Estimate full probit model

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( mafc.probit(2) )
## Formula: Acc ~ Coh + Speed + PatternType + Coh:Speed + Coh:PatternType +  
##     (1 | SubID)
##    Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   9838.6   9888.9  -4912.3   9824.6     9753 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -16.7910  -1.0133   0.3573   0.6518   0.9999 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  SubID  (Intercept) 0.395    0.6285  
## Number of obs: 9760, groups:  SubID, 30
## 
## Fixed effects:
##                       Estimate Std. Error z value Pr(>|z|)    
## (Intercept)           -1.35496    0.20236  -6.696 2.15e-11 ***
## Coh                   10.34119    1.11795   9.250  < 2e-16 ***
## Speed                 -0.07424    0.02746  -2.704  0.00685 ** 
## PatternTyperadial     -0.74667    0.16371  -4.561 5.09e-06 ***
## Coh:Speed              0.31080    0.18393   1.690  0.09108 .  
## Coh:PatternTyperadial  8.69144    1.12074   7.755 8.83e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Coh    Speed  PttrnT Ch:Spd
## Coh         -0.770                            
## Speed       -0.607  0.697                     
## PttrnTyprdl -0.389  0.435  0.069              
## Coh:Speed    0.578 -0.757 -0.941 -0.057       
## Ch:PttrnTyp  0.343 -0.434 -0.064 -0.940  0.051

Estimate reduced model

Drop Coh:Speed.

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( mafc.probit(2) )
## Formula: Acc ~ Coh + Speed + PatternType + (1 | SubID) + Coh:PatternType
##    Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   9839.5   9882.7  -4913.8   9827.5     9754 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -17.9258  -1.0129   0.3548   0.6490   0.9999 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  SubID  (Intercept) 0.3954   0.6288  
## Number of obs: 9760, groups:  SubID, 30
## 
## Fixed effects:
##                        Estimate Std. Error z value Pr(>|z|)    
## (Intercept)           -1.557017   0.165541  -9.406  < 2e-16 ***
## Coh                   11.798343   0.722069  16.340  < 2e-16 ***
## Speed                 -0.030784   0.009228  -3.336  0.00085 ***
## PatternTyperadial     -0.732936   0.161144  -4.548 5.41e-06 ***
## Coh:PatternTyperadial  8.614064   1.103524   7.806 5.90e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Coh    Speed  PttrnT
## Coh         -0.624                     
## Speed       -0.255 -0.029              
## PttrnTyprdl -0.431  0.597  0.050       
## Ch:PttrnTyp  0.379 -0.602 -0.052 -0.939

Now, we compare this reduced model to the full model.

## Data: df
## Models:
## mod.reduced.1: Acc ~ Coh + Speed + PatternType + (1 | SubID) + Coh:PatternType
## mod.full: Acc ~ Coh + Speed + PatternType + Coh:Speed + Coh:PatternType + 
## mod.full:     (1 | SubID)
##               Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)  
## mod.reduced.1  6 9839.5 9882.7 -4913.8   9827.5                           
## mod.full       7 9838.6 9888.9 -4912.3   9824.6 2.9338      1    0.08675 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The reduced model doesn’t change the fit that much, but we prefer simpler models overall, so we will retain it.