Statistics and Its Interface
Volume 14 (2021)
Robust regression model for ordinal response
Pages: 243 – 254
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.
monotone function, ordinal data, nonparametric component, semiparametric maximum likelihood estimate
This work was partially supported by the National Natural Science Foundation of China (81872710).
Received 5 November 2019
Accepted 13 August 2020
Published 9 February 2021