Skip to main content
Multilevel latent class models with Dirichlet mixing distribution
Biometrics (2011)
  • Chong-Zhi Di, Fred Hutchinson Cancer Research Center
  • Karen Bandeen-Roche, Johns Hopkins University

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we consider multilevel latent class models, in which sub-population mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. Simulation studies suggest that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random e ffects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

  • Dirichlet distribution,
  • EM algorithm,
  • latent class analysis (LCA),
  • multilevel models,
  • pairwise likelihood
Publication Date
Spring 2011
Publisher Statement
The definitive version is available at
Citation Information
Chong-Zhi Di and Karen Bandeen-Roche. "Multilevel latent class models with Dirichlet mixing distribution" Biometrics Vol. 67 Iss. 1 (2011)
Available at: