A Tale of Two (Types Of) Memberships

Abstract

We employ mixed-membership (or grade-of-membership) techniques—of growing popularity in medical diagnostics, psychology, genetics, and machine learning—in order to identify prototypical profiles of survey respondents based on their answers to questions aimed at uncovering their basic orientations or ideological predispositions. In contrast with factor analytic techniques and IRT approaches, we treat both manifest and latent variables as categorical. A mixed membership model may be thought of as a generalization of latent class modeling, in which individuals act as members of more than one class. This notion is well-aligned with earlier theoretical work of Zaller, Feldman, Stimson, and others, who at times envision respondents to be internally complex, answering survey questions probabilistically according to what Zaller calls varying “considerations.” Reanalyzing data in this way, we develop new insights into the sorts of constraints that may structure mass belief systems.