6.59 ms/it)
   objective: 13731.789983884555


Minimizing 539    Time: 0:00:03 ( 6.58 ms/it)
   objective: 13729.006960878189


Minimizing 555    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13727.289174161586


Minimizing 571    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13724.688728146186


Minimizing 587    Time: 0:00:03 ( 6.57 ms/it)
   objective: 13723.2900482084


Minimizing 603    Time: 0:00:03 ( 6.56 ms/it)
   objective: 13722.189328274551


Minimizing 619    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13720.403156938348


Minimizing 635    Time: 0:00:04 ( 6.56 ms/it)
   objective: 13717.609894018839


Minimizing 651    Time: 0:00:04 ( 6.55 ms/it)
   objective: 13716.730390128898


Minimizing 667    Time: 0:00:04 ( 6.54 ms/it)
   objective: 13708.936325129212


Minimizing 683    Time: 0:00:04 ( 6.54 ms/it)
   objective: 13707.063425156302


Minimizing 699    Time: 0:00:04 ( 6.53 ms/it)
   objective: 13704.167060769094


Minimizing 715    Time: 0:00:04 ( 6.53 ms/it)
   objective: 13699.849244329635


Minimizing 731    Time: 0:00:04 ( 6.52 ms/it)
   objective: 13695.840763415385


Minimizing 747    Time: 0:00:04 ( 6.52 ms/it)
   objective: 13692.01093774389


Minimizing 763    Time: 0:00:04 ( 6.52 ms/it)
   objective: 13687.13212978464


Minimizing 779    Time: 0:00:05 ( 6.52 ms/it)
   objective: 13677.069908886253


Minimizing 795    Time: 0:00:05 ( 6.52 ms/it)
   objective: 13654.024234759345


Minimizing 811    Time: 0:00:05 ( 6.52 ms/it)
   objective: 13614.104453965432


Minimizing 827    Time: 0:00:05 ( 6.51 ms/it)
   objective: 13613.788568352735


Minimizing 843    Time: 0:00:05 ( 6.51 ms/it)
   objective: 13604.803907695088


Minimizing 859    Time: 0:00:05 ( 6.51 ms/it)
   objective: 13604.630464047907


Minimizing 875    Time: 0:00:05 ( 6.50 ms/it)
   objective: 13602.961487197615


Minimizing 891    Time: 0:00:05 ( 6.50 ms/it)
   objective: 13601.38874628736


Minimizing 907    Time: 0:00:05 ( 6.50 ms/it)
   objective: 13601.054860473043


Minimizing 923    Time: 0:00:05 ( 6.49 ms/it)
   objective: 13598.935616920266


Minimizing 939    Time: 0:00:06 ( 6.49 ms/it)
   objective: 13598.479638011086


Minimizing 955    Time: 0:00:06 ( 6.49 ms/it)
   objective: 13597.151748670287


Minimizing 971    Time: 0:00:06 ( 6.49 ms/it)
   objective: 13597.008223813827


Minimizing 987    Time: 0:00:06 ( 6.48 ms/it)
   objective: 13595.535488268775


Minimizing 1003    Time: 0:00:06 ( 6.48 ms/it)
   objective: 13594.122640407506


Minimizing 1019    Time: 0:00:06 ( 6.48 ms/it)
   objective: 13593.790366476693


Minimizing 1035    Time: 0:00:06 ( 6.48 ms/it)
   objective: 13592.119775186657


Minimizing 1051    Time: 0:00:06 ( 6.47 ms/it)
   objective: 13591.927224109604


Minimizing 1067    Time: 0:00:06 ( 6.47 ms/it)
   objective: 13591.317683535635


Minimizing 1083    Time: 0:00:07 ( 6.47 ms/it)
   objective: 13591.091537667613


Minimizing 1099    Time: 0:00:07 ( 6.47 ms/it)
   objective: 13590.14614939368


Minimizing 1115    Time: 0:00:07 ( 6.47 ms/it)
   objective: 13589.33179672373


Minimizing 1131    Time: 0:00:07 ( 6.47 ms/it)
   objective: 13588.36655513609


Minimizing 1147    Time: 0:00:07 ( 6.46 ms/it)
   objective: 13588.197140608281


Minimizing 1163    Time: 0:00:07 ( 6.46 ms/it)
   objective: 13587.88593126805


Minimizing 1179    Time: 0:00:07 ( 6.46 ms/it)
   objective: 13587.737690082824


Minimizing 1195    Time: 0:00:07 ( 6.46 ms/it)
   objective: 13586.47765994061


Minimizing 1211    Time: 0:00:07 ( 6.46 ms/it)
   objective: 13585.42933202799


Minimizing 1227    Time: 0:00:07 ( 6.45 ms/it)
   objective: 13583.504831736427


Minimizing 1243    Time: 0:00:08 ( 6.45 ms/it)
   objective: 13580.396180351774


Minimizing 1259    Time: 0:00:08 ( 6.45 ms/it)
   objective: 13574.81962693765


Minimizing 1275    Time: 0:00:08 ( 6.45 ms/it)
   objective: 13564.54617552559


Minimizing 1291    Time: 0:00:08 ( 6.45 ms/it)
   objective: 13544.634279907892


Minimizing 1307    Time: 0:00:08 ( 6.45 ms/it)
   objective: 13535.74472746007


Minimizing 1323    Time: 0:00:08 ( 6.45 ms/it)
   objective: 13530.51660117769


