Essentially, I have two collinear variables which could be seen as either random or as fixed effects, a dependent variable I'm fitting the model to, and a variable that's assuredly a random effect.
Dependent var: Number of neuron spikes (FiringRate) in a specific region of mousebrain
Fixed effects:
1) Time at which data sample was taken (on a linear scale in days -- so day two would be 2, day 5 would be 5, and so on)
2) The Age of the mouse in days (so there's definitely collinearity between this and the Time variable, but there are enough mice of different ages to make this worthwhile as a separate variable)
Random effect: Subject -- "Name" (ID number) of the mouse
Essentially, I'm wondering if it would be appropriate to run two LMEs. In the first, I'd treat Age and Subject as random variables in order to control for the effects of Age (and thus the collinearity between Age and Time) and see if Time is a significant predictor of the # of spikes (dependent variable). In the second, I'd enter Time and Subject as random variables to see if Age was a significant predictor.
library(lme4)
a = lmer(FiringRate ~ Time + (1|Age) + (1|Subject))
b = lmer(FiringRate ~ Age + (1|Time) + (1|Subject))
