I have one dependent variable (continuous data) and 4 independent data (mix of continuous and count) collected over 35 years across several states. I am using a linear mixed effect models with a random intercept and a random slope.
model<-lmer(y ~ x1 + x2 + x3 + x4 (1+x1+x2+x3+x4|state),data=data,method="ML")
If some of my independent variables are correlated, what is the procedure of reducing the collinearity issue in a linear mixed effect model? I could spot collinerity using VIF and retain the most significant independent variables but I can do this for each factor level (levels of state) individually. But won't it result in retaining some independent variables in one factor level while deleting the same in other factor level? I guess the main question is how to spot collinearity in a mixed effect models and what to do with it when you have 5 or 6 independent variables?