Minimizing 1339    Time: 0:00:08 ( 6.45 ms/it)
   objective: 13503.889051349288


Minimizing 1355    Time: 0:00:08 ( 6.44 ms/it)
   objective: 13475.173760393358


Minimizing 1371    Time: 0:00:08 ( 6.44 ms/it)
   objective: 13465.204182424684


Minimizing 1387    Time: 0:00:08 ( 6.44 ms/it)
   objective: 13459.140621028942


Minimizing 1403    Time: 0:00:09 ( 6.44 ms/it)
   objective: 13453.316630201982


Minimizing 1419    Time: 0:00:09 ( 6.44 ms/it)
   objective: 13439.356146728474


Minimizing 1435    Time: 0:00:09 ( 6.44 ms/it)
   objective: 13436.554738460429


Minimizing 1451    Time: 0:00:09 ( 6.44 ms/it)
   objective: 13427.01158988454


Minimizing 1467    Time: 0:00:09 ( 6.44 ms/it)
   objective: 13420.863354026951


Minimizing 1483    Time: 0:00:09 ( 6.43 ms/it)
   objective: 13412.747370498182


Minimizing 1499    Time: 0:00:09 ( 6.43 ms/it)
   objective: 13410.438061958965


Minimizing 1515    Time: 0:00:09 ( 6.43 ms/it)
   objective: 13403.657913044677


Minimizing 1532    Time: 0:00:09 ( 6.43 ms/it)
   objective: 13399.144003634647


Minimizing 1548    Time: 0:00:09 ( 6.43 ms/it)
   objective: 13389.304955326137


Minimizing 1564    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13389.150569793346


Minimizing 1580    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13387.683145962772


Minimizing 1596    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13385.89510011852


Minimizing 1612    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13383.793158759014


Minimizing 1628    Time: 0:00:10 ( 6.43 ms/it)
   objective: 13382.181280678284


Minimizing 1644    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13378.931688727156


Minimizing 1660    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13377.358178517301


Minimizing 1676    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13373.93530101984


Minimizing 1692    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13372.500605841313


Minimizing 1708    Time: 0:00:10 ( 6.42 ms/it)
   objective: 13367.372125880138


Minimizing 1724    Time: 0:00:11 ( 6.42 ms/it)
   objective: 13364.283554235517


Minimizing 1740    Time: 0:00:11 ( 6.42 ms/it)
   objective: 13353.413264600298


Minimizing 1756    Time: 0:00:11 ( 6.42 ms/it)
   objective: 13326.813737791701


Minimizing 1772    Time: 0:00:11 ( 6.42 ms/it)
   objective: 13322.849093752608


Minimizing 1788    Time: 0:00:11 ( 6.42 ms/it)
   objective: 13322.62472170993


Minimizing 1804    Time: 0:00:11 ( 6.42 ms/it)
   objective: 13321.047696215479


Minimizing 1820    Time: 0:00:11 ( 6.42 ms/it)
   objective: 13319.337558728614


Minimizing 1836    Time: 0:00:11 ( 6.42 ms/it)
   objective: 13318.230944023788


Minimizing 1852    Time: 0:00:11 ( 6.41 ms/it)
   objective: 13316.730558462834


Minimizing 1868    Time: 0:00:11 ( 6.41 ms/it)
   objective: 13314.039972104933


Minimizing 1884    Time: 0:00:12 ( 6.42 ms/it)
   objective: 13313.68703543613


Minimizing 1900    Time: 0:00:12 ( 6.42 ms/it)
   objective: 13313.678294538171


Minimizing 1916    Time: 0:00:12 ( 6.42 ms/it)
   objective: 13313.678273710844


Minimizing 1932    Time: 0:00:12 ( 6.41 ms/it)
   objective: 13313.676730185936


Minimizing 1948    Time: 0:00:12 ( 6.41 ms/it)
   objective: 13313.67698261331


Minimizing 1964    Time: 0:00:12 ( 6.41 ms/it)
   objective: 13313.677830602755


Minimizing 1980    Time: 0:00:12 ( 6.41 ms/it)
   objective: 13313.676145819889


Minimizing 1996    Time: 0:00:12 ( 6.41 ms/it)
   objective: 13313.676747205114


Minimizing 2012    Time: 0:00:12 ( 6.41 ms/it)
   objective: 13313.676896949008


Minimizing 2028    Time: 0:00:13 ( 6.41 ms/it)
   objective: 13313.677184720422


Minimizing 2044    Time: 0:00:13 ( 6.41 ms/it)
   objective: 13313.676471402563


Minimizing 2060    Time: 0:00:13 ( 6.41 ms/it)
   objective: 13313.677524349827


Minimizing 2076    Time: 0:00:13 ( 6.41 ms/it)
   objective: 13313.678286879614


Minimizing 2092    Time: 0:00:13 ( 6.41 ms/it)
   objective: 13313.675911712286


Minimizing 2108    Time: 0:00:13 ( 6.41 ms/it)
   objective: 13313.6761979515


Minimizing 2116    Time: 0:00:13 ( 6.41 ms/it)

