Bivariate Associations in Multilevel Cross-Classified Latent Class Models

Multilevel cross-classified latent class models (MCCLC) extend standard latent class analysis to account for data nested within multiple groupings. These models often rely on assumptions of local independence, which require robust validation tools. Traditional global fit measures are inadequate for detecting local violations, leading to the use of bivariate residuals (BVRs). However, BVRs are computationally intensive, especially in multilevel contexts. To address this, bivariate associations (BVAs) offer a more efficient alternative by comparing observed and simulated associations without repeated model estimation. This paper extends the BVA framework—including BVA-group and BVA-pair statistics—to MCCLC models, providing practical tools for identifying model misfit. These local fit measures enhance the reliability of latent structure detection in complex, cross-classified data. Simulation studies are presented to evaluate their effectiveness in detecting possible misspecifications.