Can you use two crossed random effects when you have many levels (50+) of both? This mixed effects model is fitting atrophy in many brain regions (n=242) in a set of subjects (n=71). I have two predictors, pathlength and hazard. These vary across region, in a way that is different for each subject. I am including crossed random intercepts for region and subject.
lme_atrophy <- lmer(atrophy ~ pathlength + hazard + (1|region) + (1|subject), data = regions)
When I fit the model, pathlength and hazard are both significant predictors:
Random effects: Groups Name Variance Std.Dev. region (Intercept) 0.003332 0.05772 subject (Intercept) 0.006103 0.07812 Residual 0.014649 0.12103 Number of obs: 36784, groups: region, 242; subject, 71 Fixed effects: Estimate Std. Error t value (Intercept) 0.115157 0.010778 10.684 pathlength -0.025014 0.001716 -14.574 hazard -0.010363 0.002739 -3.784
The purpose of the model is to predict atrophy for a given subject in all 242 regions, and for the predictions to be diverse for different subjects. The problem is that the 242x1 fitted values of atrophy for different subjects end up being very highly correlated with each other - it's basically fitting the mean spatial pattern. The random intercept for region seems to dominate the estimates:
sem.model.fits(lme_atrophy) Class Family Link n Marginal Conditional 1 lmerMod gaussian identity 36784 0.009429902 0.3974807
My questions are:
- Would using a nested random intercept for region within subject make more sense? I don't care to interpret the region effects. Each individual brain is a unique spatial entity, but a given region does have some population-level consistency.
- If I try an alternative random effect for region, like using a random slope of pathlength for each region without an intercept (a possibility offered in Keep it maximal), am I ignoring the repeated-measures-in-space structure of my data to my peril (eg too much type 1 error)?
- Are the predictors just not powerful enough, and so the model settles on just predicting the mean pattern for each subject?