Minimizing 16    Time: 0:00:00 ( 6.29 ms/it)
   objective: 13915.240595604904


Minimizing 31    Time: 0:00:00 ( 6.51 ms/it)
   objective: 13901.2610708842


Minimizing 47    Time: 0:00:00 ( 6.43 ms/it)
   objective: 13882.779207309211


Minimizing 63    Time: 0:00:00 ( 6.44 ms/it)
   objective: 13875.48977801441


Minimizing 79    Time: 0:00:00 ( 6.43 ms/it)
   objective: 13861.603842398083


Minimizing 95    Time: 0:00:00 ( 6.42 ms/it)
   objective: 13854.685546419272


Minimizing 111    Time: 0:00:00 ( 6.41 ms/it)
   objective: 13856.32381588956


Minimizing 127    Time: 0:00:00 ( 6.40 ms/it)
   objective: 13833.430677708388


Minimizing 143    Time: 0:00:00 ( 6.40 ms/it)
   objective: 13826.104419500356


Minimizing 159    Time: 0:00:01 ( 6.39 ms/it)
   objective: 13815.873350028856


Minimizing 175    Time: 0:00:01 ( 6.39 ms/it)
   objective: 13811.418716469268


Minimizing 191    Time: 0:00:01 ( 6.39 ms/it)
   objective: 13799.389759321686


Minimizing 207    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13791.318370675017


Minimizing 223    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13788.875110313616


Minimizing 239    Time: 0:00:01 ( 6.38 ms/it)
   objective: 13787.124237143185


Minimizing 255    Time: 0:00:01 ( 6.37 ms/it)
   objective: 13784.618649147083


Minimizing 271    Time: 0:00:01 ( 6.37 ms/it)
   objective: 13782.599228716246


Minimizing 287    Time: 0:00:01 ( 6.37 ms/it)
   objective: 13780.82291427615


Minimizing 303    Time: 0:00:01 ( 6.37 ms/it)
   objective: 13775.130956791792


Minimizing 319    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13771.783680499018


Minimizing 335    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13769.989597159494


Minimizing 351    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13767.876035948033


Minimizing 367    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13763.176384383325


Minimizing 383    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13761.805092016362


Minimizing 399    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13758.293938999968


Minimizing 415    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13754.03484779935


Minimizing 431    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13751.888278148432


Minimizing 447    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13742.205601368865


