Nonparametric regression with ordinal responses

Abstract

In this article, we explore a nonparametric approach to proportional odds regression with ordinal responses. The setting fits in the general framework of penalized likelihood non‐Gaussian regression as developed earlier in the smoothing spline ANOVA literature. Existing results in the general setting are readily applied or adapted, covering asymptotic convergence, computation, smoothing parameter selection, and Kullback–Leibler projection. Simulation studies of limited scales are conducted to assess various practical issues, and open‐source software tools are demonstrated in the analysis of some diabetic retinopathy data.