Aim
This document shows how the hypothesis GLM for PDon vs PDoff with ‘maximal’ random effects is reduced systematically, arriving at the most appropriate model for analysis.
Warning: package 'sjPlot' was built under R version 4.2.3
Warning: package 'ggpubr' was built under R version 4.2.2
Loading required package: ggplot2
Warning: package 'ggplot2' was built under R version 4.2.2
Loading required package: pacman
Warning: package 'pacman' was built under R version 4.2.2
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (86): LARS_EP, LARS_INT, LARS_INI, LARS_NS, LARS_M, LARS_ER, LARS_C, LAR...
dbl (44): ID, Patient_Control, ACE_Attention, ACE_Memory, ACE_Fluency, ACE_L...
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Warning: NAs introduced by coercion
Below shows the output and principle components analysis for the hypothesis model with maximal random effect structure (singular fit).
<- glmer (Choice ~ Group* Recipient_s2z* scale (Reward) + * Recipient_s2z* scale (Effort) + 1 + Group* Recipient_s2z* scale (Reward) + Group* Recipient_s2z* scale (Effort) || ID), family= 'binomial' , data= PD.df, control= glmerControl (optimizer= 'bobyqa' , optCtrl= list (maxfun= 2e5 )))
boundary (singular) fit: see help('isSingular')
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula:
Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z *
scale(Effort) + (1 + Group * Recipient_s2z * scale(Reward) +
Group * Recipient_s2z * scale(Effort) || ID)
Data: PD.df
AIC BIC logLik deviance df.resid
4746.882 5206.995 -2310.441 4620.882 10912
Random effects:
Groups Name Std.Dev. Corr
ID (Intercept) 2.14621
ID.1 GroupPD off 0.94436
GroupPD on 1.73342 0.29
ID.2 Recipient_s2zself 1.38673
Recipient_s2zother 1.58506 0.81
ID.3 scale(Reward) 0.00000
ID.4 scale(Effort) 0.01512
ID.5 GroupPD off:Recipient_s2zself 1.68842
GroupPD on:Recipient_s2zself 0.75089 0.40
GroupPD off:Recipient_s2zother 1.43284 0.05 0.01
GroupPD on:Recipient_s2zother 1.31414 -0.67 -0.34 0.58
ID.6 GroupPD off:scale(Reward) 0.62406
GroupPD on:scale(Reward) 0.12628 1.00
ID.7 Recipient_s2zself:scale(Reward) 0.12635
Recipient_s2zother:scale(Reward) 0.08408 -1.00
ID.8 GroupPD off:scale(Effort) 0.04461
GroupPD on:scale(Effort) 0.05304 1.00
ID.9 Recipient_s2zself:scale(Effort) 0.03055
Recipient_s2zother:scale(Effort) 0.03078 1.00
ID.10 GroupPD off:Recipient_s2zself:scale(Reward) 1.31339
GroupPD on:Recipient_s2zself:scale(Reward) 1.62812 0.81
GroupPD off:Recipient_s2zother:scale(Reward) 1.11230 0.86 0.99
GroupPD on:Recipient_s2zother:scale(Reward) 1.46744 0.53 0.92 0.88
ID.11 GroupPD off:Recipient_s2zself:scale(Effort) 1.05065
GroupPD on:Recipient_s2zself:scale(Effort) 1.22862 0.78
GroupPD off:Recipient_s2zother:scale(Effort) 1.11228 1.00 0.76
GroupPD on:Recipient_s2zother:scale(Effort) 1.25223 0.73 1.00 0.71
Number of obs: 10975, groups: ID, 37
Fixed Effects:
(Intercept)
4.66799
GroupPD on
0.20586
Recipient_s2z1
0.93176
scale(Reward)
