Statistical methods and graphical displays for analyzing how the association between two qualitative variables differs among countries, among groups, or over time: A modified regression-type approach

Many interesting sociological questions pertain to how the association between two variables depends on a third variable. In sociological applications, the third variable often pertains to countries, to subgroups of a population, or to time periods. We propose a regression-type approach that specifies that the log-odds-ratios that describe the two-way association of interest are a linear function of latent scores for the third variable. Additive and multiplicative models currently in use by researchers are special cases of the regression-type model. To illustrate the utility of the regression-type approach, we apply this approach to analyze (1) data on occupational mobility in the United States, Britain, and Japan (comparing mobility in these countries) and (2) data on the association between religion and voting behavior in U.S. presidential elections from 1968 to 1992 (comparing this association in the different elections). We also introduce here graphical displays that can be used to obtain worthwhile information about goodness-of-fit and to aid in substantive interpretation.