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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.46 no.1 Bogotá Jan./June 2023 Epub Jan 18, 2023
https://doi.org/10.15446/rce.v46n1.105335
Original articles of research
μσ 2-Beta and μσ 2-Beta Binomial Regression Models
Modelos de regresión μσ 2 -Beta y μσ 2 -Beta binomial
1 Department of Statistics, Faculty of Sciences, Universidad Nacional de Colombia, Bogotá D.C., Colombia
This paper proposes new parameterizations of the beta and beta binomial distributions as functions of the mean and variance parameters. From these new parameterizations, new beta and beta binomial linear regression models are formulated by assuming that appropriate real functions of the mean and variance follow linear regression structures. These models were fitted to real datasets by applying Bayesian methods, using the OpenBUGS software. The new beta regression models were fitted to the Dyslexia Reading Accuracy dataset and the new beta binomial regression models were applied to the School Absenteeism Dataset. In both cases, the results obtained by fitting these models were compared with those obtained by fitting the usual mean and dispersion beta regression models and the mean and dispersion beta binomial regression models, respectively.
Key words: Mean and variance beta and beta binomial distributions; Beta and beta-binomial regression models; Bayesian methods
Este artículo propone nuevas parametrizaciones de las distribuciones beta y beta binomial como funciones de los parámetros de media y varianza. A partir de estas nuevas parametrizaciones, se formulan nuevos modelos de regresión lineal beta y beta binomial asumiendo que funciones reales apropiadas de la media y la varianza siguen estructuras de regresión lineal. Estos modelos se ajustaron a conjuntos de datos reales mediante la aplicación de métodos bayesianos, utilizando el software OpenBUGS. Los nuevos modelos de regresión beta se ajustaron al conjunto de datos de precisión de lectura de niños con dislexia y los nuevos modelos de regresión beta binomial se aplicaron al conjunto de datos de ausentismo escolar. En ambos casos, los resultados obtenidos ajustando estos modelos se compararon con los obtenidos ajustando los modelos habituales de regresión beta de media y dispersión y los modelos de regresión beta binomial de media y dispersión, respectivamente.
Palabras clave: Media y varianza; Distribución beta; Distribución beta binomial; Modelos de regresión beta y beta-binomial; Métodos bayesianos
References
Atkinson, A. B. (1970), 'On the measurement of inequality', Journal of Economic Theory 3(32), 244-263. [ Links ]
Cepeda-Cuervo, E. (2001), Modelagem da Variabilidade em Modelos Lineares Generalizados, Unpublished Ph.D. thesis, Mathematics Institute, Universidade Federal do Rio de Janeiro. URL: http://www.docentes.unal.edu.co/ecepedac/does/TESISFINAL.pdf. [ Links ]
Cepeda-Cuervo, E. (2015), 'Beta regression models: Joint mean and variance modeling', Revista Colombiana de Estadística 9(1), 134-145. [ Links ]
Cepeda-Cuervo, E. & Cifuentes-Amado, M. V. (2017), 'Double generalized beta-binomial and negative binomial regression models', Revista Colombiana de Estadística (40), 141-163. [ Links ]
Cepeda-Cuervo, E. & Garrido, L. (2015), 'Bayesian beta regression models with joint mean and dispersion modeling', Monte Carlo Methods and Applications 21(1), 49-58. [ Links ]
Cepeda-Cuervo, E. & Núñez Antón, V. (2013), 'Spatial double generalized beta regression models: extensions and application to study quality of education in Colombia', Journal of Educational and Behavioral Statistics 6(38), 604-628. [ Links ]
Cepeda, E. C. & Achcar, J. A. (2010), 'Heteroscedastic nonlinear regression models', Communications in Statistics Simulation and Computation 2(39), 405-419. [ Links ]
Cepeda, E. & Gamerman, D. (2005), 'Bayesian methodology for modeling parameters in the two parameter exponential family', Revista Estadistica 57(168-169), 93-105. [ Links ]
Cribari-Neto, F. & Zeileis, A. (2010), 'Beta regression in R', Journal of Statistical Software (34), 1-24. [ Links ]
Ferrari, S. & Cribari-Neto, F. (2004), 'Beta regression for modelling rates and proportions', Journal of Applied Statistics (31-7), 799-815. [ Links ]
Hunger, M., Döring, A. & Holle, R. (2012), 'Longitudinal beta regression models for analyzing health-related quality of life scores over time', BMC medical research methodology 1(12), 1-12. [ Links ]
Jorgensen, B. (1997), 'Proper dispersion models', Brazilian Journal of Probability and Statistics 11(2), 89-128. http://www.jstor.org/stable/43600934 [ Links ]
Paolino, P. (2001), 'Maximum likelihood estimation of models with beta-distributed dependent variables', Political Analysis 4(9), 325-346. [ Links ]
Quine, S. (1975), Achievement orientation of aboriginal and white Australian adolescents, Ph.D. thesis, Australia. [ Links ]
Quintero-Sarmiento, A., Cepeda-Cuervo, E. & Nunez-Anton, V. (2012), 'Estimating infant mortality in Colombia: some overdispersion modelling approaches', Journal of Applied Statistics 39(5), 1011-1036. [ Links ]
Simas, A. B., Barreto-Souza, W. & Rocha, A. V. (2010), 'Improved estimators for a general class of beta regression models', Computational Statistics and Data Analysis 2(54), 348-366. [ Links ]
Smithson, M. & Verkuilen, J. (2006), 'A better lemon squeezer? maximum-likelihood regression with beta-distributed dependent variables', Psychological Methods 1(11), 54. [ Links ]
Received: October 2022; Accepted: December 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