1.49964
scale(Effort)
-1.44918
GroupPD on:Recipient_s2z1
-0.26075
GroupPD on:scale(Reward)
0.23480
Recipient_s2z1:scale(Reward)
0.14094
GroupPD on:scale(Effort)
-0.00963
Recipient_s2z1:scale(Effort)
0.02481
GroupPD on:Recipient_s2z1:scale(Reward)
-0.11201
GroupPD on:Recipient_s2z1:scale(Effort)
0.04706
optimizer (bobyqa) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings
Remove Group * Recipient * Effort from random effects and convert to two way interactions. Keep Group * Recipient * Reward three-way interaction
<- glmer (Choice ~ Group* Recipient_s2z* scale (Reward) + * Recipient_s2z* scale (Effort) + 1 + Group* Recipient_s2z* scale (Reward) + scale (Effort)* Recipient_s2z + scale (Effort)* Group || ID), family= 'binomial' , data= PD.df, control= glmerControl (optimizer= 'bobyqa' , optCtrl= list (maxfun= 2e5 )))
boundary (singular) fit: see help('isSingular')
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula:
Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z *
scale(Effort) + (1 + Group * Recipient_s2z * scale(Reward) +
scale(Effort) * Recipient_s2z + scale(Effort) * Group || ID)
Data: PD.df
AIC BIC logLik deviance df.resid
4727.436 5114.515 -2310.718 4621.436 10922
Random effects:
Groups Name Std.Dev. Corr
ID (Intercept) 2.537e+00
ID.1 GroupPD off 1.200e+00
GroupPD on 1.426e+00 -0.10
ID.2 Recipient_s2zself 7.520e-01
Recipient_s2zother 1.081e+00 0.40
ID.3 scale(Reward) 6.743e-06
ID.4 scale(Effort) 1.138e-01
ID.5 GroupPD off:Recipient_s2zself 1.427e+00
GroupPD on:Recipient_s2zself 1.067e+00 0.53
GroupPD off:Recipient_s2zother 9.369e-01 -0.56 0.26
GroupPD on:Recipient_s2zother 1.457e+00 -0.56 0.16
ID.6 GroupPD off:scale(Reward) 6.251e-01
GroupPD on:scale(Reward) 1.864e-01 1.00
ID.7 Recipient_s2zself:scale(Reward) 1.186e-01
Recipient_s2zother:scale(Reward) 1.295e-01 -1.00
ID.8 Recipient_s2zself:scale(Effort) 1.022e+00
Recipient_s2zother:scale(Effort) 1.030e+00 1.00
ID.9 GroupPD off:scale(Effort) 3.283e-01
GroupPD on:scale(Effort) 6.864e-01 -0.26
ID.10 GroupPD off:Recipient_s2zself:scale(Reward) 1.327e+00
GroupPD on:Recipient_s2zself:scale(Reward) 1.632e+00 0.80
GroupPD off:Recipient_s2zother:scale(Reward) 1.091e+00 0.87 0.99
GroupPD on:Recipient_s2zother:scale(Reward) 1.444e+00 0.52 0.93
0.85
0.87
Number of obs: 10975, groups: ID, 37
Fixed Effects:
(Intercept)
4.675921
GroupPD on
0.196684
Recipient_s2z1
0.964324
scale(Reward)
1.499867
scale(Effort)
-1.449129
GroupPD on:Recipient_s2z1
-0.274799
GroupPD on:scale(Reward)
0.234028
Recipient_s2z1:scale(Reward)
0.151682
GroupPD on:scale(Effort)
-0.008908
Recipient_s2z1:scale(Effort)
0.017343
GroupPD on:Recipient_s2z1:scale(Reward)
-0.114024
GroupPD on:Recipient_s2z1:scale(Effort)
0.042630
optimizer (bobyqa) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings
Next try removing Group * Recipient * Reward from random effects and convert to two way interactions (keeping Group * Recipient * Effort interaction).
