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Centile estimation for a proportion response variable
Author(s) -
Hossain Abu,
Rigby Robert,
Stasinopoulos Mikis,
Enea Marco
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6748
Subject(s) - interval (graph theory) , variable (mathematics) , tobit model , skew , unit interval , unit (ring theory) , statistics , interval estimation , distribution (mathematics) , econometrics , mathematics , computer science , confidence interval , combinatorics , mathematical analysis , telecommunications , mathematics education
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. Copyright © 2015 John Wiley & Sons, Ltd.