I'm trying to run a mixed-effects analysis on some data that I have, but cannot determine if I am using the correct model.
First, I am trying to determine if there are between-group difference in 5 independent variables. My data consists of a number of participants who performed 31 different tasks (we'll call them Items), during which these 5 variables were measured. I would like to test for differences in these variables, not necessarily in relation to each other, but I would like to keep them in one model so as to avoid excessive testing. I would, however, like to control for the variance between these items, and if possible also between participants.
I currently am using the lme4 package to run a logistic regression:
glmer(Group~Var1+Var2+Var3+Var4+Var5 + (1|item),family=binomial)
My thinking here is that if there are group differences, then the variables should also predict group membership, effectively testing my hypothesis, if in an indirect way. Please correct me if this assumption is incorrect.
Ideally I would like to run this with Participant as an addition random factor, but I don't think that makes sense in a model testing for group differences.
The alternative is to run separate regression models for each of my independent variables, with Group, Item, and Participant as random effects. However, as I said before, I don't want to over-test the data, so I'm not sure if this is an advisable way to go about it.
Can anyone let me know if my current setup is a valid way to test for significant differences of multiple variables between 2 groups?
EDIT: If the above is NOT valid, and the test should be the other way around, lmer(Var1 ~ Group + (1|item)), is it then recommended to also model participants as random variables, or will this interfere with the fixed effect of Group?