Regression model for proportions with probability masses at zero and one
| STATISTICA & APPLICAZIONI - 2012 - 2
In many settings, the variable of interest is a proportion with high concentration of data at the
boundaries. This paper proposes a regression model for a fractional variable with nontrivial probability
masses at the extremes. In particular, the dependent variable is assumed to be a mixed random
variable, obtained as the mixture of a Bernoulli and a beta random variables. The endpoints
of zero and one are modelled by a logistic regression model. The values belonging to the interval
(0,1) are assumed to be beta distributed and their mean and dispersion are jointly modelled by
using two link functions. The regression model proposed here accommodates skewness and heteroscedastic
errors. Finally, an application to loan recovery process of Italian banks is also provided.
Keywords: Proportions, Mixed Random Variable, Beta Regression, Skewness, Heteroscedasticity.