A Dynamic, Ordinal Gaussian Process Item Response Theoretic Model

TL;DR

The paper addresses the challenge of estimating time-evolving latent traits from ordinal indicators while preserving measurement comparability across time. It introduces generalized dynamic Gaussian process item response theory (gd-gpirt), which combines Gaussian process priors on item response functions and on latent trait trajectories, enabling nonparametric IRFs and smooth temporal dynamics. An efficient MCMC framework with elliptical slice sampling and sparse GP techniques supports joint inference of latent traits, IRFs, and thresholds from longitudinal ordinal data, demonstrated on simulation and real-world studies of economic opinions and Senate ideology on abortion. Across settings, gd-gpirt yields superior measurement quality and predictive performance relative to established baselines, highlighting its potential for flexible, time-aware latent-variable modeling in social science research.

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.

Figures (5)

• Figure 1: Estimated confidence and selective irfs in taps.
• Figure 2: The upper panel illustrates the alignment between senators' estimated ideology and their party affiliations ('polarization ratio') on abortion debates using gd-gpirt. The increase in the ratio from the 92nd Congress (0.521) to the 108th Congress (0.950) indicates the growing partisan divide on abortion debate. The lower panel displays gd-gpirt scores by party spaced every two sessions, with Dem. and Rep. Senators in blue and red, respectively. Dashed lines represent the evolving ideological trajectories of selected senators.
• Figure 3: irfs of four selected roll call votes in the U.S. Senate on abortion debate between the 92th to 108th Congress that are standard, asymmetric, non-saturate and non-monotonic. Estimated probability of voting "yea" is plotted against ideology score $x$. Actual "yea" and "nay" roll-call votes are displayed as red and black dashes.
• Figure 4: Dynamic human right trends of China, Guatemala, Namibia and Uzbekistan from 1980 to 2010.
• Figure 5: Estimated irfs for four individual physical integrity variables (political imprisonment, torture, extrajudical killing and disappearances) in 1991 in the CIRI dataset. Expected level of human right indicators is plotted against latent human right score $\theta$. Low, median and high levels of observed human right indicators are displayed as black, blue and red vertical dashes. For all indicators, the estimated human rights levels are roughly monotonic increasing w.r.t to human rights scores as expected.