<- glmer (Choice ~ Group* Recipient_s2z* scale (Reward) + * Recipient_s2z* scale (Effort) + 1 + Group* Recipient_s2z* scale (Effort) + scale (Reward)* Recipient_s2z + scale (Reward)* Group || ID), family= 'binomial' , data= PD.df, control= glmerControl (optimizer= 'bobyqa' , optCtrl= list (maxfun= 2e5 )))
boundary (singular) fit: see help('isSingular')
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula:
Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z *
scale(Effort) + (1 + Group * Recipient_s2z * scale(Effort) +
scale(Reward) * Recipient_s2z + scale(Reward) * Group || ID)
Data: PD.df
AIC BIC logLik deviance df.resid
4733.265 5120.344 -2313.633 4627.265 10922
Random effects:
Groups Name Std.Dev. Corr
ID (Intercept) 2.01557
ID.1 GroupPD off 1.52686
GroupPD on 2.01935 0.44
ID.2 Recipient_s2zself 1.17809
Recipient_s2zother 1.42102 0.54
ID.3 scale(Effort) 0.04052
ID.4 scale(Reward) 1.04940
ID.5 GroupPD off:Recipient_s2zself 1.59595
GroupPD on:Recipient_s2zself 0.73656 0.64
GroupPD off:Recipient_s2zother 0.98572 0.02 0.35
GroupPD on:Recipient_s2zother 1.49570 -0.25 0.22 0.77
ID.6 GroupPD off:scale(Effort) 0.10923
GroupPD on:scale(Effort) 0.11596 1.00
ID.7 Recipient_s2zself:scale(Effort) 0.01068
Recipient_s2zother:scale(Effort) 0.01066 1.00
ID.8 Recipient_s2zself:scale(Reward) 0.92726
Recipient_s2zother:scale(Reward) 0.31015 0.97
ID.9 GroupPD off:scale(Reward) 0.40639
GroupPD on:scale(Reward) 1.14781 0.71
ID.10 GroupPD off:Recipient_s2zself:scale(Effort) 1.05807
GroupPD on:Recipient_s2zself:scale(Effort) 1.22409 0.78
GroupPD off:Recipient_s2zother:scale(Effort) 1.07468 1.00 0.76
GroupPD on:Recipient_s2zother:scale(Effort) 1.27385 0.72 1.00 0.71
Number of obs: 10975, groups: ID, 37
Fixed Effects:
(Intercept)
4.610107
GroupPD on
0.301397
Recipient_s2z1
0.991673
scale(Reward)
1.480207
scale(Effort)
-1.439516
GroupPD on:Recipient_s2z1
-0.362802
GroupPD on:scale(Reward)
0.241764
Recipient_s2z1:scale(Reward)
0.163185
GroupPD on:scale(Effort)
-0.032556
Recipient_s2z1:scale(Effort)
0.003744
GroupPD on:Recipient_s2z1:scale(Reward)
-0.149347
GroupPD on:Recipient_s2z1:scale(Effort)
0.079684
optimizer (bobyqa) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings
Next try model only containing (all possible) two way interactions in random effects
<- glmer (Choice ~ Group* Recipient_s2z* scale (Reward) + * Recipient_s2z* scale (Effort) + 1 + Group* Recipient_s2z + Group* scale (Effort) + Group* scale (Reward) + scale (Reward)* Recipient_s2z + scale (Reward)* Group + scale (Effort)* Recipient_s2z + scale (Effort)* Group || ID), family= 'binomial' , data= PD.df, control= glmerControl (optimizer= 'bobyqa' , optCtrl= list (maxfun= 2e5 )))
boundary (singular) fit: see help('isSingular')
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula:
Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z *
scale(Effort) + (1 + Group * Recipient_s2z + Group * scale(Effort) +
Group * scale(Reward) + scale(Reward) * Recipient_s2z + scale(Reward) *
Group + scale(Effort) * Recipient_s2z + scale(Effort) * Group || ID)
Data: PD.df
AIC BIC logLik deviance df.resid
4713.783 5027.828 -2313.891 4627.783 10932
Random effects:
Groups Name Std.Dev. Corr
ID (Intercept) 2.1837677
ID.1 GroupPD off 1.2457169
GroupPD on 1.8084785 0.45
ID.2 Recipient_s2zself 1.2525408
Recipient_s2zother 1.5362644 0.40
ID.3 scale(Effort) 0.0004292
ID.4 scale(Reward) 0.8586418
ID.5 GroupPD off:Recipient_s2zself 1.6004410
GroupPD on:Recipient_s2zself 0.7793218 0.25
GroupPD off:Recipient_s2zother 0.7864164 0.22 0.07
GroupPD on:Recipient_s2zother 1.3506402 -0.38 0.46 0.32
ID.6 GroupPD off:scale(Effort) 0.1826596
