HLM Unit Specific vs. Population Average Model

I am using HLM to do a 2 level longitudinal analysis of change in firearm background check denial rate. The denial rate per 100,000 is the outcome. Its Poisson and over-dispersed. Year at level one is the predictor. This is the base model. The results return a unit specific and a population average model. I do not know which result set to choose and do not understand how to differentiate the two. All predictors and outcomes are state-level that are census counts, percentages, or rates per 100,000 (i.e. not sampled). In short, it seems that the population average model is appropriate as the data does, in fact, represent the population (all 50 states and census level) rather than making specific statements about a portion of the population data (e.g. sampling within the 50 states). Help and/or guidance on how to choose between the two results would be helpful. Thanks! Dave


Omega Contributor
Not an hlm user. Is state your cluster variable, random effect? Is unit and population referring to within and between random effect estimates, respectively?
The answer to this lays largely in the inferences you are making, as you pointed out. If you are generalizing these results to a population, then you can use a population average model which will determine an odds ratio based on the averaging the cluster specific probabilities (in this case, those of all the states). If you are making inferences about specific states, then a cluster specific probability makes sense because the odds ratio is a function of each states individual cluster probability. Put another way, the population average model won't completely specify the distribution of population (because it's averaged) whereas a cluster specific model does