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Regression modelling with the tilted beta distribution: A Bayesian approach
Author(s) -
Hahn Eugene D.
Publication year - 2021
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11563
Subject(s) - beta distribution , bayesian linear regression , bayesian probability , beta (programming language) , regression analysis , regression , mathematics , statistics , econometrics , bayesian inference , computer science , programming language
Beta regression models are commonly used in the case of a dependent variable y that exists on the range (0,1). However, when y can additionally take on the values of zero and/or one, limitations of the beta distribution and beta regression models become apparent. One recent approach is to use an inflated beta regression model which has discrete point‐valued components. In this article, we introduce a new class of regression models for y ∈ [0,1] that is fully continuous. This allows the entirety of y to be treated as a continuum instead of discontinuously, which appears to be a new development for the literature. We use a Bayesian approach for estimation. We also illustrate the impact of different choices of prior distributions on empirical findings and perform a simulation study examining model fit.