GroupPD on:scale(Effort) 0.6807199 -0.84
ID.7 GroupPD off:scale(Reward) 0.4179265
GroupPD on:scale(Reward) 1.1534829 0.72
ID.8 Recipient_s2zself:scale(Reward) 1.1174467
Recipient_s2zother:scale(Reward) 0.6530178 0.87
ID.9 Recipient_s2zself:scale(Effort) 1.0584458
Recipient_s2zother:scale(Effort) 1.0497424 1.00
Number of obs: 10975, groups: ID, 37
Fixed Effects:
(Intercept)
4.6128104
GroupPD on
0.2987193
Recipient_s2z1
1.0103610
scale(Reward)
1.4788458
scale(Effort)
-1.4400608
GroupPD on:Recipient_s2z1
-0.3489802
GroupPD on:scale(Reward)
0.2439612
Recipient_s2z1:scale(Reward)
0.1692088
GroupPD on:scale(Effort)
-0.0281807
Recipient_s2z1:scale(Effort)
-0.0007723
GroupPD on:Recipient_s2z1:scale(Reward)
-0.1404463
GroupPD on:Recipient_s2z1:scale(Effort)
0.0688750
optimizer (bobyqa) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings
summary (rePCA (maxmax.red3.PDonvsPDoff))
$ID
Importance of components:
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
Standard deviation 2.1838 1.9349 1.7577 1.6798 1.49073 1.32780 1.26327
Proportion of Variance 0.1851 0.1453 0.1199 0.1095 0.08624 0.06842 0.06193
Cumulative Proportion 0.1851 0.3303 0.4502 0.5597 0.64599 0.71441 0.77634
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
Standard deviation 1.19494 1.05226 1.03859 0.85864 0.7580 0.69813 0.42937
Proportion of Variance 0.05541 0.04297 0.04186 0.02861 0.0223 0.01891 0.00715
Cumulative Proportion 0.83176 0.87472 0.91659 0.94520 0.9675 0.98641 0.99356
[,15] [,16] [,17] [,18] [,19]
Standard deviation 0.28154 0.2781 0.09677 0.0004292 0
Proportion of Variance 0.00308 0.0030 0.00036 0.0000000 0
Cumulative Proportion 0.99664 0.9996 1.00000 1.0000000 1
Singular fit. Remove recipient:effort as correlation of 1
<- glmer (Choice ~ Group* Recipient_s2z* scale (Reward) + * Recipient_s2z* scale (Effort) + 1 + Group* Recipient_s2z + Group* scale (Effort) + Group* scale (Reward) + scale (Reward)* Recipient_s2z + scale (Reward)* Group + scale (Effort)* Group || ID), family= 'binomial' , data= PD.df, control= glmerControl (optimizer= 'bobyqa' , optCtrl= list (maxfun= 2e5 )))
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula:
Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z *
scale(Effort) + (1 + Group * Recipient_s2z + Group * scale(Effort) +
Group * scale(Reward) + scale(Reward) * Recipient_s2z + scale(Reward) *
Group + scale(Effort) * Group || ID)
Data: PD.df
AIC BIC logLik deviance df.resid
4707.790 4999.925 -2313.895 4627.790 10935
Random effects:
Groups Name Std.Dev. Corr
ID (Intercept) 2.2235
ID.1 GroupPD off 1.2331
GroupPD on 1.8712 0.45
ID.2 Recipient_s2zself 1.1686
Recipient_s2zother 1.5370 0.33
ID.3 scale(Effort) 0.7876
ID.4 scale(Reward) 0.9636
ID.5 GroupPD off:Recipient_s2zself 1.6147
GroupPD on:Recipient_s2zself 0.6215 0.30
GroupPD off:Recipient_s2zother 0.6963 0.27 0.02
GroupPD on:Recipient_s2zother 1.1942 -0.44 0.33 0.17
ID.6 GroupPD off:scale(Effort) 0.7222
GroupPD on:scale(Effort) 0.9751 0.54
ID.7 GroupPD off:scale(Reward) 0.4462
GroupPD on:scale(Reward) 1.1633 0.72
ID.8 Recipient_s2zself:scale(Reward) 1.0145
Recipient_s2zother:scale(Reward) 0.4611 0.90
Number of obs: 10975, groups: ID, 37
Fixed Effects:
(Intercept)
4.6119728
GroupPD on
0.2983879
Recipient_s2z1
1.0068875
scale(Reward)
1.4786511
scale(Effort)
-1.4404275
GroupPD on:Recipient_s2z1
-0.3486789
GroupPD on:scale(Reward)
0.2437653
Recipient_s2z1:scale(Reward)
0.1678096
GroupPD on:scale(Effort)
-0.0280351
Recipient_s2z1:scale(Effort)
0.0002695
GroupPD on:Recipient_s2z1:scale(Reward)
-0.1402762
GroupPD on:Recipient_s2z1:scale(Effort)
0.0683914
This model converges and seems to be the most complex possible structure.
