Joint Maximum Likelihood Estimation for High-dimensional Exploratory Item Response Analysis

TL;DR

This paper introduces a constrained joint maximum likelihood estimator for high-dimensional exploratory item response analysis, demonstrating its statistical consistency, computational efficiency, and competitive performance against traditional methods in large datasets.

Contribution

It establishes a new statistically consistent JML estimator for high-dimensional IRT models and proposes a scalable parallel computing algorithm for large datasets.

Findings

The estimator performs comparably or better than MML in high-dimensional settings.

The proposed method is computationally more efficient for large datasets.

Simulation studies validate the estimator's effectiveness and scalability.

Abstract

Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them simultaneously by solving an optimization problem. However, the JML estimator is known to be asymptotically inconsistent for many IRT models, when the sample size goes to infinity and the number of items keeps fixed. Consequently, in the psychometrics literature, this estimator is less preferred to the marginal maximum likelihood (MML) estimator. In this paper, we re-investigate the JML estimator for high-dimensional exploratory item factor analysis, from both statistical and computational perspectives. In particular, we establish a notion of statistical consistency for a constrained JML estimator, under an asymptotic setting that both the numbers of items and people grow to infinity and that many responses may be missing. A parallel computing algorithm is proposed for this estimator that can scale to very large datasets. Via simulation studies, we show that when the dimensionality is high, the proposed estimator yields similar or even better results than those from the MML estimator, but can be obtained computationally much more efficiently. An illustrative real data example is provided based on the revised version of Eysenck's Personality Questionaire (EPQ-R).