Building flexible regression models: including the Birnbaum-Saunders distribution in the gamlss package
DOI:
https://doi.org/10.5433/1679-0375.2021v42n2p163Keywords:
Smoothing functions, Statistical modeling, Generalized additive models, Generalized linear modelsAbstract
Generalized additive models for location, scale and shape (GAMLSS) are a very flexible statistical modeling framework, being an important generalization of the well-known generalized linear models and generalized additive models. Their main advantage is that any probability distribution (that does not necessarily belong to the exponential family) can be considered to model the response variable and different regression structures can be fitted in each of its parameters. Currently, there are more than 100 distributions that are already implemented in the gamlss package in R software. Nevertheless, researchers can implement different distributions if they are not yet available, e.g., the Birnbaum-Saunders (BS) distribution, which is widely used in fatigue studies. In this paper we make available all codes regarding the inclusion of the BS distribution in the gamlss package, and then present a simple application related to air quality data for illustration purposesDownloads
Download data is not yet available.
References
ALIZADEH, M.; RAMIRES, T. G.; MIRMOSTAFAEE, S. M. T. K.; SAMIZADEH, M.; ORTEGA, E. M. M. O. A new useful four-parameter extension of the Gumbel distribution: Properties, regression model and applications using the GAMLSS framework. Communications in Statistics-Simulation and Computation, New York, v. 48, p. 1746-1767, 2019.
BIRNBAUM, Z. W., SAUNDERS, S. C. Estimation for a family of life distributions with applications to fatigue. Journal of Applied Probability, Sheffield, v. 6, p. 328–347, 1969.
DUNN, P. K.; SMYTH, G. K. Randomized quantile residuals. Journal of Computational and Graphical Statistics, Alexandria, v. 5, p. 236-245, 1996.
EILERS, P. H. C.; MARX, B. D. Flexible smoothing with B-splines and penalties. Statistical Science, Hayward, v. 11, p. 89-102, 1996.
EILERS, P. H. C.; MARX, B. D.; DURBÁN, M. Twenty years of P-splines. SORT, Barcelona, v. 39, p. 149-186, 2015.
FERNANDES, S. M.; BORNIA, A. C.; NAKAMURA, L. R. The influence of boards of directors on environmental disclosure. Management Decision, New York, v. 57, p. 2358-2382, 2019.
HAND, D. J.; DALY, F.; LUNN, A. D.; McCONWAY, K. J.; OSTROWSKI, E. A handbook of small data sets. London: Chapman and Hall, 1994. 458p.
HASTIE, T. J.; TIBSHIRANI, R. J. Generalized additive models. London: Chapman and Hall, 1990. 352p.
LEÃO, A. L. F.; URBANO, M. R. Street connectivity and walking: an empirical study in Londrina-PR. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 41, p. 31-42, 2020.
NAKAMURA, L. R.; CERQUEIRA, P. H. R.; RAMIRES, T. G.; PESCIM, R. R.; RIGBY, R. A.; STASINOPOULOS, D. M. A new continuous distribution on the unit interval applied to modelling the points ratio of football teams. Journal of Applied Statistics, Abingdon, v. 46, p. 416-431, 2019.
NAKAMURA, L. R.; RIGBY, R. A.; STASINOPOULOS, D. M.; LEANDRO, R. A.; VILLEGAS, C.; PESCIM, R. R. Modelling location, scale and shape parameters of the Birnbaum-Saunders generalized t distribution. Journal of Data Science, Taipei, v. 15, p. 221-238, 2017.
NELDER, J. A.; WEDDERBURN, R. W. M. Generalized linear models. Journal of the Royal Statistical Society. Series A (General), London, v. 135, p. 370-384, 1972.
R CORE TEAM. R: a language and environment for statistical computing. R Foundation for Statistical Computing. Vienna: [s. n.], 2021. Available in: https://www.Rproject.org/. Access on: May 01, 2021.
RAMIRES, T. G.; NAKAMURA, L. R.; RIGHETTO, A. J.; ORTEGA, E. M. M.; CORDEIRO, G. M. Predicting survival function and identifying associated factors in patients with renal insufficiency in the metropolitan area of Maringá, Paraná State, Brazil. Cadernos de Saúde Pública, Rio de Janeiro, v. 34, p. 1-13, 2018a.
