A Guide to Detecting and Modeling Local Dependence in Latent Class Analysis Models

Latent class analysis (LCA) assigns individuals to mutually exclusive classes based on response patterns to a set of indicators. A primary assumption made is local independence, which suggests class indicators are uncorrelated within each class. When the indicators are correlated and unmodeled, parameter estimates can be severely biased. We provide a comprehensive resource for applied researchers to statistically detect local independence violations and model identified correlated residuals. We explain the local independence assumption and illustrate how to detect and model conditional dependence using maximum likelihood (ML) and Bayesian estimation. For ML, we discuss two detection methods (bivariate residual associations, and the modification index) and one modeling technique (LCA residual associations model). We also demonstrate how to use the restrictive prior strategy to detect and model conditional dependence when using Bayesian estimation. These techniques are illustrated with simulated datasets; code is provided in the online supplemental materials.