Variational Estimation for Multidimensional Graded Response Model

Likert-type items with ordinal responses are frequently used in tests to assess multiple latent traits. The multidimensional graded response model (MGRM) is the preferred model for describing the relationship between these ordinal items and latent traits. In this article, we propose a novel Gaussian variational expectation maximization (GVEM) method for parameter estimation in MGRM. Rather than relying on direct numerical approximations for intractable integrals over multidimensional latent traits, our GVEM employs a carefully derived variational lower bound to approximate the marginal log-likelihood function, resulting in closed-form estimates. This method significantly improves the computational efficiency and is viable when dealing with high-dimensional latent variables. Additionally, an importance-weighted GVEM (IW-GVEM) algorithm is developed for MGRM to address the bias issue. Simulation studies show that our GVEM and IW-GVEM run significantly faster than the MH-RM algorithm and are of competitiveness in both confirmatory and exploratory analysis. Our proposed algorithms are illustrated by analyzing a real dataset from the Big-Five Personality test. Supplemental materials for the article are available online.