The following shows the summary output and principle components analysis, and comparison with complex model
summary (maxmax.red4.PDonvsPDoff)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula:
Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z *
scale(Effort) + (1 + Group * Recipient_s2z + Group * scale(Effort) +
Group * scale(Reward) + scale(Reward) * Recipient_s2z + scale(Reward) *
Group + scale(Effort) * Group || ID)
Data: PD.df
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))
AIC BIC logLik deviance df.resid
4707.8 4999.9 -2313.9 4627.8 10935
Scaled residuals:
Min 1Q Median 3Q Max
-104.173 0.009 0.048 0.181 13.436
Random effects:
Groups Name Variance Std.Dev. Corr
ID (Intercept) 4.9438 2.2235
ID.1 GroupPD off 1.5205 1.2331
GroupPD on 3.5014 1.8712 0.45
ID.2 Recipient_s2zself 1.3657 1.1686
Recipient_s2zother 2.3625 1.5370 0.33
ID.3 scale(Effort) 0.6203 0.7876
ID.4 scale(Reward) 0.9285 0.9636
ID.5 GroupPD off:Recipient_s2zself 2.6073 1.6147
GroupPD on:Recipient_s2zself 0.3863 0.6215 0.30
GroupPD off:Recipient_s2zother 0.4849 0.6963 0.27 0.02
GroupPD on:Recipient_s2zother 1.4261 1.1942 -0.44 0.33 0.17
ID.6 GroupPD off:scale(Effort) 0.5216 0.7222
GroupPD on:scale(Effort) 0.9509 0.9751 0.54
ID.7 GroupPD off:scale(Reward) 0.1991 0.4462
GroupPD on:scale(Reward) 1.3533 1.1633 0.72
ID.8 Recipient_s2zself:scale(Reward) 1.0292 1.0145
Recipient_s2zother:scale(Reward) 0.2126 0.4611 0.90
Number of obs: 10975, groups: ID, 37
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.6119728 0.5195696 8.877 < 2e-16
GroupPD on 0.2983879 0.4462602 0.669 0.5037
Recipient_s2z1 1.0068875 0.2405970 4.185 2.85e-05
scale(Reward) 1.4786511 0.2364835 6.253 4.04e-10
scale(Effort) -1.4404275 0.1990988 -7.235 4.66e-13
GroupPD on:Recipient_s2z1 -0.3486789 0.2047100 -1.703 0.0885
GroupPD on:scale(Reward) 0.2437653 0.2100617 1.160 0.2459
Recipient_s2z1:scale(Reward) 0.1678096 0.0977907 1.716 0.0862
GroupPD on:scale(Effort) -0.0280351 0.1899532 -0.148 0.8827
Recipient_s2z1:scale(Effort) 0.0002695 0.0687693 0.004 0.9969
GroupPD on:Recipient_s2z1:scale(Reward) -0.1402762 0.1044689 -1.343 0.1794
GroupPD on:Recipient_s2z1:scale(Effort) 0.0683914 0.0942539 0.726 0.4681
(Intercept) ***
GroupPD on
Recipient_s2z1 ***
scale(Reward) ***
scale(Effort) ***
GroupPD on:Recipient_s2z1 .
GroupPD on:scale(Reward)
Recipient_s2z1:scale(Reward) .
