Efficiently Testing the Latent Dimensionality of Categorical Data Through Bayesian Structured Dependence Models

A Bayesian framework is proposed in which dependence models serve as proxy to evaluate the psychometric properties of measurement scales from categorical data. Structured dependence models (SDMs) specify the association of scale factors through the structure of variance-covariance matrices. A Hamiltonian Monte Carlo (HMC) algorithm utilizes the explicit matrix structure to obtain efficient samples of dependence parameters. In a simulation study, SDMs outperformed a state-of-the-art implementation of confirmatory factor analysis (CFA) in discriminating between unidimensional and bi-factor structures from categorical data. A proposed Bayes factor showed satisfying type-1 and type-2 error rates for small (N = 100) to moderate (N = 500) sample sizes. An empirical example illustrates testing psychometric properties of vertically scaled data. Overall, we conclude that dependence models can provide added value over existing approaches when sample sizes are moderate to small and/or complex measurement scales are investigated.