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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Lizandra C. Fabio & Francisco J. A. Cysneiros & Gilberto A. Paula & Jalmar M. F. Carrasco, 2022. "Hierarchical and multivariate regression models to fit correlated asymmetric positive continuous outcomes," Computational Statistics, Springer, vol. 37(3), pages 1435-1459, July.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:3:d:10.1007_s00180-021-01163-7
    DOI: 10.1007/s00180-021-01163-7
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    References listed on IDEAS

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    1. Jeremias Leão & Francisco Cysneiros & Helton Saulo & N. Balakrishnan, 2016. "Constrained test in linear models with multivariate power exponential distribution," Computational Statistics, Springer, vol. 31(4), pages 1569-1592, December.
    2. Peng Zhang & Peter X.-K. Song & Annie Qu & Tom Greene, 2008. "Efficient Estimation for Patient-Specific Rates of Disease Progression Using Nonnormal Linear Mixed Models," Biometrics, The International Biometric Society, vol. 64(1), pages 29-38, March.
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    4. Fabio, Lizandra C. & Paula, Gilberto A. & Castro, Mário de, 2012. "A Poisson mixed model with nonnormal random effect distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1499-1510.
    5. Alonso, A. & Litière, S. & Molenberghs, G., 2008. "A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4474-4486, May.
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