A mixture of generalized latent variable models for mixed mode and heterogeneous data

• Published in: Computational statistics & data analysis Vol. 55; no. 11; pp. 2889 - 2907
• Main Authors: Cai, Jing-Heng, Song, Xin-Yuan, Lam, Kwok-Hap, Ip, Edward Hak-Sing
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2011; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Applications; Bayesian approach; Bayesian approach Generalized latent variable model Heterogeneous data; Biology, psychology, social sciences; Computer simulation; Counting; Data processing; Exact sciences and technology; General topics; Generalized latent variable model; Heterogeneity; Heterogeneous data; Mathematical analysis; Mathematical models; Mathematics; Monte Carlo methods; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Sciences and techniques of general use; Statistics; Generalized latent variable model; Bayesian approach; Heterogeneous data; Bayes estimation; Mixed distribution; Monte Carlo method; Data analysis; Social sciences; Model selection; Latent variable model; Stochastic method; Statistical simulation; Sociometry; Markov chain; Statistical method; Heterogeneity; Statistical computation; Selection method; Sample survey
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2011.05.011

In the behavioral, biomedical, and social–psychological sciences, mixed data types such as continuous, ordinal, count, and nominal are common. Subpopulations also often exist and contribute to heterogeneity in the data. In this paper, we propose a mixture of generalized latent variable models (GLVMs) to handle mixed types of heterogeneous data. Different link functions are specified to model data of multiple types. A Bayesian approach, together with the Markov chain Monte Carlo (MCMC) method, is used to conduct the analysis. A modified DIC is used for model selection of mixture components in the GLVMs. A simulation study shows that our proposed methodology performs satisfactorily. An application of mixture GLVM to a data set from the National Longitudinal Surveys of Youth (NLSY) is presented.