# A Dynamic, Ordinal Gaussian Process Item Response Theoretic Model

arXiv: https://arxiv.org/abs/2504.02643 · HTML: https://mlsanity.com/paper/2504.02643/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 80 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Enhancing Item Response Theory for Cognitive Diagnosis](https://mlsanity.com/paper/1905.10957/) (2019)
- [β3-IRT: A New Item Response Model and its Applications](https://mlsanity.com/paper/1903.04016/) (2019)
- [Probabilistic selection of inducing points in sparse Gaussian processes](https://mlsanity.com/paper/2010.09370/) (2020)
- [GPIRT: A Gaussian Process Model for Item Response Theory](https://mlsanity.com/paper/2006.09900/) (2020)
- [A Spectral Approach to Item Response Theory](https://mlsanity.com/paper/2210.04317/) (2022)
- [Modeling repeated self-reported outcome data: a continuous-time longitudinal Item Response Theory model](https://mlsanity.com/paper/2109.13064/) (2021)

## Abstract (arXiv)

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.