Variable selection in generalized linear models with canonical link functions

This paper studies a class of AIC-like model selection criteria for a generalized linear model with the canonical link. They have the form of log L - p * C, where log L is the maximized log-likelihood, p is the number of parameters and C is a term depending on the sample size n and satisfying C/n → 0 and C/log log n → ∞ as n → ∞. Under suitable conditions, this class of criteria is shown to be strongly consistent. A simulation study was also conducted to assess the finite-sample performance with various choices of C for variable selection in a logit model and a log-linear model.