A simulation of the performance of C_p in model selection for logistic and Poisson regression

We evaluate performance of Mallows' C_p in best subsets selection for logistic and Poisson regression models using computer simulations. Comparison of success rate in recognizing correct and incorrect models is made with the likelihood ratio (LR) statistic and with the score statistic (S). We find that performance of C_p is compatible with that of LR and S. C_p rejects both the correct and incorrect models at least as often as the other two statistics. Thus, C_p appears to be a conservative selection criterion in the sense that it has lower sensitivity but higher specificity than LR or S.