Minimizing 463    Time: 0:00:02 ( 6.36 ms/it)
   objective: 13738.496291554433


Minimizing 479    Time: 0:00:03 ( 6.36 ms/it)
   objective: 13730.37966335241


Minimizing 495    Time: 0:00:03 ( 6.36 ms/it)
   objective: 13725.092041913504


Minimizing 511    Time: 0:00:03 ( 6.36 ms/it)
   objective: 13720.215467107071


Minimizing 527    Time: 0:00:03 ( 6.36 ms/it)
   objective: 13704.360552810482


Minimizing 543    Time: 0:00:03 ( 6.37 ms/it)
   objective: 13694.719074881286


Minimizing 559    Time: 0:00:03 ( 6.37 ms/it)
   objective: 13686.08542426614


Minimizing 575    Time: 0:00:03 ( 6.37 ms/it)
   objective: 13681.828138176134


Minimizing 591    Time: 0:00:03 ( 6.37 ms/it)
   objective: 13679.556836213756


Minimizing 607    Time: 0:00:03 ( 6.36 ms/it)
   objective: 13674.007340035983


Minimizing 623    Time: 0:00:03 ( 6.36 ms/it)
   objective: 13661.742846375833


Minimizing 639    Time: 0:00:04 ( 6.36 ms/it)
   objective: 13656.729179170088


Minimizing 655    Time: 0:00:04 ( 6.36 ms/it)
   objective: 13646.181190453266


Minimizing 671    Time: 0:00:04 ( 6.36 ms/it)
   objective: 13636.901718987887


Minimizing 687    Time: 0:00:04 ( 6.36 ms/it)
   objective: 13630.60877998206


Minimizing 768    Time: 0:00:05 ( 6.55 ms/it)
   objective: 13594.663564268303


Minimizing 790    Time: 0:00:05 ( 6.54 ms/it)
   objective: 13590.351950952194


Minimizing 806    Time: 0:00:05 ( 6.54 ms/it)
   objective: 13589.557297018713


Minimizing 822    Time: 0:00:05 ( 6.54 ms/it)
   objective: 13571.968723858408


Minimizing 838    Time: 0:00:05 ( 6.54 ms/it)
   objective: 13568.655147295489


Minimizing 854    Time: 0:00:05 ( 6.53 ms/it)
   objective: 13563.446668548793


Minimizing 870    Time: 0:00:05 ( 6.53 ms/it)
   objective: 13559.281427300106


Minimizing 886    Time: 0:00:05 ( 6.53 ms/it)
   objective: 13555.859757495884


Minimizing 902    Time: 0:00:05 ( 6.52 ms/it)
   objective: 13548.863468538613


Minimizing 918    Time: 0:00:05 ( 6.52 ms/it)
   objective: 13499.22230984128


Minimizing 934    Time: 0:00:06 ( 6.52 ms/it)
   objective: 13495.156650959492


Minimizing 950    Time: 0:00:06 ( 6.51 ms/it)
   objective: 13491.82816111204


Minimizing 966    Time: 0:00:06 ( 6.51 ms/it)
   objective: 13490.479967751511


Minimizing 982    Time: 0:00:06 ( 6.51 ms/it)
   objective: 13486.769002955596


Minimizing 998    Time: 0:00:06 ( 6.51 ms/it)
   objective: 13482.027886992655


Minimizing 1014    Time: 0:00:06 ( 6.50 ms/it)
   objective: 13476.92123740138


Minimizing 1030    Time: 0:00:06 ( 6.50 ms/it)
   objective: 13471.907739471164


Minimizing 1046    Time: 0:00:06 ( 6.50 ms/it)
   objective: 13459.666428320328


Minimizing 1062    Time: 0:00:06 ( 6.50 ms/it)
   objective: 13449.096829575908


Minimizing 1078    Time: 0:00:07 ( 6.50 ms/it)
   objective: 13436.80808103249


Minimizing 1094    Time: 0:00:07 ( 6.49 ms/it)
   objective: 13381.30034951646


Minimizing 1110    Time: 0:00:07 ( 6.49 ms/it)
   objective: 13371.177089510224


Minimizing 1126    Time: 0:00:07 ( 6.49 ms/it)
   objective: 13365.022672128296


Minimizing 1142    Time: 0:00:07 ( 6.49 ms/it)
   objective: 13357.739883477901


Minimizing 1158    Time: 0:00:07 ( 6.49 ms/it)
   objective: 13354.214090207694


Minimizing 1174    Time: 0:00:07 ( 6.48 ms/it)
   objective: 13345.704820772342


Minimizing 1190    Time: 0:00:07 ( 6.48 ms/it)
   objective: 13341.14952587137


Minimizing 1206    Time: 0:00:07 ( 6.48 ms/it)
   objective: 13324.815465965003


Minimizing 1222    Time: 0:00:07 ( 6.48 ms/it)
   objective: 13316.375420988596


Minimizing 1238    Time: 0:00:08 ( 6.48 ms/it)
   objective: 13269.073023155113


Minimizing 1254    Time: 0:00:08 ( 6.47 ms/it)
   objective: 13267.389867186983


