A mixture latent variable model for modeling mixed data in heterogeneous populations and its applications

Leila Amiri, Mojtaba Khazaei () and Mojtaba Ganjali
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Leila Amiri: Shahid Beheshti University
Mojtaba Khazaei: Shahid Beheshti University
Mojtaba Ganjali: Shahid Beheshti University

AStA Advances in Statistical Analysis, 2018, vol. 102, issue 1, No 5, 95-115

Abstract: Abstract Latent variable models are widely used for jointly modeling of mixed data including nominal, ordinal, count and continuous data. In this paper, we consider a latent variable model for jointly modeling relationships between mixed binary, count and continuous variables with some observed covariates. We assume that, given a latent variable, mixed variables of interest are independent and count and continuous variables have Poisson distribution and normal distribution, respectively. As such data may be extracted from different subpopulations, consideration of an unobserved heterogeneity has to be taken into account. A mixture distribution is considered (for the distribution of the latent variable) which accounts the heterogeneity. The generalized EM algorithm which uses the Newton–Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. The standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. Analysis of the primary biliary cirrhosis data is presented as an application of the proposed model.

Keywords: Mixed data; Latent variable model; Mixture distribution; Generalized linear model; The EM algorithm; The SEM algorithm (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10182-017-0294-3

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