Estimation of Diagnostic Classification Models without Constraints: Issues with Class Label Switching

Abstract

Diagnostic classification models (DCMs) may suffer from the latent class label switching issue. Label switching refers to the situation where the labels for the parameters switch across replications of the same estimation. It happens when there are the permutations of the number of latent classes (k!) with statistically equivalent solutions to the estimation, resulting from a symmetry parameter space. With uncertainty in the accuracy of the labels in the parameters, the interpretation of results could be invalid and misleading. A simulation study is used to investigate the prevalence of label switching in DCMs. Three independent variables are involved, including the model constraints, the effect size of the measurement model parameters, and the q-matrix specifications. The data is generated via R, and estimated via Mplus. Label switching is operationally defined as, for the same dataset, the existence of any difference in the estimated parameters between the model without constraints and the model with constraints, given that they have the same log likelihood. Results show that local optimal solutions prevail in some conditions, making it difficult to identify label switching. Given the same log likelihoods between models, 13.9 to 40 percent of those replications show label switching.