Exploratory multilevel analysis when group-level variables are of importance

Steve Miller writes:

Much of what I do is cross-national analyses of survey data (largely World Values Survey). . . . My big question pertains to (what I would call) exploratory analysis of multilevel data, especially when the group-level predictors are of theoretical importance. A lot of what I do involves analyzing cross-national survey items of citizen attitudes, typically of political leadership. These survey items are usually yes/no responses, or four-part responses indicating a level of agreement (strongly agree, agree, disagree, strongly disagree) that can be condensed into a binary variable. I believe these can be explained by reference to country-level factors. Much of the group-level variables of interest are count variables with a modal value of 0, which can be quite messy.

How would you recommend exploring the variation in the dependent variable as it could be explained by the group-level count variable of interest, before fitting the multilevel model itself? When the variables of interest are at the individual-level, I know it’s practical to run a separate regression on each country and plot the results. However, it’s the group-level variables that interest me. Further, I’m not sure if doing a simple cross-tab of group-level averages of the dependent variable, as it coincides with different values of the group-level independent variable, is appropriate since the DV itself is at the individual-level.

What I’m trying to avoid is wasting time estimating computationally-intensive multilevel models (with often an N between 60,000 and 90,000 and a J of anywhere between 60 and 80) as a means to exploring the data as they pertain to my research question of interest.

My reply: I discussed this a bit in my article, Two-Stage Regression and Multilevel Modeling: A Commentary, in Political Analysis several years ago. Actually, that article is pretty much a direct answer to your above questions.