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 Questionnaire (EPQ-R).
Bibliographical noteFunding Information:
We would like to thank the Editor, the Associate Editor, and the reviewers for many helpful and constructive comments. We also would like to thank Dr. Barrett for sharing the EPQ-R dataset analyzed in Sect. 5. This work was partially supported by a NAEd/Spencer Postdoctoral Fellowship [to Yunxiao Chen] and NSF grant DMS 1712657 [to Xiaoou Li].
- alternating minimization
- high-dimensional data
- item response theory
- joint maximum likelihood estimator
- personality assessment
- projected gradient descent