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.
Highlights
A relevant problem in applied statistics concerns modeling rates, proportions or, more generally, continuous variables restricted to the interval (0, 1) (Kieschnick and McCullough, 2003)
When modeling responses bounded to the unit interval, the FB regression (FBR) model turns out to be a good compromise between tractability and flexibility
Even when data are simulated from a beta or a BR regression (BRR) model, or more generally are unimodal the FBR model shows a comparable or, more often, better performance, especially in terms of fitting criteria
Summary
A relevant problem in applied statistics concerns modeling rates, proportions or, more generally, continuous variables restricted to the interval (0, 1) (Kieschnick and McCullough, 2003). Some simulation studies confirmed that convergence to the posterior distribution may be hard to achieve in this case and, even considering long chains, the simulated distribution is sensible to initial values The aim of this contribution is to provide (adopting a Bayesian approach) a new regression model, that can handle the trade-off between flexibility and tractability. To this end, we introduce the flexible beta (FB) distribution (univariate version of the flexible Dirichlet distribution (Ongaro and Migliorati, 2013)), which is a special mixture of two beta distributions with arbitrary means and common variance. In the latter section a comparison with the general BM regression model is provided as well
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