GroupPD on:scale(Effort)
Recipient_s2z1:scale(Effort)
GroupPD on:Recipient_s2z1:scale(Reward)
GroupPD on:Recipient_s2z1:scale(Effort)
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpPDo Rcp_21 scl(R) scl(E) GrPDo:R_21 GPDo:(R R_21:(R
GroupPD on -0.314
Recpnt_s2z1 0.176 -0.266
scale(Rwrd) 0.104 -0.094 0.083
scal(Effrt) -0.095 0.090 -0.049 -0.054
GrpPDo:R_21 -0.175 0.241 -0.534 -0.069 0.054
GrpPDon:(R) -0.094 0.275 -0.056 -0.095 0.054 0.115
Rcpn_21:(R) 0.083 -0.057 0.301 0.370 -0.029 -0.241 -0.103
GrpPDon:(E) 0.079 -0.225 0.038 0.048 -0.297 -0.077 -0.141 0.019
Rcpn_21:(E) -0.047 0.035 -0.267 -0.020 0.096 0.271 0.012 -0.236
GPDo:R_21:(R -0.057 0.083 -0.211 -0.083 0.027 0.451 0.138 -0.525
GPDo:R_21:(E 0.028 -0.037 0.168 0.014 -0.065 -0.370 -0.014 0.145
GPDo:(E R_21:(E GPDo:R_21:(R
GroupPD on
Recpnt_s2z1
scale(Rwrd)
scal(Effrt)
GrpPDo:R_21
GrpPDon:(R)
Rcpn_21:(R)
GrpPDon:(E)
Rcpn_21:(E) -0.090
GPDo:R_21:(R -0.034 0.199
GPDo:R_21:(E 0.098 -0.698 -0.282
summary (rePCA (maxmax.red4.PDonvsPDoff))
$ID
Importance of components:
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
Standard deviation 2.2235 1.9883 1.7552 1.6239 1.20967 1.10256 1.09882
Proportion of Variance 0.2025 0.1619 0.1262 0.1080 0.05994 0.04979 0.04946
Cumulative Proportion 0.2025 0.3644 0.4906 0.5986 0.65855 0.70835 0.75780
[,8] [,9] [,10] [,11] [,12] [,13] [,14]
Standard deviation 1.08443 1.0446 1.03375 0.96360 0.78760 0.66755 0.54453
Proportion of Variance 0.04817 0.0447 0.04377 0.03803 0.02541 0.01825 0.01215
Cumulative Proportion 0.80597 0.8507 0.89444 0.93247 0.95788 0.97613 0.98828
[,15] [,16] [,17]
Standard deviation 0.40321 0.29851 0.18562
Proportion of Variance 0.00666 0.00365 0.00141
Cumulative Proportion 0.99494 0.99859 1.00000
anova (maxmax.red0.PDonvsPDoff, maxmax.red4.PDonvsPDoff)
Data: PD.df
Models:
maxmax.red4.PDonvsPDoff: Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z * scale(Effort) + (1 + Group * Recipient_s2z + Group * scale(Effort) + Group * scale(Reward) + scale(Reward) * Recipient_s2z + scale(Reward) * Group + scale(Effort) * Group || ID)
maxmax.red0.PDonvsPDoff: Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z * scale(Effort) + (1 + Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z * scale(Effort) || ID)
npar AIC BIC logLik deviance Chisq Df
maxmax.red4.PDonvsPDoff 40 4707.8 4999.9 -2313.9 4627.8
maxmax.red0.PDonvsPDoff 63 4746.9 5207.0 -2310.4 4620.9 6.9078 23
Pr(>Chisq)
maxmax.red4.PDonvsPDoff
maxmax.red0.PDonvsPDoff 0.9995
This shows that the reduced model is not inferior to the singular-fitting maximal model
Finally, as per Bates et al, I will build the same model but with correlation parameter
<- glmer (Choice ~ Group* Recipient_s2z* scale (Reward) + * Recipient_s2z* scale (Effort) + 1 + Group* Recipient_s2z + Group* scale (Effort) + Group* scale (Reward) + scale (Reward)* Recipient_s2z + scale (Reward)* Group + scale (Effort)* Group | ID), family= 'binomial' , data= PD.df, control= glmerControl (optimizer= 'bobyqa' , optCtrl= list (maxfun= 2e5 )))
