Aim of this contribution is to propose a new regression model for continuous variables bounded to the unit interval (e.g. proportions) based on the flexible beta (FB) distribution. The latter is a special mixture of two betas, which greatly extends the shapes of the beta distribution mainly in terms of asymmetry, bimodality and heavy tail behaviour. Its special mixture structure ensures good theoretical properties, such as strong identifiability and likelihood boundedness, quite uncommon for mixture models. Moreover, it makes the model computationally very tractable also within the Bayesian framework here adopted. At the same time, the FB regression model displays easiness of interpretation as well as remarkable fitting capacity for a variety of data patterns, including unimodal and bimodal ones, heavy tails and presence of outliers. Indeed, simulation studies and applications to real datasets show a general better performance of the FB regression model with respect to competing ones, namely the beta (Ferrari and Cribari-Neto, 2004) and the beta rectangular (Bayes et al., 2012), in terms of precision of estimates, goodness of fit and posterior predictive intervals.

Migliorati, S., Di Brisco, A., Ongaro, A. (2018). A new regression model for bounded responses. BAYESIAN ANALYSIS, 13(3), 845-872 [10.1214/17-BA1079].

A new regression model for bounded responses

Migliorati, S;Di Brisco, A
;
Ongaro, A
2018

Abstract

Aim of this contribution is to propose a new regression model for continuous variables bounded to the unit interval (e.g. proportions) based on the flexible beta (FB) distribution. The latter is a special mixture of two betas, which greatly extends the shapes of the beta distribution mainly in terms of asymmetry, bimodality and heavy tail behaviour. Its special mixture structure ensures good theoretical properties, such as strong identifiability and likelihood boundedness, quite uncommon for mixture models. Moreover, it makes the model computationally very tractable also within the Bayesian framework here adopted. At the same time, the FB regression model displays easiness of interpretation as well as remarkable fitting capacity for a variety of data patterns, including unimodal and bimodal ones, heavy tails and presence of outliers. Indeed, simulation studies and applications to real datasets show a general better performance of the FB regression model with respect to competing ones, namely the beta (Ferrari and Cribari-Neto, 2004) and the beta rectangular (Bayes et al., 2012), in terms of precision of estimates, goodness of fit and posterior predictive intervals.
Articolo in rivista - Articolo scientifico
Beta regression; Flexible beta; Heavy tails; MCMC; Mixture models; Outliers; Proportions;
proportions; beta regression; flexible beta; mixture models; MCMC; outliers; heavy tails
English
2018
2018
13
3
845
872
reserved
Migliorati, S., Di Brisco, A., Ongaro, A. (2018). A new regression model for bounded responses. BAYESIAN ANALYSIS, 13(3), 845-872 [10.1214/17-BA1079].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/173482
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