Multivariate quasi-beta regression models for continuous bounded data
-
Ricardo R. Petterle
,
Wagner H. Bonat
,
Cassius T. Scarpin
Abstract
We propose a multivariate regression model to deal with multiple continuous bounded data. The proposed model is based on second-moment assumptions, only. We adopted the quasi-score and Pearson estimating functions for estimation of the regression and dispersion parameters, respectively. Thus, the proposed approach does not require a multivariate probability distribution for the variable response vector. The multivariate quasi-beta regression model can easily handle multiple continuous bounded outcomes taking into account the correlation between the response variables. Furthermore, the model allows us to analyze continuous bounded data on the interval [0, 1], including zeros and/or ones. Simulation studies were conducted to investigate the behavior of the NORmal To Anything (NORTA) algorithm and to check the properties of the estimating function estimators to deal with multiple correlated response variables generated from marginal beta distributions. The model was motivated by a data set concerning the body fat percentage, which was measured at five regions of the body and represent the response variables. We analyze each response variable separately and compare it with the fit of the multivariate proposed model. The multivariate quasi-beta regression model provides better fit than its univariate counterparts, as well as allows us to measure the correlation between response variables. Finally, we adapted diagnostic tools to the proposed model. In the supplementary material, we provide the data set and R code.
Acknowledgments
The authors thank the two referees for their helpful comments and suggestions that greatly improved the presentation of this paper.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Supplementary material
http://www.leg.ufpr.br/doku.php/publications:papercompanions:multquasibeta
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Research Articles
- The method of envelopes to concisely calculate semiparametric efficient scores under parametric restrictions
- A machine learning-based approach for estimating and testing associations with multivariate outcomes
- Shrinkage estimation applied to a semi-nonparametric regression model
- Multivariate quasi-beta regression models for continuous bounded data
- Integrative analysis with a system of semiparametric projection non-linear regression models
- Seemingly unrelated regression with measurement error: estimation via Markov Chain Monte Carlo and mean field variational Bayes approximation
- Alternatives to the Kaplan–Meier estimator of progression-free survival
- Two-stage receiver operating-characteristic curve estimator for cohort studies
- Estimating the area under a receiver operating characteristic curve using partially ordered sets
- Modelling ethnic differences in the distribution of insulin resistance via Bayesian nonparametric processes: an application to the SABRE cohort study
- Co-localization analysis in fluorescence microscopy via maximum entropy copula
Artikel in diesem Heft
- Frontmatter
- Research Articles
- The method of envelopes to concisely calculate semiparametric efficient scores under parametric restrictions
- A machine learning-based approach for estimating and testing associations with multivariate outcomes
- Shrinkage estimation applied to a semi-nonparametric regression model
- Multivariate quasi-beta regression models for continuous bounded data
- Integrative analysis with a system of semiparametric projection non-linear regression models
- Seemingly unrelated regression with measurement error: estimation via Markov Chain Monte Carlo and mean field variational Bayes approximation
- Alternatives to the Kaplan–Meier estimator of progression-free survival
- Two-stage receiver operating-characteristic curve estimator for cohort studies
- Estimating the area under a receiver operating characteristic curve using partially ordered sets
- Modelling ethnic differences in the distribution of insulin resistance via Bayesian nonparametric processes: an application to the SABRE cohort study
- Co-localization analysis in fluorescence microscopy via maximum entropy copula
