Bayesian Nonparametric Measurement with Gaussian Processes: From Static to Dynamic Item Response Theory

Item response theory (IRT) is a widely used framework for estimating latent traits from observed indicators in educational testing, psychometrics, and political science. However, standard IRT models impose strong parametric assumptions on item response functions—typically assuming monotonicity, symmetry, and saturation—that often fail in practice. I present a Bayesian nonparametric approach that places Gaussian process priors on the latent functions relating traits to responses. This allows simultaneous estimation of flexible item response functions and latent trait scores while making minimal assumptions about functional form. I then extend this framework to handle ordinal responses and dynamic settings where latent traits evolve over time, using Gaussian process time series to ensure measurement comparability across periods. Applications to roll-call voting in Congress, panel surveys of economic attitudes, and personality measurement demonstrate that this approach recovers substantively meaningful non-monotonic and asymmetric response patterns missed by parametric alternatives, improves predictive performance, and enables principled active learning for computerized adaptive testing.

Host: Xuming He

Jacob M. Montgomery is Professor of Political Science at Washington University in St. Louis. He holds a Ph.D. in Political Science and a Masters in Statistical Sciences from Duke University. His research focuses on political methodology, with particular emphasis on measurement and machine learning applications in the social sciences. His work has appeared in PNAS as well as leading outlets in political science and computer science. Substantively, his work examines the intersection of technology and politics, including research on misinformation and social media, the use of large language models to study bias and stereotyping, and the global spread of populist rhetoric across digital platforms. His research has been supported by grants from the National Science Foundation and the Carnegie Foundation.