I've been looking at mixed effects modelling using the lme4 package in R. I'm primarily using the
lmer command so I'll pose my question through code that uses that syntax. I suppose a general easy question might be, is it OK to compare any two models constructed in
lmer using likelihood ratios based on identical datasets? I believe the answer to that must be, "no", but I could be incorrect. I've read conflicting information on whether the random effects have to be the same or not, and what component of the random effects is meant by that? So, I'll present a few examples. I'll take them from repeated measures data using word stimuli, perhaps something like Baayen (2008) would be useful in interpreting.
Let's say I have a model where there are two fixed effects predictors, we'll call them A, and B, and some random effects... words and subjects that perceived them. I might construct a model like the following.
m <- lmer( y ~ A + B + (1|words) + (1|subjects) )
(note that I've intentionally left out
data = and we'll assume I always mean
REML = FALSE for clarity's sake)
Now, of the following models, which are OK to compare with a likelihood ratio to the one above and which are not?
m1 <- lmer( y ~ A + B + (A+B|words) + (1|subjects) ) m2 <- lmer( y ~ A + B + (1|subjects) ) m3 <- lmer( y ~ A + B + (C|words) + (A+B|subjects) ) m4 <- lmer( y ~ A + B + (1|words) ) m5 <- lmer( y ~ A * B + (1|subjects) )
I acknowledge that the interpretation of some of these differences may be difficult, or impossible. But let's put that aside for a second. I just want to know if there's something fundamental in the changes here that precludes the possibility of comparing. I also want to know whether, if LRs are OK, and AIC comparisons as well.