Variable selection for proportional odds model

In this paper we study the problem of variable selection for the proportional odds model, which is a useful alternative to the proportional hazards model and might be appropriate when the proportional hazards assumption is not satisfied. We propose to fit the proportional odds model by maximizing the marginal likelihood subject to a shrinkage-type penalty, which encourages sparse solutions and hence facilitates the process of variable selection. Two types of shrinkage penalties are considered: the LASSO and the adaptive-LASSO (ALASSO) penalty. In the ALASSO penalty, different weights are imposed on different coefficients such that important variables are more protectively retained in the final model while unimportant ones are more likely to be shrunk to zeros. We further provide an efficient computation algorithm to implement the proposed methods, and demonstrate their performance through simulation studies and an application to real data. Numerical results indicate that both methods can produce accurate and interpretable models, and the ALASSO tends to work better than the usual LASSO.