R help - Feb 2009 - Choosing how to vary slopes and intercepts in a hierarchical model

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?

Thanks.
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