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A Copula-Based GLMM Model for Multivariate Longitudinal Data with Mixed-Types of Responses

Weiping Zhang, MengMeng Zhang and Yu Chen ()
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Weiping Zhang: University of Science and Technology of China
MengMeng Zhang: University of Science and Technology of China
Yu Chen: University of Science and Technology of China

Sankhya B: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 7, 353-379

Abstract: Abstract We propose a copula-based generalized linear mixed model (GLMM) to jointly analyze multivariate longitudinal data with mixed types, including continuous, count and binary responses. The association of repeated measurements is modelled through the GLMM model, meanwhile a pair-copula construction (D-vine) is adopted to measure the dependency structure between different responses. By combining mixed models and D-vine copulas, our proposed approach could not only deal with unbalanced data with arbitrary margins but also handle moderate dimensional problems due to the efficiency and flexibility of D-vines. Based on D-vine copulas, algorithms for sampling mixed data and computing likelihood are also developed. Leaving the random effects distribution unspecified, we use nonparametric maximum likelihood for model fitting. Then an E-M algorithm is used to obtain the maximum likelihood estimates of parameters. Both simulations and real data analysis show that the nonparametric models are more efficient and flexible than the parametric models.

Keywords: Longitudinal data; Mixed types; Joint estimate; D-vine copula; Nonparametric maximum likelihood; E-M algorithm; Primary 62G05; Secondary 62J12 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13571-019-00197-8

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