# Sparse Bayesian Multidimensional Item Response Theory

arXiv: https://arxiv.org/abs/2310.17820 · HTML: https://mlsanity.com/paper/2310.17820/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 47 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## Builds on (most cited first, 6 of 6)

- [Conjugate Bayes for probit regression via unified skew-normal distributions](https://mlsanity.com/paper/1802.09565/) (2018)
- [Bayesian conjugacy in probit, tobit, multinomial probit and extensions: A review and new results](https://mlsanity.com/paper/2206.08118/) (2022)
- [Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications](https://mlsanity.com/paper/1712.08966/) (2017)
- [A Joint MLE Approach to Large-Scale Structured Latent Attribute Analysis](https://mlsanity.com/paper/2009.04096/) (2020)
- [When it counts -- Econometric identification of the basic factor model based on GLT structures](https://mlsanity.com/paper/2301.06354/) (2023)
- [On Posterior Consistency of Bayesian Factor Models in High Dimensions](https://mlsanity.com/paper/2006.01055/) (2020)

## Built on by (most cited first, 3 of 3)

- [Latency-Response Theory Model: Evaluating Large Language Models via Response Accuracy and Chain-of-Thought Length](https://mlsanity.com/paper/2512.07019/) (2025)
- [Discrete Causal Representations from Heterogeneous Domains: A Bayesian Approach with Social Survey Applications](https://mlsanity.com/paper/2606.06288/) (2026)
- [An efficient adaptive dimension selection algorithm for multidimensional probit graded response models](https://mlsanity.com/paper/2607.17654/) (2026)

## Abstract (arXiv)

Multivariate Item Response Theory (MIRT) is sought-after widely by applied researchers looking for interpretable (sparse) explanations underlying response patterns in questionnaire data. There is, however, an unmet demand for such sparsity discovery tools in practice. Our paper develops a Bayesian platform for binary and ordinal item MIRT which requires minimal tuning and scales well on large datasets due to its parallelizable features. Bayesian methodology for MIRT models has traditionally relied on MCMC simulation, which cannot only be slow in practice, but also often renders exact sparsity recovery impossible without additional thresholding. In this work, we develop a scalable Bayesian EM algorithm to estimate sparse factor loadings from mixed continuous, binary, and ordinal item responses. We address the seemingly insurmountable problem of unknown latent factor dimensionality with tools from Bayesian nonparametrics which enable estimating the number of factors. Rotations to sparsity through parameter expansion further enhance convergence and interpretability without identifiability constraints. In our simulation study, we show that our method reliably recovers both the factor dimensionality as well as the latent structure on high-dimensional synthetic data even for small samples. We demonstrate the practical usefulness of our approach on three datasets: an educational assessment dataset, a quality-of-life measurement dataset, and a bio-behavioral dataset. All demonstrations show that our tool yields interpretable estimates, facilitating interesting discoveries that might otherwise go unnoticed under a pure confirmatory factor analysis setting.