Composite Marginal Likelihood Estimation of High-Dimensional Confirmatory Item Response Theory Model
Year: 2026
Type: preprint
Abstract: In item response theory (IRT), the two-tier IRT model can be considered a general confirmatory IRT model, in which multiple correlated primary factors and orthogonal specific factors are loaded onto items. Although full information maximum likelihood estimation combined with the dimension reduction technique has been successful, it becomes computationally infeasible when the number of primary factors increases. In this study, we propose a composite marginal likelihood (CML) estimation via the expectation-maximization algorithm to alleviate this computational demand. We adopt the pairwise fitting approach, where item responses are divided into subsets according to primary factor pairs. Combined with the dimension reduction technique, this approach can, in certain cases, reduce the required numerical integration to as few as three latent variables, regardless of the total number of primary and specific factors in the model. The potential of the CML method for the two-tier IRT model is demonstrated by a simulation study and applications to two empirical datasets.
Source: PsyArXiv (OSF Preprints)
Authors: Minho Lee, Cheng Liu
Institution: University of Notre Dame
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7167268051