Single and Multiple Ability Estimation in the SEM Framework: A Non-Informative Bayesian Estimation Approach

Latent variable models with many categorical items and multiple latent constructs result in many dimensions of numerical integration, and the traditional frequentist estimation approach, such as maximum likelihood (ML), tends to fail due to model complexity. In such cases, Bayesian estimation with diffuse priors can be used as a viable alternative to ML estimation. The present study compares the performance of Bayesian estimation to ML estimation in estimating single or multiple ability factors across two types of measurement models in the structural equation modeling framework: a multidimensional item response theory (MIRT) model and a multiple-indicator multiple-cause (MIMIC) model. A Monte Carlo simulation study demonstrates that Bayesian estimation with diffuse priors, under various conditions, produces quite comparable results to ML estimation in the single- and multi-level MIRT and MIMIC models. Additionally, an empirical example utilizing the Multistate Bar Examination is provided to compare the practical utility of the MIRT and MIMIC models. Structural relationships among the ability factors, covariates, and a binary outcome variable are investigated through the single- and multi-level measurement models. The paper concludes with a summary of the relative advantages of Bayesian estimation over ML estimation in MIRT and MIMIC models and suggests strategies for implementing these methods.