# collinearity in linear mixed effects model

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?

• It will depend on how strongly they are correlated. For example, with Financial data, the question is usually not "Are the independent variables at all correlated?" but rather "To what degree is there multicollinearity?". In other words, it may be ok to run the regression as-is (as long as the correlation is not particularly strong). Also, dropping one or more of the independent variables is usually the way to go... – Steve S Jul 7 '14 at 21:24
• Are you stuck with a mixed effects model? In order to select the best predictive variables and account for collinearity, why not run a penalized regression (eg, lasso, ridge regression, or elastic net) on your model, with each state as a separate dummy variable. – RobertF Jul 7 '14 at 23:35
• Could I ask for a clarification. If I use a state as a dummy variable, what if I want to predict for a new State which the original model was not really calibrated on? – 89_Simple Jun 14 '18 at 14:29