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

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.

30 pages; 12 figures; accepted for publication in Psychometrika

References in corpus (14)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• On the Convergence of Adam and Beyond
• On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima
• Describing disability through individual-level mixture models for multivariate binary data
• Adaptive Bound Optimization for Online Convex Optimization
• On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization
• Inference Suboptimality in Variational Autoencoders
• Tighter Variational Bounds are Not Necessarily Better
• Escaping Saddle Points with Adaptive Gradient Methods
• A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
• Variational Item Response Theory: Fast, Accurate, and Expressive
• Doubly Reparameterized Gradient Estimators for Monte Carlo Objectives
• MIWAE: Deep Generative Modelling and Imputation of Incomplete Data
• ${\beta }^3$-IRT: A New Item Response Model and its Applications

Cited by in corpus (2)

• py-irt: A Scalable Item Response Theory Library for Python
• A Note on Improving Variational Estimation for Multidimensional Item Response Theory