Variable selection through adaptive elastic net for proportional odds model

In this paper, we propose a method for fitting the proportional odds model by maximizing the marginal likelihood while incorporating an elastic net penalty. We assign adaptive weights to different coefficients, allowing important variables to receive smaller penalties and be more protectively retained in the final model, while unimportant variables receive larger penalties and are more likely to be eliminated. This approach combines the strengths of adaptively weighted LASSO shrinkage and quadratic regularization, resulting in optimal large sample performance and the ability to effectively handle collinearity. We also present a computational algorithm for the proposed method and compare its performance to that of LASSO, elastic net, and adaptive LASSO through simulation studies and applications to real datasets. The results demonstrate that the proposed method tends to perform better than existing approaches.