An overview of collapsibility

Abstract

Collapsing over variables is a necessary procedure in much empirical research. Consequences are yet not always properly evaluated. In this paper, different definitions of collapsibility (simple, strict, strong, etc.) and corresponding necessary and sufficient conditions are reviewed and evaluated. We point out the relevance and limitations of the main contributions within a unifying interpretative framework. We deem such work to be useful since the debate on the topic has often developed in terms that are neither focused nor clear.