GPIRT: A Gaussian Process Model for Item Response Theory

• In Event: Advances in Measurement

Abstract

Political scientists measuring political actors' ideology often assume a specific functional form for the mapping between ideology and observed responses (e.g. roll-call votes). However, we do not truly know the mapping between ideology and response, and assumptions imposed by such models may be incorrect. For example, they may assume monotonicity of response in ideology, which precludes "ends against the middle voting," or they may assume response probabilities approach 0 or 1; in many contexts these assumptions are inappropriate. We develop a model that allows researchers to avoid such assumptions and simultaneously perform inference on the latent traits and the mapping between traits and response. We do so by extending a machine learning technique, Gaussian process classification, to place a prior distribution over the possible functions mapping ideology to response, and implement in open source software an algorithm to simulate the posterior distribution of latent traits and item response functions. Our approach offers a number of advantages, including avoiding strong assumptions that may be unfounded, and incorporating our uncertainty about the form of the item response functions in our estimates of actors' ideology.

Authors

• JBrandon Duck-Mayr, Washington University in St. Louis

• Jacob M. Montgomery, Washington University in St. Louis