summary (maxmax.red4corr.PDonvsPDoff)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula:
Choice ~ Group * Recipient_s2z * scale(Reward) + Group * Recipient_s2z *
scale(Effort) + (1 + Group * Recipient_s2z + Group * scale(Effort) +
Group * scale(Reward) + scale(Reward) * Recipient_s2z + scale(Reward) *
Group + scale(Effort) * Group | ID)
Data: PD.df
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))
AIC BIC logLik deviance df.resid
4701.0 5117.3 -2293.5 4587.0 10918
Scaled residuals:
Min 1Q Median 3Q Max
-121.296 0.008 0.047 0.181 14.307
Random effects:
Groups Name Variance Std.Dev. Corr
ID (Intercept) 8.7303 2.9547
GroupPD on 5.2725 2.2962 -0.28
Recipient_s2z1 1.5141 1.2305 -0.04 -0.28
scale(Effort) 1.2697 1.1268 0.27 0.08 0.21
scale(Reward) 1.7014 1.3044 0.42 -0.06 0.16 -0.11
GroupPD on:Recipient_s2z1 0.3700 0.6083 -0.02 0.19 -0.47 0.11
GroupPD on:scale(Effort) 0.7991 0.8939 -0.03 -0.20 0.07 -0.26
GroupPD on:scale(Reward) 1.0313 1.0155 -0.10 0.17 -0.56 0.01
Recipient_s2z1:scale(Reward) 0.1616 0.4019 -0.25 -0.08 0.88 0.13
-0.33
-0.18 -0.28
-0.08 0.40 -0.06
0.25 -0.48 -0.27 -0.58
Number of obs: 10975, groups: ID, 37
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.65860 0.53996 8.628 < 2e-16
GroupPD on 0.24239 0.50946 0.476 0.634241
Recipient_s2z1 0.88953 0.26796 3.320 0.000901
scale(Reward) 1.78506 0.27350 6.527 6.72e-11
scale(Effort) -1.32823 0.21855 -6.078 1.22e-09
GroupPD on:Recipient_s2z1 -0.30530 0.22499 -1.357 0.174786
GroupPD on:scale(Reward) 0.12295 0.28794 0.427 0.669376
Recipient_s2z1:scale(Reward) 0.17421 0.13497 1.291 0.196809
GroupPD on:scale(Effort) -0.03339 0.22862 -0.146 0.883888
Recipient_s2z1:scale(Effort) 0.02133 0.06991 0.305 0.760321
GroupPD on:Recipient_s2z1:scale(Reward) -0.20496 0.11518 -1.779 0.075160
GroupPD on:Recipient_s2z1:scale(Effort) 0.06411 0.09702 0.661 0.508761
(Intercept) ***
GroupPD on
Recipient_s2z1 ***
scale(Reward) ***
scale(Effort) ***
GroupPD on:Recipient_s2z1
GroupPD on:scale(Reward)
Recipient_s2z1:scale(Reward)
GroupPD on:scale(Effort)
Recipient_s2z1:scale(Effort)
GroupPD on:Recipient_s2z1:scale(Reward) .
GroupPD on:Recipient_s2z1:scale(Effort)
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) GrpPDo Rcp_21 scl(R) scl(E) GrPDo:R_21 GPDo:(R R_21:(R
GroupPD on -0.375
Recpnt_s2z1 0.100 -0.262
scale(Rwrd) 0.499 -0.219 0.224
scal(Effrt) 0.099 0.172 0.090 -0.118
GrpPDo:R_21 -0.117 0.257 -0.498 -0.202 0.097
GrpPDon:(R) -0.224 0.474 -0.332 -0.351 0.060 0.205
Rcpn_21:(R) 0.006 -0.103 0.721 0.301 0.049 -0.322 -0.284
GrpPDon:(E) 0.078 -0.345 0.059 -0.050 -0.414 -0.163 -0.119 -0.101
Rcpn_21:(E) -0.040 0.037 -0.222 0.002 0.099 0.260 -0.003 -0.134
GPDo:R_21:(R -0.062 0.094 -0.189 -0.099 0.023 0.441 0.145 -0.412
GPDo:R_21:(E 0.024 -0.047 0.141 -0.008 -0.068 -0.359 0.007 0.071
GPDo:(E R_21:(E GPDo:R_21:(R
GroupPD on
Recpnt_s2z1
scale(Rwrd)
scal(Effrt)
GrpPDo:R_21
GrpPDon:(R)
Rcpn_21:(R)
GrpPDon:(E)
Rcpn_21:(E) -0.091
GPDo:R_21:(R -0.039 0.172
GPDo:R_21:(E 0.115 -0.697 -0.248