A Dynamic, Ordinal Gaussian Process Item Response Theoretic Model

2025-04-03

AI Summary

Social scientists frequently infer dynamic latent variables—such as public opinion or ideological positioning—from longitudinal ordinal indicators, yet conventional Item Response Theory (IRT) models lack flexibility in characterizing continuous-time latent evolution and nonlinear item response functions. To address this, we propose the Generalized Dynamic Gaussian Process IRT (GPIRT) framework, the first to integrate Bayesian nonparametric IRT with Gaussian process (GP) temporal modeling. GPIRT employs dynamic GP priors to represent latent trajectories continuously over time, supports data-driven estimation of diverse nonlinear response functions, and introduces a tailored MCMC algorithm for scalable posterior inference. Simulation studies demonstrate substantial gains in accuracy and robustness over state-of-the-art dynamic IRT methods. Empirical applications to economic sentiment and congressional abortion ideology uncover fine-grained, time-varying patterns that standard approaches fail to detect.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

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.

Problem

• Estimating dynamic latent traits from ordinal indicators
• Combining Bayesian nonparametric IRT with Gaussian processes
• Modeling time-varying public opinions and ideologies

Innovation

• Combines Bayesian nonparametric IRT with Gaussian processes
• Proposes GD-GPIRT for dynamic latent trait estimation
• Uses MCMC sampling for latent traits and response functions