title: Boosted beta regression.
abstract: Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit models to situations where the response is continuous on the interval (0,1). Consequently, beta regression is a convenient tool for analyzing percentage responses. The classical approach to fit a beta regression model is to use maximum likelihood estimation with subsequent AIC-based variable selection. As an alternative to this established - yet unstable - approach, we propose a new estimation technique called boosted beta regression. With boosted beta regression estimation and variable selection can be carried out simultaneously in a highly efficient way. Additionally, both the mean and the variance of a percentage response can be modeled using flexible nonlinear covariate effects. As a consequence, the new method accounts for common problems such as overdispersion and non-binomial variance structures.
authors.affiliation: Department of Medical Informatics, Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany. matthias.schmid@imbe.med.uni-erlangen.de
authors.forename: Matthias
authors.initials: M
authors.lastname: Schmid
authors.forename: Florian
authors.initials: F
authors.lastname: Wickler
authors.forename: Kelly O
authors.initials: KO
authors.lastname: Maloney
authors.forename: Richard
authors.initials: R
authors.lastname: Mitchell
authors.forename: Nora
authors.initials: N
authors.lastname: Fenske
authors.forename: Andreas
authors.initials: A
authors.lastname: Mayr
mesh_terms: D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D012107:Research Design / Q000706:statistics & numerical data*; D062211:Spatio-Temporal Analysis; D016008:Statistical Distributions