Bayesian Rule Set: A Quantitative Alternative to Qualitative Comparative Analysis

Abstract

We introduce the Bayesian Rule Set (BRS) as an alternative to Qualitative Comparative Analysis (QCA) when data are large and noisy. BRS is an interpretable machine learning algorithm that classifies observations using rule sets, which are conditions connected by logical operators (e.g., IF (condition A AND condition B) OR (condition C), THEN Y = TRUE). Like QCA, BRS is highly interpretable and capable of revealing complex nonlinear relationships in data. It also has several advantages over QCA: it is compatible with probabilistically generated data, it avoids overfitting and improves interpretability by making direct trade-offs between in-sample fitness and complexity, and it remains computationally efficient with many covariates. Our contributions are threefold: we modify the BRS algorithm to facilitate its usage in the social sciences, propose methods to quantify uncertainties of rule sets, and develop graphical tools for presenting rule sets. We illustrate these methods with two empirical examples from political science.