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

Published online by Cambridge University Press:  01 January 2025

Christopher J. Urban Open the ORCID record for Christopher J. Urban [Opens in a new window]  and
Daniel J. Bauer
Christopher J. Urban*
Affiliation:
University of North Carolina at Chapel Hill
Daniel J. Bauer
Affiliation:
University of North Carolina at Chapel Hill
*
Correspondence should be made to Christopher J. Urban, L. L. Thurstone Psychometric Laboratory in the Department of Psychology and Neuroscience, University of North Carolina at Chapel Hill, Chapel Hill, USA. Email: [email protected]
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Abstract

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.

Keywords

Deep learningartificial neural networkvariational inferencevariational autoencoderimportance samplingimportance weighted autoencoderitem response theorycategorical factor analysislatent variable modeling
Type
Theory and Methods
Information
Psychometrika , Volume 86 , Issue 1 , March 2021 , pp. 1 - 29
Copyright
Copyright © 2021 The Psychometric Society

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Footnotes

We would like to thank to the Editor, the Associate Editor, and the reviewers for their many constructive comments. We are also grateful to Dr. David Thissen for his extensive suggestions, feedback, and support.

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