Optimizing Maximum Likelihood Estimation in Performance Factor Analysis: A Comparative Study of Estimation Methods

Assessment methods impact learning and ensure alignment with course goals. However, formative assessments face model selection challenges influenced by factors like class size and item availability. These factors compromise assessment validity in item response models for small populations. Performance factor analysis, an alternative model class, effectively provides detailed student performance information and parameter estimation per learning object or latent attribute. To address challenges in sample size and multidimensionality of latent attribute-item matrices in formative assessments, this study explores limited-memory Broyden-Fletcher-Goldfarb-Shanno with bound (L-BFGS-B) and Nelder-Mead optimization methods of maximum likelihood estimation for performance factor analysis. Comparison of their accuracy using various criteria indicates that L-BFGS-B and Nelder-Mead methods are robust for handling small to moderate sample sizes in both unidimensional and multidimensional Q matrix scenarios.