Multivariate quasi-beta regression models for continuous bounded data

Petterle Ricardo R. (), Bonat Wagner H., Scarpin Cassius T., Jonasson Thaísa and Borba Victória Z. C.
Additional contact information
Petterle Ricardo R.: Department of Integrative Medicine, Federal University of Parana, Curitiba, Brazil
Bonat Wagner H.: Laboratory of Statistics and Geoinformation, Department of Statistics, Federal University of Parana, Curitiba, Brazil
Scarpin Cassius T.: Research Group of Technology Applied to Optimization (GTAO), Federal University of Parana, Curitiba, Brazil
Jonasson Thaísa: Internal Medicine, Federal University of Parana, Curitiba, Brazil
Borba Victória Z. C.: Endocrine Division, Hospital de Clínicas da Universidade Federal do Paraná (SEMPR), Federal University of Parana, Curitiba, Brazil

The International Journal of Biostatistics, 2021, vol. 17, issue 1, 39-53

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.

Keywords: correlated data; estimating functions; multiple continuous bounded outcomes; NORTA algorithm; simulation study; unit interval (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/ijb-2019-0163 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:ijbist:v:17:y:2021:i:1:p:39-53:n:12

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/ijb/html

DOI: 10.1515/ijb-2019-0163

Access Statistics for this article

The International Journal of Biostatistics is currently edited by Antoine Chambaz, Alan E. Hubbard and Mark J. van der Laan

More articles in The International Journal of Biostatistics from De Gruyter
Bibliographic data for series maintained by Peter Golla ().