TY - JOUR
T1 - Robustness against outliers
T2 - A new variance inflated regression model for proportions
AU - Di Brisco, Agnese Maria
AU - Migliorati, Sonia
AU - Ongaro, Andrea
N1 - Publisher Copyright:
© 2019 SAGE Publications.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - 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.
AB - 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.
KW - Bayesian inference
KW - Beta regression
KW - Hamiltonian Monte Carlo
KW - bounded response
KW - mixture model
KW - outlier
UR - http://www.scopus.com/inward/record.url?scp=85062476393&partnerID=8YFLogxK
U2 - 10.1177/1471082X18821213
DO - 10.1177/1471082X18821213
M3 - Article
SN - 1471-082X
VL - 20
SP - 274
EP - 309
JO - Statistical Modelling
JF - Statistical Modelling
IS - 3
ER -