# A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis

arXiv: https://arxiv.org/abs/2001.07859 · HTML: https://mlsanity.com/paper/2001.07859/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2020.

## Built on by (most cited first, 5 of 5)

- [py-irt: A Scalable Item Response Theory Library for Python](https://mlsanity.com/paper/2203.01282/) (2022)
- [Generative Adversarial Networks for High-Dimensional Item Factor Analysis: A Deep Adversarial Learning Algorithm](https://mlsanity.com/paper/2502.10650/) (2025)
- [Deep Learning-Based Estimation and Goodness-of-Fit for Large-Scale Confirmatory Item Factor Analysis](https://mlsanity.com/paper/2109.09500/) (2021)
- [Introducing Flexible Monotone Multiple Choice Item Response Theory Models and Bit Scales](https://mlsanity.com/paper/2410.01480/) (2024)
- [Federated Item Response Models: A Gradient-driven Privacy-preserving Framework for Distributed Psychometric Estimation](https://mlsanity.com/paper/2506.21744/) (2025)

## Abstract (arXiv)

Marginal maximum likelihood (MML) estimation is the preferred approach to fitting item response theory models in psychometrics due to the MML estimator's consistency, normality, and efficiency as the sample size tends to infinity. However, state-of-the-art MML estimation procedures such as the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm as well as approximate MML estimation procedures such as variational inference (VI) are computationally time-consuming when the sample size and the number of latent factors are very large. In this work, we investigate a deep learning-based VI algorithm for exploratory item factor analysis (IFA) that is computationally fast even in large data sets with many latent factors. The proposed approach applies a deep artificial neural network model called an importance-weighted autoencoder (IWAE) for exploratory IFA. The IWAE approximates the MML estimator using an importance sampling technique wherein increasing the number of importance-weighted (IW) samples drawn during fitting improves the approximation, typically at the cost of decreased computational efficiency. We provide a real data application that recovers results aligning with psychological theory across random starts. Via simulation studies, we show that the IWAE yields more accurate estimates as either the sample size or the number of IW samples increases (although factor correlation and intercepts estimates exhibit some bias) and obtains similar results to MH-RM in less time. Our simulations also suggest that the proposed approach performs similarly to and is potentially faster than constrained joint maximum likelihood estimation, a fast procedure that is consistent when the sample size and the number of items simultaneously tend to infinity.