Solved – How to specify partially crossed random effect in lme

lme4-nlmemixed modelr

I am new to R and would like your help with lme formula for partially crossed random effect in a random-intercept, random-slope model. In the longitudinal data I have, each subject (barring some dropouts) was tested at 5 different occasions. The standardized tests were administered by 3 different examiners, with 2 of them present at all occasions, and the 3rd one administering tests only on the last two occasions. The subjects were randomly assigned to the examiners.

Mock data: 

data <- data.frame(subject=rep(A,5), time=1:5, examiner=c(2,1,2,2,3), 
                   covariate=c(1,1.3,0.8,1,0.6), score=c(46,56,60,68,70))

I tested the following models:

>model1 <- lme(score~time*covariate, random=~time|subject, method="REML", 
               na.action=na.omit, data=dat)
>model2 <- lme(score~time*covariate, random=list(examiner=~1,subject=~time), 
               method="REML", na.action=na.omit, data=dat)

>anova(model1, model2) #gives p<0.05 with better model fit for model2.

I would like to know if model2 is the correct way to specify the partially
crossed random effect in the data I described.

Best Answer

This is not a direct answer for lme's syntax.

I would argue that while in theory a specific examiner is part of the greater examiner population and it does make sense to have it as a random effect, you have only 2 (and occasionally 3) replicates. It will most probably be more sensible to use it as fixed effect (possibly as an interaction).

Moreover I would not be too fast to jump on ANOVA for model selection. Assuming you do not want to consider issues of cross-validation etc., maybe an information criterion like AIC will be equally easy to apply and probably slightly more coherent.

I think your first model is quite reasonable as it stands. Maybe try a (0+time|subject)+(1|subject) random structure so that you will fit independently the slope and the intercept of the model...

I scavenged this thread from R-sig-mixed (I had also seen your question there about a fortnight ago) and these two older ones from R-help (thread1, thread2) that might be helpful as they contain some expert opinions on the matter.

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