Mixture Modeling for Longitudinal Data

• Published in: Journal of computational and graphical statistics Vol. 25; no. 4; pp. 1117 - 1137
• Main Authors: Tang, Xiwei, Qu, Annie
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.12.2016; American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Algorithms; Asymptotic methods; Correlation analysis; Estimating techniques; Expectation-estimating-equation algorithm; Generalized linear models; Latent variable; Model-based clustering; Multivariate Bernoulli distribution; Probability distribution; Studies; Temporal Data Analysis; Unbiased estimating equation
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2015.1092979

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.