Statistics and Its Interface

Volume 14 (2021)

Number 3

Robust regression model for ordinal response

Pages: 243 – 254

DOI: https://dx.doi.org/10.4310/20-SII631

Authors

Ao Yuan (Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington, D.C., U.S.A.)

Chongyang Duan (Department of Biostatistics, School of Public Health, Southern Medical University, Guangzhou, China)

Ming T. Tan (Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington, D.C., U.S.A.)

Abstract

Ordinal outcome data with covariates occur frequently in statistical practice including applications from biomedicine to marketing research. Most existing methods for this type of data have relied on subjectively specified models that allow order restriction. There are also some semiparametric ordinal models which are more flexible than parametric ones, with fixed link function, they are still not flexible enough to capture the true link or the relationship between the response and covariates. We propose a broadly applicable robust semiparametric ordinal regression model, in which the relationship between the response and covariates is modelled with a nonparametric monotone increasing link function and parametric regression coefficients. This model is more robust and flexible than existing semiparametric and parametric models for this problem. The semiparametric maximum likelihood estimate is used to estimate the model parameters, and the asymptotic properties of the estimates are derived. Simulation studies show clear advantages of the proposed model over existing parametric models, and a real data analysis illustrates the utility of the proposed method.

Keywords

monotone function, ordinal data, nonparametric component, semiparametric maximum likelihood estimate

Received 5 November 2019

Accepted 13 August 2020

Published 9 February 2021