title: Centile estimation for a proportion response variable.
abstract: This paper introduces two general models for computing centiles when the response variable Y can take values between 0 and 1, inclusive of 0 or 1. The models developed are more flexible alternatives to the beta inflated distribution. The first proposed model employs a flexible four parameter logit skew Student t (logitSST) distribution to model the response variable Y on the unit interval (0, 1), excluding 0 and 1. This model is then extended to the inflated logitSST distribution for Y on the unit interval, including 1. The second model developed in this paper is a generalised Tobit model for Y on the unit interval, including 1. Applying these two models to (1-Y) rather than Y enables modelling of Y on the unit interval including 0 rather than 1. An application of the new models to real data shows that they can provide superior fits.
authors.affiliation: STORM, London Metropolitan University, London, U.K.
authors.forename: Abu
authors.initials: A
authors.lastname: Hossain
authors.affiliation: STORM, London Metropolitan University, London, U.K.
authors.forename: Robert
authors.initials: R
authors.lastname: Rigby
authors.affiliation: STORM, London Metropolitan University, London, U.K.
authors.forename: Mikis
authors.initials: M
authors.lastname: Stasinopoulos
authors.affiliation: University of Palermo, Palermo, Italy.
authors.forename: Marco
authors.initials: M
authors.lastname: Enea
mesh_terms: D003198:Computer Simulation; D006801:Humans; D016018:Least-Squares Analysis; D016015:Logistic Models; D008168:Lung / Q000502:physiology*; D008297:Male; D015233:Models, Statistical; D016008:Statistical Distributions
keywords: GAMLSS; beta inflated distribution; fractional data; generalised Tobit model; logit skew Student t distribution