A Copula-Based Joint Model for Speed and Accuracy

Abstract

This study proposes a copula-based model that relaxes the multivariate normality assumption among latent traits in the joint modeling of multimodal data, such as item response and response times. In the structural model, the joint distribution of latent traits is defined via a copula with tail dependence. An expectation-maximization algorithm with stochastic approximation is implemented for parameter estimation. A simulation study evaluates the proposed method's accuracy in ability estimation under various conditions, comparing it to traditional approaches. By better capturing the dependence structure between latent ability and speed, the proposed method outperforms the traditional approach with multivariate normality assumption. Applied to a variety of empirical datasets, the proposed method's flexibility and the improvement in model fit are illustrated. The copula-based latent variable modeling can be generalized to broader applications in psychological testing involving multivariate latent traits.