MCMC – How to Perform an MCMC Hypothesis Test on a Mixed Effect Regression Model with Random Slopes

mixed modelmonte carlorstatistical significance

The library languageR provides a method (pvals.fnc) to do MCMC significance testing of the fixed effects in a mixed effect regression model fit using lmer. However, pvals.fnc gives an error when the lmer model includes random slopes.

Is there a way to do an MCMC hypothesis test of such models?
If so, how? (To be accepted an answer should have a worked example in R)
If not, is there a conceptual/computation reason why there is no way?

This question might be related to this one but I didn't understand the content there well enough to be certain.

Edit 1: A proof of concept showing that pvals.fnc() still does 'something' with lme4 models, but that it doesn't do anything with random slope models.

library(lme4)
library(languageR)
#the example from pvals.fnc
data(primingHeid) 
# remove extreme outliers
primingHeid = primingHeid[primingHeid$RT < 7.1,]
# fit mixed-effects model
primingHeid.lmer = lmer(RT ~ RTtoPrime * ResponseToPrime + Condition + (1|Subject) + (1|Word), data = primingHeid)
mcmc = pvals.fnc(primingHeid.lmer, nsim=10000, withMCMC=TRUE)
#Subjects are in both conditions...
table(primingHeid$Subject,primingHeid$Condition)
#So I can fit a model that has a random slope of condition by participant
primingHeid.lmer.rs = lmer(RT ~ RTtoPrime * ResponseToPrime + Condition + (1+Condition|Subject) + (1|Word), data = primingHeid)
#However pvals.fnc fails here...
mcmc.rs = pvals.fnc(primingHeid.lmer.rs)

It says: Error in pvals.fnc(primingHeid.lmer.rs) :
MCMC sampling is not yet implemented in lme4_0.999375
for models with random correlation parameters

Additional question: Is pvals.fnc performing as expected for random intercept model? Should the outputs be trusted?

Best Answer

It looks like your error message isn't about varying slopes, it is about correlated random effects. You can fit the uncorrelated as well; that is, a mixed-effects model with independent random effects: 

Linear mixed model fit by REML
Formula: Reaction ~ Days + (1 | Subject) + (0 + Days | Subject)
Data: sleepstudy

from http://www.stat.wisc.edu/~bates/IMPS2008/lme4D.pdf

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