How to determine random effects in mixed model I want to model frequency of a social effect by state over several years as potentially predicted by several demographic factors. I have been reading that one is supposed to determine the random effect structure before trying to determine the fixed effects structure. One thing I want to be sure to test for fixed effects is an interaction with time for each fixed effect.
Do I want to just have intercept|State or do I want to look at slope of each possible fixed factor per state, as well. How would I do the latter if I have not yet built the fixed effects portion of the model? Would I also look at fixed:time for each potential fixed effect as random effects?
I want to avoid dredging. I have only 459 points for each variable (9 years, 50 states + DC). However, I also want to be able to contrast model predictions for the full model vs. a fixed-effect only model.
 A: You can test if the variance in slopes (and covariance between slope and intercept) is significant by modeling one model with just the random intercept and another model with the random slope and intercept. Then you can do a nested model comparison between the two:
mod1 <- lmer(... + (1|state), ...)
mod2 <- lmer(... + (1+predictor|state), ...)
anova(mod1,mod2)

This will give you a p-value that you need to correct, though. You can do so with this code:
1-(.5*pchisq(anova(mod1,mod2, refit=FALSE)$Chisq[[2]],df=2)+
   .5*pchisq(anova(mod1,mod2, refit=FALSE)$Chisq[[2]],df=1))

P-value correction is found here or here.
A: Exploratory analyses for describing correlation structures in dependent data include variograms for continuous spatio-temporal data, intraclass correlation coefficients for clustered data, lorelograms for binary outcomes.
Other descriptive statistics include bootstrapped or profile likelihood confidence intervals for variance components in random effects models, goodness-of-fit tests with unstructured covariance structures or saturated specification of random and fixed effects.
Formal inference for the hypothesis of random effects having 0 dispersion can be done testing nested models with likelihood ratio tests. Be sure to change software settings to fit models with maximum likelihood and not REML when conducting these tests. 
