Bayesian Analysis of Comparative Survey Data

Bayesian hierarchical models provide a useful way of analyzing multilevel survey data. The Bayesian estimates have good statistical properties, make good predictions, and realistically account for clustering in the data. Still the Bayesian estimates can be biased in the presence of omitted variables and fixed effect models might sometimes be preferable. Bayesian statistics for model comparison and evaluation—posterior predictive checks and the Deviance Information Criterion—assist an empirical approach to distinguishing between hierarchical models and their alternatives. These ideas are illustrated with an analysis of migration data from 22 villages in the Nang Rong district of Thailand. Bayesian statistics can make a special contribution to comparative and historical social science. Comparative data are often not generated by a welldefined probability mechanism, so a researcher’s uncertainty may be better described by a degree-of-belief than the frequency behavior of sample statistics (Berk et al. 1994). Comparative and historical researchers also unearth rich qualitative information about particular countries, regions, and historical periods. In a classicial analysis, this nonsample information generally provides informal guides to model choice or the post hoc interpretation of results. Bayesian prior distributions explicitly incorporate non-sample information that often influences data analysis in a more informal way (Western and Jackman 1994). Prior information can have a large effect in comparative analysis because data sets can be small and collinear. Under these conditions, the final results may also depend closely on the choice of models. Bayesian statistics can incorporate uncertainty about the model specification, pushing inference in a more conservative direction (Western 1995). Finally, a key message of comparative social science is that social and political processes vary across countries, regions, and time periods. Bayesian hierarchical models help us analyze these kinds of heterogeneity (Western 1998; Western and Kleykamp 2004). This symposium on the analysis of multilevel survey data provides another opportunity to apply Bayesian methods to the special methodological problems of comparative research. Multilevel survey data are collected from, say, a dozen or more countries, perhaps at several points in time. This data structure shares some features with the pooled time series familiar to comparative researchers—observations are clustered by country and there is likely causal heterogeneity across countries. But unlike other comparative data, multilevel survey data provide enough information about each country to