A general class of zero-or-one inflated beta regression models

By Raydonal Ospina, Silvia L. P. Ferrari. Computational Statistics & Data Analysis, 2011

542 citations recorded by the source corpus.

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented.

Subfields: Artificial Intelligence, Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/80ba5f6f5d929a7bdfa851ca3195a957b3b29c34

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Citations in the corpus

Beta regression for time series analysis of bounded data, with application to Canada Google Flu Trends. (2014, methodology): “Finally, the model can be extended to allow for exact zeros and ones, by using the zero-or-one beta inflated regression model [Ospina and Ferrari (2012)] to define the univariate marginal distributions.”
Kumaraswamy autoregressive moving average models for double bounded environmental data (2017, background): “…for example, which resembles the generalized linear models (GLM) (McCullagh and Nelder, 1989), has been generalized, improved and applied in several works (Cribari-Neto and Zeileis, 2010; Simas et al., 2010; Ospina and Ferrari, 2012; Bayer and Cribari-Neto, 2013; Souza and Cribari-Neto, 2015).”
Analysing continuous proportions in ecology and evolution: A practical introduction to beta and Dirichlet regression (2019, methodology): “…exact zeros, as an alternative to the transformations above, it is possible to apply the so‐called zero‐inflated beta regression (Fang & Kong, 2015; Ospina & Ferrari, 2012), perhaps more properly referred to as zero‐augmented beta regression (Wright, Irvine, Warren, & Barnett, 2017), given the…”