Modified cross-validation procedure in selection shrinkage parameter of Poisson ridge regression model

Abstract

Poisson regression is a fundamental framework for modeling count data; however, the maximum likelihood estimator becomes unreliable under multicollinearity, yielding unstable estimates with large variance and weak inferential performance. Ridge regression offers a remedy by shrinking regression coefficients, but its effectiveness depends crucially on selecting an appropriate shrinkage parameter. This paper proposes a modified cross‑validation (MCV) procedure for Poisson ridge regression that explicitly targets this instability. The method repeatedly reassigns observations to folds, re‑computes the optimal shrinkage parameter over many replications, and then uses an appropriately chosen quantile of the resulting distribution of optimal values as the final tuning parameter; the quantile is itself selected via cross‑validated prediction error. Extensive Monte Carlo simulations, conducted over varying sample sizes, numbers of predictors, intercept values, and correlation levels, show that the MCV‑based Poisson ridge estimator consistently achieves lower mean squared error than maximum likelihood, standard cross‑validation, and generalized cross‑validation, with particularly notable gains under strong multicollinearity. A real data analysis further demonstrates that the proposed procedure improves prediction performance in practical count data applications.