Hi, Is there any set of rules for deciding exactly how to vary slopes and intercepts in a HLM? I have NOMINATE scores from the senate over three years. So I have multiple observations of senators, nested in states, nested in years. Covariates include level-1 (senator in a specific year) variables and state-level variables. I am having a hard time figuring out which combination of random slopes and intercepts to use. What is the best way to compare model specifications using the lmer() function? Should it just be a likelihood ratio test? Also, how do I test whether the random effects for a particular coefficient are significant? The model I fit first based on theory fit reasonably well, but I have been able to get specifications with higher likelihoods. How do I justify reporting those fits?
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