Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis

Yunxiao Chen, Xiaoou Li, Siliang Zhang

Research output: Contribution to journalArticle

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 Questionnaire (EPQ-R).

Original languageEnglish (US)
Pages (from-to)124-146
Number of pages23
JournalPsychometrika
Volume84
Issue number1
DOIs
StatePublished - Mar 15 2019

Fingerprint

Maximum likelihood estimation
Factor analysis
Factor Analysis
Maximum Likelihood Estimation
Maximum Likelihood Estimator
Maximum likelihood
Statistical Factor Analysis
High-dimensional
Joints
Marginal Maximum Likelihood
Model Theory
Estimator
Infinity
Psychometrics
Sample Size
Personality
Parallel processing systems
Parallel Computing
Large Data Sets
Inconsistent

Keywords

  • IRT
  • alternating minimization
  • high-dimensional data
  • item response theory
  • joint maximum likelihood estimator
  • personality assessment
  • projected gradient descent

PubMed: MeSH publication types

  • Journal Article
  • Research Support, Non-U.S. Gov't

Cite this

Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis. / Chen, Yunxiao; Li, Xiaoou; Zhang, Siliang.

In: Psychometrika, Vol. 84, No. 1, 15.03.2019, p. 124-146.

Research output: Contribution to journalArticle

Chen, Yunxiao ; Li, Xiaoou ; Zhang, Siliang. / Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis. In: Psychometrika. 2019 ; Vol. 84, No. 1. pp. 124-146.
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