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

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

Data from @barrseyfedd2010

Some of the data from @barrseyfedd2010 are available as the data frame bs10 in the RePsychLing package.

str(bs10)

As with other data frames in this package, the subject and item factors are called subj and item. The response being modelled, dif, is the difference in two response times.

The two experimental factors S and F, both at two levels, are represented in the -1/+1 encoding, as is their interaction, SF. The S factor is the speaker condition with levels -1 for the same speaker in both trials and +1 for different speakers. The F factor is the filler condition with levels -1 for NS and +1 for FP.

Maximal linear mixed model (maxLMM)

The maximal model has a full factorial design 1+S+F+SF for the fixed-effects and for potentially correlated vector-valued random effects for subj and for item. We use the parameter estimates from an lmm fit using the MixedModels package package for Julia, which can be much faster than fitting this model with lmer. (In addition to being faster, the fit from lmm produced a significantly lower deviance.)

m0 <- lmer(dif ~ 1+S+F+SF + (1+S+F+SF|subj) + (1+S+F+SF|item), bs10, REML=FALSE, start=thcvg$bs10$m0,
           control=lmerControl(optimizer="Nelder_Mead",optCtrl=list(maxfun=1L),
                               check.conv.grad="ignore",check.conv.hess="ignore"))
summary(m0)

The model converges with warnings. Six of 12 correlation parameters are estimated at the +/-1 boundary.

Notice that there are only 12 items. Expecting to estimate 4 variances and 6 covariances from 12 items is optimistic.

PCA analysis of the maxLMM

A summary of a principal components analysis (PCA) of the random-effects variance-covariance matrices shows

summary(rePCA(m0))

For both the by-subject and the by-item random effects the estimated variance-covariance matrices are singular. There are at least 2 dimensions with no variation in the subject-related random-effects and 3 directions with no variation for the item-related random-effects.

Clearly the model is over-specified.

Zero-correlation-parameter linear mixed model (zcpLMM)

A zero-correlation-parameter model fits independent random effects for the intercept, the experimental factors and their interaction for each of the subj and item grouping factors. It can be conveniently specified using the || operator in the random-effects terms.

print(summary(m1 <- lmer(dif ~ 1+S+F+SF + (1+S+F+SF||subj) + (1+S+F+SF||item), bs10, REML=FALSE)), corr=FALSE)
anova(m1, m0)

The zcpLMM fits significantly worse than the maxLMM. However, the results strongly suggest that quite a few of the variance components are not supported by the data.

PCA for the zcpLMM

summary(rePCA(m1))

The random effect for filler, F, by subject has essentially zero variance and the random effect for the interaction, SF, accounts for less than 15% of the total variation in the random effects. There is no evidence for item-related random effects in m1.

Iterative reduction of model complexity

Remove all variance components estimated with a value of zero.

print(summary(m2 <- lmer(dif ~ 1+S+F+SF +  (1+S+SF||subj), bs10,  REML=FALSE)), corr=FALSE)

Naturally, the fit for this model is equivalent to that for m1 because it is only the variance components with zero estimates that are eliminated.

anova(m2,m1)

Next we check whether the variance component for the interaction, SF, could reasonably be zero.

print(summary(m3 <- lmer(dif ~ 1+S+F+SF +  (1+S||subj), bs10, REML=FALSE)), corr=FALSE)
anova(m3, m2)

Not quite significant, but could be considered. The fit is still worse than for the maxLMM m0. We now reintroduce a correlation parameters in the vector-valued random effects for subj.

Extending the reduced LMM with correlation parameters

print(summary(m4 <- lmer(dif ~ 1+S+F+SF + (1+S|subj), bs10,  REML=FALSE)), corr=FALSE)
anova(m3, m4, m0)

Looks like we have evidence for a significant correlation parameter. Moreover, LMM m4 fits as well as maxLMM.

Summary

LMM m4 is the optimal model. It might be worth while to check the theoretical contribution of the correlation parameter.

Versions of packages used

sessionInfo()

References

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