Latent variable modeling of multivariate binary data using general correlation structures
Abstract
Latent class models are widely used for analyzing correlated binary data. The underlying premise is that these data arise from a population consisting of different latent classes. Traditional latent class modeling assumes that the observed variables are independent conditional on the latent membership. This independence assumption is rarely valid in practice. While various latent class models have been developed to incorporate the likely dependence among variables, these models either do not provide direct inference on the correlations, or assume a restricted correlation structure. We propose a probit latent class model that combines the features of latent class analysis and multivariate probit analysis. Within each latent class, the observed variables are modeled using a multivariate probit model with a general correlation structure. The features of the probit latent class model enable not only the direct inference on the within-class associations among the variables but also classification of the latent membership of the subjects. The maximum likelihood inference of the probit latent class is carried out using the parameter expanded expectation maximization algorithm. Important issues of the probit latent class models, including the model identifiability and goodness-of-fit testing are explored. Simulation studies and applications of the model to the real world problems demonstrate the importance of model selection and correct specification of the dependence structure. The proposed algorithm using parameter expanded expectation maximization algorithm is also applied to multivariate probit analysis, which is a special case of the probit latent class model with a single latent class. Examples show that this algorithm converges very rapidly and overcome some of the previous computational difficulties of earlier approaches.
Degree
Ph.D.
Advisors
Craig, Purdue University.
Subject Area
Statistics
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