Poisson Mixed-Effects Count Regression Model Based on Double SCAD Penalty and Its Simulation Study

This paper focuses on variable selection and parameter estimation for mixed-effects Poisson count regression models. To simultaneously select important variables in both fixed effects and random effects, we propose a double-penalized Poisson count regression model with the Smoothly Clipped Absolute Deviation (SCAD) penalty imposed on both components. To estimate the unknown parameters, we develop a new iterative algorithm called the Double SCAD–Local Quadratic Approximation (DSCAD-LQA) algorithm. Under regularity conditions, the consistency and Oracle property of the proposed estimator are established. Simulation studies are conducted under two types of penalty parameter selection criteria: the Schwarz Information Criterion (SIC) and the Generalized Approximate Cross-Validation (GACV). We evaluate the performance of the proposed method under different levels of correlation among explanatory variables and different covariance structures of random effects. Comparisons are also carried out with the non-penalized model, the single-penalized model, and the double LASSO-penalized model. The results demonstrate that the proposed double SCAD penalty method performs better than the other three methods in terms of important variable selection and coefficient estimation, and is especially effective for sparse models.