Minimizing 1270    Time: 0:00:08 ( 6.47 ms/it)
   objective: 13267.054339865528


Minimizing 1286    Time: 0:00:08 ( 6.47 ms/it)
   objective: 13266.969979616159


Minimizing 1302    Time: 0:00:08 ( 6.47 ms/it)
   objective: 13266.982937387933


Minimizing 1318    Time: 0:00:08 ( 6.47 ms/it)
   objective: 13266.986370756684


Minimizing 1334    Time: 0:00:08 ( 6.47 ms/it)
   objective: 13267.000510401063


Minimizing 1350    Time: 0:00:08 ( 6.47 ms/it)
   objective: 13266.985665113854


Minimizing 1366    Time: 0:00:08 ( 6.47 ms/it)
   objective: 13266.974524978868


Minimizing 1382    Time: 0:00:08 ( 6.46 ms/it)
   objective: 13266.961140640546


Minimizing 1398    Time: 0:00:09 ( 6.46 ms/it)
   objective: 13266.997452665004


Minimizing 1414    Time: 0:00:09 ( 6.46 ms/it)
   objective: 13266.96188082089


Minimizing 1430    Time: 0:00:09 ( 6.46 ms/it)
   objective: 13266.972005899326


Minimizing 1446    Time: 0:00:09 ( 6.46 ms/it)
   objective: 13266.964906121444


Minimizing 1462    Time: 0:00:09 ( 6.46 ms/it)
   objective: 13266.98884150316


Minimizing 1478    Time: 0:00:09 ( 6.46 ms/it)
   objective: 13266.968447811858


Minimizing 1493    Time: 0:00:09 ( 6.46 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0167 0.0142 -1.18 0.2388 0.6317
Test: c5.1 -0.0222 0.0439 -0.51 0.6135 1.4354
Test: c234.15 -0.0110 0.1704 -0.06 0.9487 0.3056
Test: c2.34 0.0053 0.0775 0.07 0.9454 1.5786
Test: c3.4 -0.0033 0.0450 -0.07 0.9408 1.6105
a1 0.2486 0.0484 5.14 <1e-06
Sex: Boys 0.1882 0.0142 13.27 <1e-39
Test: c5.1 & a1 0.2475 0.1489 1.66 0.0965
Test: c234.15 & a1 -0.2309 0.5804 -0.40 0.6907
Test: c2.34 & a1 0.0994 0.2681 0.37 0.7110
Test: c3.4 & a1 0.2373 0.1522 1.56 0.1191
Test: c5.1 & Sex: Boys 0.0913 0.0439 2.08 0.0377
Test: c234.15 & Sex: Boys -0.8431 0.1704 -4.95 <1e-06
Test: c2.34 & Sex: Boys -0.0770 0.0775 -0.99 0.3201
Test: c3.4 & Sex: Boys -0.0410 0.0450 -0.91 0.3619
a1 & Sex: Boys -0.0644 0.0484 -1.33 0.1832
Test: c5.1 & a1 & Sex: Boys -0.0996 0.1489 -0.67 0.5035
Test: c234.15 & a1 & Sex: Boys 0.3286 0.5804 0.57 0.5713
Test: c2.34 & a1 & Sex: Boys -0.1146 0.2681 -0.43 0.6691
Test: c3.4 & a1 & Sex: Boys -0.0447 0.1522 -0.29 0.7691
Residual 0.0000 
VarCorr(m_Child_SDC)
Column Variance Std.Dev Corr.
Child (Intercept) 0.51177718 0.71538603
Test: Star_r 0.46816168 0.68422341 +0.45
Test: S20_r 0.81274710 0.90152488 -0.08 -0.11
Test: SLJ 0.58255428 0.76325243 -0.28 +0.71 -0.25
Test: BPT 1.15100691 1.07284990 +0.01 -0.44 -0.28 -0.39
Residual 0.00000000 0.00001918 
VarCorr(m_Child_HeC)
Column Variance Std.Dev Corr.
Child (Intercept) 0.44356367 0.66600576
Test: Star_r 0.11791566 0.34338850 +0.14
Test: S20_r 0.11022251 0.33199775 -0.09 -0.44
Test: SLJ 0.07788965 0.27908717 -0.29 +0.68 +0.22
Test: BPT 0.03371912 0.18362765 -0.10 +0.10 -0.14 -0.23
Residual 0.00000000 0.00004141 
VarCorr(m_Child_HyC)
Column Variance Std.Dev Corr.
Child (Intercept) 0.54689359 0.73952254
Test: BPT-other 0.87972542 0.93793679 +1.00
Test: Star-End 0.66492813 0.81543125 +0.17 +0.16
Test: S20-Star 1.66285448 1.28951715 -0.10 -0.09 -0.54
Test: SLJ-S20 1.16524928 1.07946713 -0.09 -0.10 +0.89 -0.63
Residual 0.00000000 0.00002298 
VarCorr(m_Child_PCA)
Column Variance Std.Dev Corr.
Child (Intercept) 0.3990042 0.6316678
Test: c5.1 2.0602684 1.4353635 -0.08
Test: c234.15 0.0933852 0.3055900 -0.18 -0.84
Test: c2.34 2.4920554 1.5786245 +0.49 +0.42 -0.84
Test: c3.4 2.5937623 1.6105161 -0.02 -0.07 +0.01 -0.04
Residual 0.0000000 0.0000084

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 26    Time: 0:00:00 ( 3.89 ms/it)
   objective: 13889.244574017242


Minimizing 52    Time: 0:00:00 ( 3.95 ms/it)
   objective: 13887.847190508171


Minimizing 77    Time: 0:00:00 ( 3.97 ms/it)

