Clustering Time: Applying Bayesian Mixture Models to Estimate Temporally Heterogeneous Effects in Longitudinal Analysis

Abstract

The presence of temporally heterogeneous effects is prevalent in longitudinal (panel) analysis in the social sciences. The effects of predictors on outcomes of interest may vary across time, often following complex patterns. Though unit heterogeneity is more commonly addressed in quantitative studies using longitudinal data, a growing body of literature has begun to directly model the presence of time-varying effects using methods such as time fixed-effects, time interactions, unstructured time models, structural break models, and dynamic linear models. This study considers an alternative approach that allows researchers to answer questions regarding (1) temporally heterogeneous effects and (2) how these effects are clustered over time. Using the debate surrounding the presence of a resource curse (Ross 2012) as an example, we apply a Bayesian mixture modeling (BMM) framework to address time-varying effects of oil wealth on democratic governance. Results indicate that the BMM approach provides evidence for the presence of a resource curse for the periods 1960-1987 and 1995-2003, with null effects in the 1987-1990 period and positive effects in the 1991-1994 era. The advantage to the BMM framework, we argue, is the lack of \textit{ad hoc} temporal modeling which can often lead to high model dependence; instead by using a data-based approach to temporal clustering, we flexibly allow for hypotheses of theoretical interest to be tested against the data rather than be assumed by the model.

Keywords: Longitudinal analysis, temporal heterogeneity, dynamic effects, clusters, Bayes, mixture models, resource curse