A Dynamic, Ordinal Gaussian Process Item Response Theoretic Model
This work addresses a methodological challenge for social scientists analyzing longitudinal ordinal data, representing an incremental improvement by integrating existing techniques.
The authors tackled the problem of estimating latent traits from ordinal indicators over time by combining Bayesian nonparametric item response theory with Gaussian process time series methods, resulting in the proposed GD-GPIRT model and an MCMC algorithm for estimation, evaluated in simulations and applied to studies on public opinions and congressional ideology.
Social scientists are often interested in using ordinal indicators to estimate latent traits that change over time. Frequently, this is done with item response theoretic (IRT) models that describe the relationship between those latent traits and observed indicators. We combine recent advances in Bayesian nonparametric IRT, which makes minimal assumptions on shapes of item response functions, and Gaussian process time series methods to capture dynamic structures in latent traits from longitudinal observations. We propose a generalized dynamic Gaussian process item response theory (GD-GPIRT) as well as a Markov chain Monte Carlo sampling algorithm for estimation of both latent traits and response functions. We evaluate GD-GPIRT in simulation studies against baselines in dynamic IRT, and apply it to various substantive studies, including assessing public opinions on economy environment and congressional ideology related to abortion debate.