RAMIRES, T. G.; NAKAMURA, L. R.; RIGHETTO, A. J.; PESCIM, R. R.; MAZUCHELI, J.; CORDEIRO, G. M. A new semiparametric Weibull cure rate model: fitting different behaviors within GAMLSS. Journal of Applied Statistics, Abingdon, v. 46, n. 15, p. 2744-2760, 2019.
RAMIRES, T. G.; CORDEIRO, G. M.; KATTAN, M. W.; HENS, N.; ORTEGA, E. M. M. Predicting the cure rate of breast cancer using a new regression model with four regression structures. Statistical methods in medical research, London, v. 27, n. 11, p. 3207-3223, 2018b.
RAMIRES, T. G.; NAKAMURA, L. R.; RIGHETTO, A. J.; CARVALHO, R. J.; VIEIRA, L. A.; PEREIRA, C. A. B. Comparison between Highly Complex Location Models and GAMLSS. Entropy, Basel, v. 23, n. 4, p. 469, 2021.
RIGBY, R. A.; STASINOPOULOS, D. M. Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society. Series C, Applied Statistics, London, v. 54, p. 507-554, 2005.
RIGHETTO, A. J.; RAMIRES, T. G.; NAKAMURA, L. R.; CASTANHO, P. L. D. B.; FAES, C.; SAVIAN, T. V. Predicting weed invasion in a sugarcane cultivar using multispectral image. Journal of Applied Statistics, Sheffield, v. 46, p. 1-12, 2019.
SOUZA, R. C.; RAMINELLI, J. Aplicação do modelo linear na avaliação de dados de estabilidade de medicamento. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 34, p. 57-66, 2013.
STASINOPOULOS, D. M.; RIGBY, R. A. Generalized additive models for location, scale and shape (GAMLSS). Journal of Statistical Software, [California], v. 23, p. 1-64, 2007.
STASINOPOULOS, M. D.; RIGBY, R. A.; HELLER, G. Z.; VOUDOURIS, V.; BASTIANI, F. Flexible Regression and Smoothing: Using GAMLSS. Boca Raton: Chapman and Hall, 2017. 549p.
VAN BUUREN, S.; FREDRIKS, M. Worm plot: a simple diagnostic device for modelling growth reference curves. Statistics in Medicine, Chichester, v. 20, p. 1259-1277, 2001.
BIRNBAUM, Z. W., SAUNDERS, S. C. Estimation for a family of life distributions with applications to fatigue. Journal of Applied Probability, Sheffield, v. 6, p. 328–347, 1969.
DUNN, P. K.; SMYTH, G. K. Randomized quantile residuals. Journal of Computational and Graphical Statistics, Alexandria, v. 5, p. 236-245, 1996.
EILERS, P. H. C.; MARX, B. D. Flexible smoothing with B-splines and penalties. Statistical Science, Hayward, v. 11, p. 89-102, 1996.
EILERS, P. H. C.; MARX, B. D.; DURBÁN, M. Twenty years of P-splines. SORT, Barcelona, v. 39, p. 149-186, 2015.
FERNANDES, S. M.; BORNIA, A. C.; NAKAMURA, L. R. The influence of boards of directors on environmental disclosure. Management Decision, New York, v. 57, p. 2358-2382, 2019.
HAND, D. J.; DALY, F.; LUNN, A. D.; McCONWAY, K. J.; OSTROWSKI, E. A handbook of small data sets. London: Chapman and Hall, 1994. 458p.
HASTIE, T. J.; TIBSHIRANI, R. J. Generalized additive models. London: Chapman and Hall, 1990. 352p.
LEÃO, A. L. F.; URBANO, M. R. Street connectivity and walking: an empirical study in Londrina-PR. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 41, p. 31-42, 2020.
NAKAMURA, L. R.; CERQUEIRA, P. H. R.; RAMIRES, T. G.; PESCIM, R. R.; RIGBY, R. A.; STASINOPOULOS, D. M. A new continuous distribution on the unit interval applied to modelling the points ratio of football teams. Journal of Applied Statistics, Abingdon, v. 46, p. 416-431, 2019.
NAKAMURA, L. R.; RIGBY, R. A.; STASINOPOULOS, D. M.; LEANDRO, R. A.; VILLEGAS, C.; PESCIM, R. R. Modelling location, scale and shape parameters of the Birnbaum-Saunders generalized t distribution. Journal of Data Science, Taipei, v. 15, p. 221-238, 2017.
