Statistical Modelling 20 (3) (2020), 274–309
Robustness against outliers: A new variance inflated regression model for proportions
Agnese Maria Di Brisco,
Department of Economics,
Management and Statistics,
University of Milan-Bicocca,
Milan,
Italy
e-mail: agnese.dibrisco@unimib.it
Sonia Migliorati,
Department of Economics,
Management and Statistics,
University of Milan-Bicocca,
Milan,
Italy
Andrea Ongaro
Department of Economics,
Management and Statistics,
University of Milan-Bicocca,
Milan,
Italy
Abstract:
This article addresses the issue of building regression models for bounded responses, which are robust in the presence of outliers. To this end, a new distribution on (0,1) and a regression model based on it are proposed and some properties are derived. The distribution is a mixture of two beta components. One of them, showing a higher variance (variance inflated) is expected to capture outliers. Within a Bayesian approach, an extensive robustness study is performed to compare the new model with three competing ones present in the literature. A broad range of inferential tools are considered, aimed at measuring the influence of various outlier patterns from diverse perspectives. It emerges that the new model displays a better performance in terms of stability of regression coefficients’ posterior distributions and of regression curves under all outlier patterns. Moreover, it exhibits an adequate behaviour under all considered settings, unlike the other models.
Keywords:
Bayesian inference; Beta regression; bounded response; Hamiltonian Monte Carlo; mixture model; outlier.
Downloads:
Example data, code and supplementary material in
zipped archive.
back