Minimizing 26    Time: 0:00:00 ( 3.94 ms/it)
   objective: 13836.663953929225


Minimizing 51    Time: 0:00:00 ( 3.99 ms/it)
   objective: 13798.676818615999


Minimizing 77    Time: 0:00:00 ( 3.99 ms/it)
   objective: 13787.650802895241


Minimizing 102    Time: 0:00:00 ( 4.04 ms/it)
   objective: 13783.362729403352


Minimizing 127    Time: 0:00:00 ( 4.04 ms/it)
   objective: 13776.908355023059


Minimizing 152    Time: 0:00:00 ( 4.04 ms/it)
   objective: 13770.991462187732


Minimizing 183    Time: 0:00:00 ( 4.14 ms/it)
   objective: 13742.237219848092


Minimizing 213    Time: 0:00:00 ( 4.12 ms/it)
   objective: 13735.521161216115


Minimizing 238    Time: 0:00:00 ( 4.12 ms/it)
   objective: 13698.616873771472


Minimizing 263    Time: 0:00:01 ( 4.11 ms/it)
   objective: 13694.423279015657


Minimizing 289    Time: 0:00:01 ( 4.10 ms/it)
   objective: 13693.246898926693


Minimizing 315    Time: 0:00:01 ( 4.09 ms/it)
   objective: 13691.095471705128


Minimizing 340    Time: 0:00:01 ( 4.09 ms/it)
   objective: 13685.111036862992


Minimizing 365    Time: 0:00:01 ( 4.10 ms/it)
   objective: 13664.27698705504


Minimizing 390    Time: 0:00:01 ( 4.09 ms/it)
   objective: 13647.820004656875


Minimizing 415    Time: 0:00:01 ( 4.09 ms/it)
   objective: 13637.631476909999


Minimizing 440    Time: 0:00:01 ( 4.09 ms/it)
   objective: 13591.423765087566


Minimizing 464    Time: 0:00:01 ( 4.11 ms/it)
   objective: 13558.448283367099


Minimizing 487    Time: 0:00:02 ( 4.13 ms/it)
   objective: 13475.309612143254


Minimizing 510    Time: 0:00:02 ( 4.15 ms/it)
   objective: 13420.522190881267


Minimizing 533    Time: 0:00:02 ( 4.16 ms/it)
   objective: 13330.53685667897


Minimizing 554    Time: 0:00:02 ( 4.20 ms/it)
   objective: 13318.784790886668


Minimizing 574    Time: 0:00:02 ( 4.23 ms/it)
   objective: 13251.12725928238


Minimizing 594    Time: 0:00:02 ( 4.26 ms/it)
   objective: 13235.318568890492


Minimizing 614    Time: 0:00:02 ( 4.29 ms/it)
   objective: 13174.685463456204


Minimizing 634    Time: 0:00:02 ( 4.32 ms/it)
   objective: 13174.513677228737


Minimizing 658    Time: 0:00:02 ( 4.32 ms/it)
   objective: 13174.68047518385


Minimizing 683    Time: 0:00:02 ( 4.31 ms/it)
   objective: 13174.626292521629


Minimizing 708    Time: 0:00:03 ( 4.30 ms/it)
   objective: 13174.366614197526


Minimizing 714    Time: 0:00:03 ( 4.30 ms/it)

Minimizing 26    Time: 0:00:00 ( 3.91 ms/it)
   objective: 13878.481472114516


Minimizing 51    Time: 0:00:00 ( 4.20 ms/it)
   objective: 13864.140083335364


Minimizing 73    Time: 0:00:00 ( 4.68 ms/it)
   objective: 13766.88384663307


Minimizing 95    Time: 0:00:00 ( 4.69 ms/it)
   objective: 13735.497750146718


Minimizing 117    Time: 0:00:00 ( 4.69 ms/it)
   objective: 13690.442168218673


Minimizing 141    Time: 0:00:00 ( 4.62 ms/it)
   objective: 13670.417521041258


Minimizing 164    Time: 0:00:00 ( 4.59 ms/it)
   objective: 13667.536298513478


Minimizing 187    Time: 0:00:00 ( 4.58 ms/it)
   objective: 13663.546698861646


Minimizing 210    Time: 0:00:00 ( 4.56 ms/it)
   objective: 13654.63252949356


Minimizing 233    Time: 0:00:01 ( 4.59 ms/it)
   objective: 13650.402396275415


Minimizing 256    Time: 0:00:01 ( 4.57 ms/it)
   objective: 13647.089747736383


Minimizing 280    Time: 0:00:01 ( 4.55 ms/it)
   objective: 13645.237775027854


Minimizing 303    Time: 0:00:01 ( 4.54 ms/it)
   objective: 13635.935231661038


Minimizing 326    Time: 0:00:01 ( 4.54 ms/it)
   objective: 13631.71012644656


Minimizing 348    Time: 0:00:01 ( 4.62 ms/it)
   objective: 13622.568752557752


Minimizing 366    Time: 0:00:01 ( 4.68 ms/it)
   objective: 13620.509396743364


Minimizing 386    Time: 0:00:01 ( 4.70 ms/it)
   objective: 13612.713967153803


Minimizing 407    Time: 0:00:01 ( 4.71 ms/it)
   objective: 13609.608359529884


Minimizing 429    Time: 0:00:02 ( 4.70 ms/it)
   objective: 13601.450076221612


Minimizing 452    Time: 0:00:02 ( 4.70 ms/it)
   objective: 13575.229819122862


Minimizing 474    Time: 0:00:02 ( 4.69 ms/it)
   objective: 13499.695549062759


Minimizing 497    Time: 0:00:02 ( 4.68 ms/it)
   objective: 13498.145073997584


Minimizing 521    Time: 0:00:02 ( 4.66 ms/it)
   objective: 13482.973003270265


Minimizing 545    Time: 0:00:02 ( 4.64 ms/it)
   objective: 13404.922759628345


Minimizing 569    Time: 0:00:02 ( 4.62 ms/it)
   objective: 13394.241999101578


Minimizing 593    Time: 0:00:02 ( 4.61 ms/it)
   objective: 13362.412599945907


Minimizing 617    Time: 0:00:02 ( 4.59 ms/it)
   objective: 13367.406104932918


Minimizing 641    Time: 0:00:02 ( 4.58 ms/it)
   objective: 13311.257255820208


Minimizing 666    Time: 0:00:03 ( 4.56 ms/it)
   objective: 13302.700321656186


Minimizing 690    Time: 0:00:03 ( 4.55 ms/it)
   objective: 13284.418954744164


Minimizing 715    Time: 0:00:03 ( 4.53 ms/it)
   objective: 13271.114483031954


Minimizing 738    Time: 0:00:03 ( 4.53 ms/it)
   objective: 13271.15430458657


Minimizing 768    Time: 0:00:03 ( 4.54 ms/it)
   objective: 13271.115703047297


Minimizing 796    Time: 0:00:03 ( 4.53 ms/it)
   objective: 13271.09197374931


Minimizing 805    Time: 0:00:03 ( 4.52 ms/it)

