Parsimonious covariate selection for a multicategory ordered response

Abstract

We propose a flexible continuation ratio (CR) model for an ordinal categorical response with potentially ultrahigh dimensional data that characterizes the unique covariate effects at each response level. The CR model is the logit of the conditional discrete hazard function for each response level given covariates. We propose two modeling strategies, one that keeps the same covariate set for each hazard function but allows regression coefficients to arbitrarily change with response level, and one that allows both the set of covariates and their regression coefficients to arbitrarily change with response. Evaluating a covariate set is accomplished by using the nonparametric bootstrap to estimate prediction error and their robust standard errors that do not rely on proper model specification. To help with interpretation of the selected covariate set, we flexibly estimate the conditional cumulative distribution function given the covariates using the separate hazard function models. The goodness-of-fit of our flexible CR model is assessed with graphical and numerical methods based on the cumulative sum of residuals. Simulation results indicate the methods perform well in finite samples. An application to B-cell acute lymphocytic leukemia data is provided.