Centile estimation for a proportion response variable.
TL;DR: Two general models for computing centiles when the response variable Y can take values between 0 and 1, inclusive of 0 or 1 are introduced, and can provide superior fits.
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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.
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Figures
Figure 4. Z statistics for a) LMS b) BEINF1 c) Inflated logitSST d) Generalised Tobit 
Table 1. Comparison of Fitted Models 
Table 2. Comparison of fitted centile percentages 
Figure 1. Centile curves for model a) LMS b) BEINF1 c) Inflated logitSST d) Generalised Tobit 
Figure 2. Twin worm plot for LMS (dark points) and BEINF1 (light points) models.
Citations
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