NELDER, J. A.; WEDDERBURN, R. W. M. Generalized linear models. Journal of the Royal Statistical Society. Series A (General), London, v. 135, p. 370-384, 1972.
R CORE TEAM. R: a language and environment for statistical computing. R Foundation for Statistical Computing. Vienna: [s. n.], 2021. Available in: https://www.Rproject.org/. Access on: May 01, 2021.
RAMIRES, T. G.; NAKAMURA, L. R.; RIGHETTO, A. J.; ORTEGA, E. M. M.; CORDEIRO, G. M. Predicting survival function and identifying associated factors in patients with renal insufficiency in the metropolitan area of Maringá, Paraná State, Brazil. Cadernos de Saúde Pública, Rio de Janeiro, v. 34, p. 1-13, 2018a.
RAMIRES, T. G.; NAKAMURA, L. R.; RIGHETTO, A. J.; PESCIM, R. R.; MAZUCHELI, J.; CORDEIRO, G. M. A new semiparametric Weibull cure rate model: fitting different behaviors within GAMLSS. Journal of Applied Statistics, Abingdon, v. 46, n. 15, p. 2744-2760, 2019.
RAMIRES, T. G.; CORDEIRO, G. M.; KATTAN, M. W.; HENS, N.; ORTEGA, E. M. M. Predicting the cure rate of breast cancer using a new regression model with four regression structures. Statistical methods in medical research, London, v. 27, n. 11, p. 3207-3223, 2018b.
RAMIRES, T. G.; NAKAMURA, L. R.; RIGHETTO, A. J.; CARVALHO, R. J.; VIEIRA, L. A.; PEREIRA, C. A. B. Comparison between Highly Complex Location Models and GAMLSS. Entropy, Basel, v. 23, n. 4, p. 469, 2021.
RIGBY, R. A.; STASINOPOULOS, D. M. Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society. Series C, Applied Statistics, London, v. 54, p. 507-554, 2005.
RIGHETTO, A. J.; RAMIRES, T. G.; NAKAMURA, L. R.; CASTANHO, P. L. D. B.; FAES, C.; SAVIAN, T. V. Predicting weed invasion in a sugarcane cultivar using multispectral image. Journal of Applied Statistics, Sheffield, v. 46, p. 1-12, 2019.
SOUZA, R. C.; RAMINELLI, J. Aplicação do modelo linear na avaliação de dados de estabilidade de medicamento. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 34, p. 57-66, 2013.
STASINOPOULOS, D. M.; RIGBY, R. A. Generalized additive models for location, scale and shape (GAMLSS). Journal of Statistical Software, [California], v. 23, p. 1-64, 2007.
STASINOPOULOS, M. D.; RIGBY, R. A.; HELLER, G. Z.; VOUDOURIS, V.; BASTIANI, F. Flexible Regression and Smoothing: Using GAMLSS. Boca Raton: Chapman and Hall, 2017. 549p.
VAN BUUREN, S.; FREDRIKS, M. Worm plot: a simple diagnostic device for modelling growth reference curves. Statistics in Medicine, Chichester, v. 20, p. 1259-1277, 2001.
Downloads
Published
2021-11-03
How to Cite
Roquim, F. V., Ramires, T. G., Nakamura, L. R., Righetto, A. J., Lima, R. R., & Gomes, R. A. (2021). Building flexible regression models: including the Birnbaum-Saunders distribution in the gamlss package. Semina: Ciências Exatas E Tecnológicas, 42(2), 163–168. https://doi.org/10.5433/1679-0375.2021v42n2p163
Issue
Section
Original Article
License
The Copyright Declaration for articles published in this journal is the author’s right. Since manuscripts are published in an open access Journal, they are free to use, with their own attributions, in educational and non-commercial applications. The Journal has the right to make, in the original document, changes regarding linguistic norms, orthography, and grammar, with the purpose of ensuring the standard norms of the language and the credibility of the Journal. It will, however, respect the writing style of the authors. When necessary, conceptual changes, corrections, or suggestions will be forwarded to the authors. In such cases, the manuscript shall be subjected to a new evaluation after revision. Responsibility for the opinions expressed in the manuscripts lies entirely with the authors.
This journal is licensed with a license Creative Commons Attribution-NonCommercial 4.0 International.
