In dmbates/RePsychLing: Data sets from Psychology and Linguistics experiments

library(RePsychLing)
library(lme4)
library(knitr)
opts_chunk$set(comment=NA)
options(width=92,show.signif.stars = FALSE)

Data from @Gann:Barr:2014

These data, also used in the online supplement to @Barr:Levy:Scheepers:Tily:13, are available as gb12 in the RePsychLing package.

str(gb12)
summary(gb12)

Maximal linear mixed model (maxLMM)

We assume P, the partner, is a between-session factor and F, feedback, is a between-item factor (i.e., they are not included in RE terms). The model fit in the paper is:

m0 <- lmer(
    sottrunc2 ~ 1+T+P+F+TP+TF+PF+TPF+(1+T+F+TF|session)+(1+T+P+TP|item),
    gb12, REML=FALSE, start=thcvg$gb12$m0,
    control=lmerControl(optimizer="Nelder_Mead",optCtrl=list(maxfun=1L),
                        check.conv.grad="ignore",check.conv.hess="ignore"))
print(summary(m0),corr=FALSE)

The model converges without problems, but two correlation parameters are estimated as 1.

Principal components analysis for maxLMM

summary(rePCA(m0))

The PCA results indicate two dimensions with no variability in the random effects for session and another two dimensions in the random effects for item.

Zero-correlation-parameter linear mixed model (zcpLMM)

m1 <- 
  lmer(sottrunc2 ~ 1+T+P+F+TP+TF+PF+TPF + (1+T+F+TF||session) + (1+T+P+TP||item),
       gb12, REML=FALSE)
VarCorr(m1)
anova(m1, m0)

The zcpLMM fits significantly worse than the maxLMM, but it reveals several variance components with values close to or of zero.

Iterative reduction of model complexity

Let's refit the model without small variance components.

m2 <-
  lmer(sottrunc2 ~ 1+T+P+F+TP+TF+PF+TPF + (1+T+F||session) + (1+T||item), 
       gb12, REML=FALSE)
VarCorr(m2)
anova(m2, m1, m0)

Let's check the support of item-related variance components

m3 <-
  lmer(sottrunc2 ~ 1+T+P+F+TP+TF+PF+TPF + (1+T+F||session) + (1|item),
       gb12, REML=FALSE)
VarCorr(m3)
anova(m3, m2)

Marginally significant drop. (Deleting the intercept too leads to a significant drop in goodness of fit.)

Extending the reduced LMM with correlation parameters

Let's check correlation parameters for item

m4 <- 
  lmer(sottrunc2 ~ 1+T+P+F+TP+TF+PF+TPF + (1+T+F|session) + (1|item), 
       gb12, REML=FALSE)
VarCorr(m4)
anova(m3, m4)

The correlation parameter is significant, but one correlation is 1.000, indicating a singular model. Let's remove the small correlation parameters.

Pruning small correlation parameters

m5 <-
  lmer(sottrunc2 ~ 1+T+P+F+TP+TF+PF+TPF + (1+F|session) + (0+T|session) + (1|item),
       gb12, REML=FALSE)
VarCorr(m5)
anova(m5, m4)

Now the model is clearly degenerate: The correlation is at the boundary (-1); theta returns a zero value for one of the variance components.

Summary

Versions of packages used

sessionInfo()

References

dmbates/RePsychLing documentation built on May 15, 2019, 9:19 a.m.