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Activity Number: 81
Type: Contributed
Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
Sponsor: Biometrics Section
Abstract #316121
Title: Nonparametric Regression Models for Ordinal Predictors
Author(s): Bradley Turnbull* and Sujit Ghosh
Companies: North Carolina State University and SAMSI/North Carolina State University
Keywords: ordinal data ; ordinal predictors ; non-parametric regression ; latent variable ; Bayesian
Abstract:

Ordinal data is encountered in almost all scientific fields. Since 1980 there has been an increasing focus on developing methods that distinguish between ordinal and categorical data. While there has been notable progress and attention paid to regression scenarios featuring ordinal response variables, there has been much less attention given to the case of ordinal predictors. The few methods specifically designed for ordinal predictors generally require strong assumptions which often result in bias parameter estimates. Using the well accepted ideology that ordinal variables are a manifestation of an underlying continuous variable, we propose a flexible non-parametric regression model which models the response variable against that said latent variable using a linear combination of basis functions. We provide both Bayesian inference and frequentist maximum likelihood procedures to obtain parameter estimates. We also provide an approximate likelihood approach which offers significant relief in computation time. Through a collection of simulation studies we show that our assumption free approach renders unbiased and more efficient main effects estimates than popular competing methods.


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