Mixture Modeling for Longitudinal Data

Xiwei Tang, Annie Qu

Research output: Contribution to journalArticlepeer-review


In this article, we propose an unbiased estimating equation approach for a two-component mixture model with correlated response data. We adapt the mixture-of-experts model and a generalized linear model for component distribution and mixing proportion, respectively. The new approach only requires marginal distributions of both component densities and latent variables. We use serial correlations from subjects’ subgroup memberships, which improves estimation efficiency and classification accuracy, and show that estimation consistency does not depend on the choice of the working correlation matrix. The proposed estimating equation is solved by an expectation-estimating-equation (EEE) algorithm. In the E-step of the EEE algorithm, we propose a joint imputation based on the conditional linear property for the multivariate Bernoulli distribution. In addition, we establish asymptotic properties for the proposed estimators and the convergence property using the EEE algorithm. Our method is compared to an existing competitive mixture model approach in both simulation studies and an election data application. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1117-1137
Number of pages21
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - Oct 1 2016


  • Expectation-estimating-equation algorithm
  • Latent variable
  • Model-based clustering
  • Multivariate Bernoulli distribution
  • Unbiased estimating equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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