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

Area of Science:

• Psychometrics
• Statistical Modeling
• Computational Statistics

Background:

• Joint Maximum Likelihood (JML) is an early method for Item Response Theory (IRT) models.
• JML is often asymptotically inconsistent and less preferred than Marginal Maximum Likelihood (MML).
• High-dimensional exploratory item factor analysis presents unique statistical and computational challenges.

Purpose of the Study:

• To re-investigate the Joint Maximum Likelihood (JML) estimator in high-dimensional exploratory item factor analysis.
• To establish statistical consistency for a constrained JML estimator under specific asymptotic conditions.
• To develop and evaluate a computationally efficient parallel algorithm for the JML estimator.

Main Methods:

• Developed a constrained Joint Maximum Likelihood (JML) estimator.
• Established statistical consistency under an asymptotic setting where both item and person counts grow infinitely.
• Proposed a parallel computing algorithm for scalability to large datasets.
• Conducted simulation studies to compare JML with Marginal Maximum Likelihood (MML).

Main Results:

• The constrained JML estimator demonstrates statistical consistency under joint asymptotic growth.
• A parallel computing algorithm enables efficient estimation for very large datasets.
• In high-dimensional settings, the proposed JML estimator performs similarly or better than MML.
• The JML approach offers significantly improved computational efficiency compared to MML.

Conclusions:

• The constrained JML estimator is a statistically consistent and computationally efficient alternative for high-dimensional IRT models.
• The proposed parallel algorithm makes JML feasible for large-scale psychometric analyses.
• JML can be a competitive approach to MML, especially in high-dimensional scenarios where computational cost is a concern.