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 
##   5628.1   5678.0  -2807.0   5614.1     9273 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -35.939   0.103   0.239   0.399   0.890 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  SubID  (Intercept) 0.2317   0.4813  
## Number of obs: 9280, groups:  SubID, 29
## 
## Fixed effects:
##                        Estimate Std. Error z value Pr(>|z|)    
## (Intercept)           -0.803185   0.158934  -5.054 4.34e-07 ***
## Coh                    2.979081   0.318422   9.356  < 2e-16 ***
## Speed                 -0.007001   0.019622  -0.357 0.721268    
## PatternTyperadial      0.795109   0.118030   6.736 1.62e-11 ***
## Coh:Speed              0.197364   0.051216   3.854 0.000116 ***
## Coh:PatternTyperadial -0.598986   0.302907  -1.977 0.047990 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Coh    Speed  PttrnT Ch:Spd
## Coh         -0.748                            
## Speed       -0.618  0.692                     
## PttrnTyprdl -0.407  0.450  0.034              
## Coh:Speed    0.523 -0.733 -0.890 -0.023       
## Ch:PttrnTyp  0.340 -0.463 -0.029 -0.890  0.030

Estimate reduced model

Drop Coh:PatternType from model.

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( mafc.probit(2) )
## Formula: Acc ~ Coh + Speed + PatternType + (1 | SubID) + Coh:Speed
##    Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   5630.0   5672.8  -2809.0   5618.0     9274 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -30.2531   0.1012   0.2383   0.4000   0.8800 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  SubID  (Intercept) 0.2308   0.4805  
## Number of obs: 9280, groups:  SubID, 29
## 
## Fixed effects:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       -0.699940   0.148736  -4.706 2.53e-06 ***
## Coh                2.695789   0.281955   9.561  < 2e-16 ***
## Speed             -0.008061   0.019514  -0.413     0.68    
## PatternTyperadial  0.588726   0.053920  10.918  < 2e-16 ***
## Coh:Speed          0.200462   0.051129   3.921 8.83e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Coh    Speed  PttrnT
## Coh         -0.707                     
## Speed       -0.646  0.765              
## PttrnTyprdl -0.238  0.090  0.016       
## Coh:Speed    0.544 -0.811 -0.889  0.013

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

## Data: df
## Models:
## mod.reduced.1: Acc ~ Coh + Speed + PatternType + (1 | SubID) + Coh:Speed
## 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 5630.0 5672.8  -2809   5618.0                           
## mod.full       7 5628.1 5678.0  -2807   5614.1 3.9038      1    0.04818 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

This improves the fit. We observe that this model says p(correct) increases with increasing coherence, is larger for radial patterns, and the slope of the coherence by p(correct) relation is steeper at the faster (8 deg/s) speed.

Testing age effect

Our plots suggest that there may be an effect of age in years. So, we estimate the influence of age in years as a fixed effect.

The model including age in years has a better fit. We note that the p(corr) is larger for each of the age groups, and that there is an ordinal relationship to the age-related influences on p(corr).