Minimizing 26    Time: 0:00:00 ( 4.31 ms/it)
   objective: 13881.75001732227


Minimizing 49    Time: 0:00:00 ( 4.37 ms/it)
   objective: 13861.130856591346


Minimizing 72    Time: 0:00:00 ( 4.38 ms/it)
   objective: 13785.79378001137


Minimizing 95    Time: 0:00:00 ( 4.39 ms/it)
   objective: 13769.568149092798


Minimizing 118    Time: 0:00:00 ( 4.39 ms/it)
   objective: 13765.5802958099


Minimizing 142    Time: 0:00:00 ( 4.39 ms/it)
   objective: 13755.370411729298


Minimizing 166    Time: 0:00:00 ( 4.37 ms/it)
   objective: 13745.785656006863


Minimizing 191    Time: 0:00:00 ( 4.34 ms/it)
   objective: 13720.637179654816


Minimizing 216    Time: 0:00:00 ( 4.31 ms/it)
   objective: 13697.562926770766


Minimizing 240    Time: 0:00:01 ( 4.34 ms/it)
   objective: 13651.93104760364


Minimizing 263    Time: 0:00:01 ( 4.36 ms/it)
   objective: 13592.985551442034


Minimizing 285    Time: 0:00:01 ( 4.38 ms/it)
   objective: 13574.096439434143


Minimizing 308    Time: 0:00:01 ( 4.38 ms/it)
   objective: 13521.21837539396


Minimizing 331    Time: 0:00:01 ( 4.46 ms/it)
   objective: 13503.452237604244


Minimizing 350    Time: 0:00:01 ( 4.51 ms/it)
   objective: 13465.809285074938


Minimizing 371    Time: 0:00:01 ( 4.53 ms/it)
   objective: 13409.650270635597


Minimizing 392    Time: 0:00:01 ( 4.56 ms/it)
   objective: 13407.710520838169


Minimizing 415    Time: 0:00:01 ( 4.56 ms/it)
   objective: 13350.510369608673


Minimizing 439    Time: 0:00:01 ( 4.54 ms/it)
   objective: 13338.785155392557


Minimizing 462    Time: 0:00:02 ( 4.54 ms/it)
   objective: 13321.1878738808


Minimizing 485    Time: 0:00:02 ( 4.54 ms/it)
   objective: 13312.691508943171


Minimizing 507    Time: 0:00:02 ( 4.55 ms/it)
   objective: 13306.074056626385


Minimizing 529    Time: 0:00:02 ( 4.55 ms/it)
   objective: 13273.033766790337


Minimizing 552    Time: 0:00:02 ( 4.55 ms/it)
   objective: 13260.859229422058


Minimizing 575    Time: 0:00:02 ( 4.55 ms/it)
   objective: 13234.196342149226


Minimizing 598    Time: 0:00:02 ( 4.54 ms/it)
   objective: 13234.28395489155


Minimizing 621    Time: 0:00:02 ( 4.54 ms/it)
   objective: 13234.219867060965


Minimizing 643    Time: 0:00:02 ( 4.54 ms/it)
   objective: 13234.275085206158


Minimizing 666    Time: 0:00:03 ( 4.54 ms/it)
   objective: 13234.141180639403


Minimizing 680    Time: 0:00:03 ( 4.59 ms/it)
Est. SE z p σ_Child
(Intercept) -0.0161 0.0143 -1.13 0.2595 0.7694
Test: c5.1 -0.0269 0.0463 -0.58 0.5613 1.3132
Test: c234.15 -0.0432 0.1738 -0.25 0.8039 1.1383
Test: c2.34 0.0092 0.0765 0.12 0.9047 1.8897
Test: c3.4 -0.0020 0.0422 -0.05 0.9618 0.8193
a1 0.2398 0.0488 4.91 <1e-06
Sex: Boys 0.1883 0.0143 13.15 <1e-38
Test: c5.1 & a1 0.2807 0.1572 1.79 0.0742
Test: c234.15 & a1 -0.2615 0.5927 -0.44 0.6590
Test: c2.34 & a1 0.1411 0.2648 0.53 0.5943
Test: c3.4 & a1 0.2313 0.1428 1.62 0.1052
Test: c5.1 & Sex: Boys 0.0986 0.0463 2.13 0.0333
Test: c234.15 & Sex: Boys -0.8399 0.1738 -4.83 <1e-05
Test: c2.34 & Sex: Boys -0.0784 0.0765 -1.02 0.3054
Test: c3.4 & Sex: Boys -0.0349 0.0422 -0.83 0.4081
a1 & Sex: Boys -0.0696 0.0488 -1.43 0.1541
Test: c5.1 & a1 & Sex: Boys -0.0984 0.1572 -0.63 0.5315
Test: c234.15 & a1 & Sex: Boys 0.2994 0.5927 0.51 0.6135
Test: c2.34 & a1 & Sex: Boys -0.1268 0.2648 -0.48 0.6321
Test: c3.4 & a1 & Sex: Boys -0.0268 0.1428 -0.19 0.8513
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 13888
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test | Child) 36 13297 591 10 <1e-99 
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 13174
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test | Child) 36 13335 -161 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 13271
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test | Child) 36 13314 -43 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 13234
zScore ~ 1 + Test + a1 + Sex + Test & a1 + Test & Sex + a1 & Sex + Test & a1 & Sex + (1 + Test | Child) 36 13267 -33 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 13174.3 13226.3 13395.8
2 PCA0 26 13234.1 13286.1 13455.6
3 HyC0 26 13271.0 13323.0 13492.4
4 SDC0 26 13887.8 13939.8 14109.3

