Robustness against outliers: A new variance inflated regression model for proportions. (June 2020)

• Record Type: Journal Article
• Authors: Di Brisco, Agnese Maria; Migliorati, Sonia; Ongaro, Andrea
• Is Part Of: Statistical modelling. Volume 20:Number 3(2020)
• Page Start: 274
• Page End: 309
• Publication Date: 2020-06
• Subjects: Bayesian inference -- Beta regression -- bounded response -- Hamiltonian Monte Carlo -- mixture model -- outlier; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X18821213
• Languages: English
• ISSNs: 1471-082X

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.