Statistical Analysis of Strategic Interaction with Unobserved Player Actions: Introducing a Strategic Probit with Partial Observability

The strategic nature of political interactions has long captured the attention of political scientists. A traditional statistical approach to modeling strategic interactions involves multi-stage estimation, which improves parameter estimates associated with one stage by using the information from other stages. The application of such multi-stage approaches, however, imposes rather strict demands on data availability: data on the dependent variable must be available for each strategic actor at each stage of the interaction. Limited or no data make such approaches difficult or impossible to implement. Political science data, however, especially in the fields of international relations and comparative politics, are not always structured in a manner that is conducive to these approaches. For example, we observe and have plentiful data on the onset of civil wars, but not the preceding stages, in which opposition groups decide to rebel or governments decide to repress them. In this article, I derive an estimator that probabilistically estimates unobserved actor choices related to earlier stages of strategic interactions. I demonstrate the advantages of the estimator over traditional and split-population binary estimators both using Monte Carlo simulations and a substantive example of the strategic rebel–government interaction associated with civil wars.