Penalized Likelihood Estimation of Continuation Ratio Models for Ordinal Response and Its Application in CGSS Data

The continuation ratio model is a crucial tool for analyzing ordinal response data. However, its explanatory power diminishes under high-dimensional settings where the number of covariates p is large. To address this, we introduce, for the first time, the smoothly clipped absolute deviation (SCAD) penalty into the forward continuation ratio model framework. We propose a corresponding penalized likelihood estimation method that performs simultaneous variable selection and parameter estimation and provides an efficient algorithm for its implementation. Numerical simulations demonstrate the favorable properties of the SCAD penalty: it precisely identifies significant variables while more aggressively shrinking the coefficients of irrelevant ones to zero, outperforming alternative penalties like Lasso and elastic net in selection accuracy. Finally, we illustrate the practical utility of our method through an empirical application using data from the Chinese General Social Survey (CGSS).