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 151    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13874.437474322702


Minimizing 305    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13872.961033798761


Minimizing 457    Time: 0:00:00 ( 0.67 ms/it)
   objective: 13872.932146690862


Minimizing 557    Time: 0:00:00 ( 0.67 ms/it)

Minimizing 153    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13905.342076292793


Minimizing 304    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13898.34514364379


Minimizing 457    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13898.320648491279


Minimizing 613    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13898.319675311397


Minimizing 767    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13898.319521040747


Minimizing 781    Time: 0:00:00 ( 0.66 ms/it)

Minimizing 152    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13886.901128914196


Minimizing 308    Time: 0:00:00 ( 0.65 ms/it)
   objective: 13873.570126676612


Minimizing 464    Time: 0:00:00 ( 0.65 ms/it)
   objective: 13872.984090919967


Minimizing 620    Time: 0:00:00 ( 0.65 ms/it)
   objective: 13872.934791313859


Minimizing 776    Time: 0:00:00 ( 0.67 ms/it)
   objective: 13872.93154953655


Minimizing 920    Time: 0:00:00 ( 0.68 ms/it)
   objective: 13872.931510480761


Minimizing 950    Time: 0:00:00 ( 0.68 ms/it)

Minimizing 144    Time: 0:00:00 ( 0.70 ms/it)
   objective: 13875.29122053444


Minimizing 301    Time: 0:00:00 ( 0.67 ms/it)
   objective: 13873.217543409655


Minimizing 459    Time: 0:00:00 ( 0.66 ms/it)
   objective: 13872.966805899752


Minimizing 617    Time: 0:00:00 ( 0.65 ms/it)
   objective: 13872.93571945615


Minimizing 776    Time: 0:00:00 ( 0.65 ms/it)
   objective: 13872.931701307007


Minimizing 934    Time: 0:00:00 ( 0.65 ms/it)
   objective: 13872.931539049376


Minimizing 1056    Time: 0:00:00 ( 0.65 ms/it)

VarCorr(m_School_SeqDiff)
Column Variance Std.Dev Corr.
School (Intercept) 0.025779 0.160557
Test: Star_r 0.125794 0.354674 +0.11
Test: S20_r 0.197625 0.444550 -0.15 -0.29
Test: SLJ 0.095517 0.309058 -0.03 -0.44 -0.51
Test: BPT 0.069908 0.264402 -0.33 +0.01 -0.06 -0.30
a1 0.062525 0.250051 +0.46 +0.03 -0.19 +0.29 -0.78
Residual 0.864399 0.929730 
VarCorr(m_School_Helmert)
Column Variance Std.Dev Corr.
School (Intercept) 0.0000000 0.0000000
Test: Star_r 0.0373126 0.1931647 +NaN
Test: S20_r 0.0204324 0.1429419 +NaN +0.07
Test: SLJ 0.0030792 0.0554903 +NaN -0.45 +0.29
Test: BPT 0.0020132 0.0448687 +NaN -0.31 +0.16 +0.23
a1 0.1156160 0.3400236 +NaN -0.02 -0.16 +0.09 -0.70
Residual 0.8863058 0.9414381 
VarCorr(m_School_Hypo)
Column Variance Std.Dev Corr.
School (Intercept) 0.025776 0.160550
Test: BPT-other 0.880787 0.938503 -0.50
Test: Star-End 0.125689 0.354526 +0.11 -0.32
Test: S20-Star 0.197711 0.444647 -0.15 +0.26 -0.29
Test: SLJ-S20 0.095528 0.309076 -0.03 -0.00 -0.44 -0.51
a1 0.062848 0.250694 +0.45 -0.76 +0.03 -0.19 +0.29
Residual 0.864390 0.929726 
VarCorr(m_School_PCA)
Column Variance Std.Dev Corr.
School (Intercept) 0.025777 0.160552
Test: c5.1 0.098180 0.313337 -0.39
Test: c234.15 2.076545 1.441022 +0.22 +0.22
Test: c2.34 0.604907 0.777758 +0.18 -0.41 -0.06
Test: c3.4 0.095552 0.309115 +0.03 +0.49 +0.53 -0.19
a1 0.062926 0.250851 +0.45 -0.61 +0.32 +0.11 -0.29
Residual 0.864370 0.929715

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
4×5 DataFrame
Row zcpLMM dof deviance AIC BIC
String Int64 Float64 Float64 Float64
1 HeC0 27 13883.8 13937.8 14113.7
2 PCA0 27 13886.4 13940.4 14116.4
3 HyC0 27 13892.0 13946.0 14121.9
4 SDC0 27 13894.8 13948.8 14124.8

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

This page was rendered from git revision 1a894e8 using Quarto 1.7.29.

Back to top