A Riemannian Optimization Algorithm for Joint Maximum Likelihood Estimation of High-Dimensional Exploratory Item...

Area of Science:

• Psychometrics
• Statistical modeling
• Machine learning

Background:

• Item factor analysis (IFA) is a statistical method used to identify underlying latent factors that explain the correlations among observed variables (items).
• Joint maximum likelihood (JML) estimation is a method for estimating parameters in statistical models, particularly useful for complex models like IFA.
• Recent interest in JML for IFA stems from its efficiency in handling high-dimensional datasets and multiple latent factors.

Purpose of the Study:

• To develop and present an efficient Riemannian optimization algorithm for JML estimation in exploratory IFA.
• To specifically address dichotomous response data, common in many psychological and educational assessments.
• To evaluate the performance of the proposed algorithm against existing methods.

Main Methods:

• The study proposes a novel algorithm leveraging the differential geometry of the fixed-rank matrix manifold for JML estimation.
• This Riemannian optimization approach is applied to exploratory item factor analysis with dichotomous data.
• A benchmark method involving alternating gradient ascent steps for person and item parameters is used for comparison.

Main Results:

• The proposed Riemannian optimization algorithm demonstrates substantially faster convergence times compared to the benchmark method.
• Simulations were conducted to evaluate the algorithm's performance in accurately recovering latent dimensionality, response probabilities, item parameters, and factor scores.
• The algorithm shows promise for efficient and accurate estimation in complex IFA models.

Conclusions:

• The developed Riemannian optimization algorithm offers an efficient solution for JML estimation in exploratory IFA with dichotomous data.
• This method provides a significant improvement in computational speed over traditional approaches.
• The findings suggest this algorithm is a valuable tool for analyzing high-dimensional psychometric data.