Penalized Poisson Regression Model using adaptive modified Elastic Net Penalty

Variable selection in count data using penalized Poisson regression is one of the challenges in applying Poisson regression model when the explanatory variables are correlated. To tackle both estimate the coefficients and perform variable selection simultaneously, elastic net penalty was successfully applied in Poisson regression. However, elastic net has two major limitations. First it does not encouraging grouping effects when there is no high correlation. Second, it is not consistent in variable selection. To address these issues, a modification of the elastic net (AEN) and its adaptive modified elastic net (AAEM), are proposed to take into account the small and medium correlation between explanatory variables and to provide the consistency of the variable selection simultaneously. Our simulation and real data results show that AEN and AAEN have advantage with small, medium, and extremely correlated variables in terms of both prediction and variable selection consistency comparing with other existing penalized methods.