IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v37y2022i3d10.1007_s00180-021-01163-7.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-021-01163-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-021-01163-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Bijlsma Ineke & van den Brakel Jan & van der Velden Rolf & Allen Jim, 2020. "Estimating Literacy Levels at a Detailed Regional Level: an Application Using Dutch Data," Journal of Official Statistics, Sciendo, vol. 36(2), pages 251-274, June.
    3. Jie Huang & Haiming Zhou & Nader Ebrahimi, 2022. "Bayesian Bivariate Cure Rate Models Using Copula Functions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(3), pages 1-9, May.
    4. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
    5. Myung-Jae Hwang & Jong-Hun Kim & Hae-Kwan Cheong, 2020. "Short-Term Impacts of Ambient Air Pollution on Health-Related Quality of Life: A Korea Health Panel Survey Study," IJERPH, MDPI, vol. 17(23), pages 1-11, December.
    6. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    7. Zhengxin Zhang & Xiaosheng Si & Changhua Hu & Xiangyu Kong, 2015. "Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity," Journal of Risk and Reliability, , vol. 229(4), pages 343-355, August.
    8. Francesco BARTOLUCCI & Silvia BACCI & Claudia PIGINI, 2015. "A Misspecification Test for Finite-Mixture Logistic Models for Clustered Binary and Ordered Responses," Working Papers 410, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    9. Shun Yu & Xianzheng Huang, 2019. "Link misspecification in generalized linear mixed models with a random intercept for binary responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 827-843, September.
    10. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    11. Masahiro Kojima & Tatsuya Kubokawa, 2013. "Bartlett Adjustments for Hypothesis Testing in Linear Models with General Error Covariance Matrices," CIRJE F-Series CIRJE-F-884, CIRJE, Faculty of Economics, University of Tokyo.
    12. Sun-Joo Cho & Paul Boeck & Susan Embretson & Sophia Rabe-Hesketh, 2014. "Additive Multilevel Item Structure Models with Random Residuals: Item Modeling for Explanation and Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 84-104, January.
    13. Ward, Eric J., 2008. "A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools," Ecological Modelling, Elsevier, vol. 211(1), pages 1-10.
    14. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2017. "Mixed generalized Akaike information criterion for small area models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1229-1252, October.
    15. Mojtaba Ganjali & Taban Baghfalaki, 2018. "Application of Penalized Mixed Model in Identification of Genes in Yeast Cell-Cycle Gene Expression Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(2), pages 38-41, April.
    16. Kauermann, Goran & Xu, Ronghui & Vaida, Florin, 2008. "Stacked Laplace-EM algorithm for duration models with time-varying and random effects," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2514-2528, January.
    17. Philipp F. M. Baumann & Enzo Rossi & Alexander Volkmann, 2020. "What Drives Inflation and How: Evidence from Additive Mixed Models Selected by cAIC," Papers 2006.06274, arXiv.org, revised Aug 2022.
    18. Jiang, Jiming & Nguyen, Thuan & Rao, J. Sunil, 2009. "A simplified adaptive fence procedure," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 625-629, March.
    19. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    20. Eric F. Lock & Nidhi Kohli & Maitreyee Bose, 2018. "Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 733-750, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:37:y:2022:i:3:d:10.1007_s00180-021-01163-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.