MODEL SELECTION FOR EXTENDED QUASI-LIKELIHOOD MODELS IN SMALL SAMPLES

We develop a small sample criterion (AIC(c)) for the selection of extended quasi-likelihood models. In contrast to the Akaike information criterion (AIC), AIC(c) provides a more nearly unbiased estimator for the expected Kullback-Leibler information. Consequently, it often selects better models than AIC in small samples. For the Logistic regression model, Monte Carlo results show that AIC(c) outperforms AIC, Pregibon's (1979, Data Analytic Methods for Generalized Linear Models. Ph.D, thesis. University of Toronto) C*(p), and the C-p selection criteria of Hosmer et al. (1989, Biometrics 45, 1265-1270). Two examples are presented.