Hierarchical and multivariate regression models to fit correlated asymmetric positive continuous outcomes

Lizandra C. Fabio (), Francisco J. A. Cysneiros (), Gilberto A. Paula () and Jalmar M. F. Carrasco ()
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Lizandra C. Fabio: Federal University of Bahia
Francisco J. A. Cysneiros: Federal University of Pernambuco
Gilberto A. Paula: University of Sao Paulo
Jalmar M. F. Carrasco: Federal University of Bahia

Computational Statistics, 2022, vol. 37, issue 3, No 17, 1435-1459

Abstract: Abstract In the extant literature, hierarchical models typically assume a flexible distribution for the random-effects. The random-effects approach has been used in the inferential procedure of the generalized linear mixed models . In this paper, we propose a random intercept gamma mixed model to fit correlated asymmetric positive continuous outcomes. The generalized log-gamma (GLG) distribution is assumed as an alternative to the normality assumption for the random intercept. Numerical results demonstrate the impact on the maximum likelihood (ML) estimator when the random-effect distribution is misspecified. The extended inverted Dirichlet (EID) distribution is derived from the random intercept gamma-GLG model that leads to the EID regression model by supposing a particular parameter setting of the hierarchical model. Monte Carlo simulation studies are performed to evaluate the asymptotic behavior of the ML estimators from the proposed models. Analysis of diagnostic methods based on quantile residual and COVARATIO statistic are used to assess departures from the EID regression model and identify atypical subjects. Two applications with real data are presented to illustrate the proposed methodology.

Keywords: Generalized linear mixed model; Generalized log-gamma distribution; Misspecification of the random-effects; Extended inverted Dirichlet model; Diagnostic analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00180-021-01163-7

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