A multi-index model for quantile regression with ordinal data

Abstract

In this paper, we propose a quantile approach to the multi-index semiparametric model for an ordinal response variable. Permitting non-parametric transformation of the response, the proposed method achieves a root-n rate of convergence and has attractive robustness properties. Further, the proposed model allows additional indices to model the remaining correlations between covariates and the residuals from the single-index, considerably reducing the error variance and thus leading to more efficient prediction intervals (PIs). The utility of the model is demonstrated by estimating PIs for functional status of the elderly based on data from the second longitudinal study of aging. It is shown that the proposed multi-index model provides significantly narrower PIs than competing models. Our approach can be applied to other areas in which the distribution of future observations must be predicted from ordinal response data.

Keywords:

• dimension reduction
• health economics
• multi-index model
• ordinal response
• quantile regression

Acknowledgements

The authors thank Xuming He for his helpful comments on an earlier draft of this manuscript.