Bayesian Analysis for the Social Sciences

In many social science settings, the data available for analysis span multiple groups. In these settings it is often plausible that any statistical model we might fit to the data will fit need to flexible, so as to capture variation across the groups, typically accomplished by letting some or all of the parameters vary across the groups. Examples include survey data gathered over a set of locations (e.g., states, Congressional districts, countries); experimental studies deployed in multiple locations; and perhaps the locus classicus of hierarchical modeling in the social sciences, studies of educational outcomes where the subjects are students, who are grouped in classes or schools, which nest in school districts, which in turn nest in states. In studies of data of this type, the researcher is interested in parameters that vary at the group level. These group level parameters go by different names, in different contexts, in different disciplines, and depending on the estimation method being used. Examples include “contextual effects”, “fixed effects”, “random effects”, and “varying” or “stochastic coefficients”. This between-group parameter variation is potentially of great substantive interest, since it speaks to a fundamental issue in empirical social science. Generally, we prefer more parsimonious models to more complicated models. In the search for generalizable propositions about social processes — ideally, perhaps, with the status of a scientific law — we seek simple explanations and simple models, with fewer parameters, rather than