Time Series Models for Discrete Data: solutions to a problem with quantitative studies of international conflict

Discrete dependent variables with a time series structure occupy something of a statistical limbo for even well-trained political scientists, prompting awkward methodological compromises and dubious substantive conclusions. An important example is the use of binary response models in the analysis of longitudinal data on international conflict: researchers understand that the data are not independent, but lack any way to model serial dependence in the data. Here I survey methods for modeling categorical data with a serial structure. I consider a number of simple models that enjoy frequent use outside of political science (originating in biostatistics), as well as a logit model with an autoregressive error structure (the latter model is fit via Bayesian simulation using Markov chain Monte Carlo methods). I illustrate these models in the context of international conflict data. Like other re-analyses of these data addressing the issue of serial dependence, (e.g., Beck, Katz and Tucker 1998), I find economic interdependence does not lessen the chances of international conflict. Other findings include a number of interesting asymmetries in the effects of covariates on transitions from peace to war (and vice versa). Any reasonable model of international conflict should take into account the high levels of persistence in the data; the models I present here suggest a number of methods for doing so.