The Integration of Bayesian Regression Analysis and Bayesian Process Tracing in Mixed-Methods Research

In this article, we develop a mixed-methods design that combines Bayesian regression with Bayesian process tracing. A fully Bayesian multimethod design allows one to include empirical knowledge at each stage of the analysis and to coherently transfer information from the quantitative to the qualitative analysis, and vice versa. We present a complete mixed-methods workflow explaining how this is accomplished and how to integrate both methods. It is demonstrated how to use the posterior highest density interval and the Bayes factor from the regression analysis to update the prior level of confidence about what mechanisms possibly connect the cause to the outcome. It is further shown how to choose cases for the qualitative analysis through posterior predictive sampling. We illustrate this approach with an empirical analysis of colonial development and compare it with alternative designs, including nested analysis and the Bayesian integration of qualitative and quantitative methods.