A MODIFIED AKAIKE CRITERION FOR MODEL CHOICE IN GENERALIZED LINEAR-MODELS

In Bonneu (1988) a prediction criterion for model selection is defined for Generalized Linear Models (GLM). This criterion, similar to AIC ( Akaike, H. (1973)), Sakamoto, Y. and Akaike, H. (1978)) is based on th e expected Kullback-Leibler discrepancy (Kullback, S. 1959)), especial ly defined for prediction. The model selection strategy is employed to select a Nelder's link function (1972) and a small subset of explanat ory variables. Data are observed from an experimental design with uneq ual numbers of replications. This paper deals with the asymptotic esti mate of this prediction criterion and compares it with a simulated boo tstrap estimate. Usually asymptotic criteria for model selection can b e written as the sum of a statistic and a bias (see Linhart, H. and Vo lkers, P. (1984); Linhart, H. and Zucchini, W. (1986)). In the present paper, asymptotic arguments are investigated in a different way, taki ng into account the prediction objective and GLM framework with unequa l numbers of replicates. Our asymptotic criterion is the sum of two te rms: the deviance of GLM, the trace of a matrix product. The use of th is asymptotic criterion is illustrated by two binomial examples; we ge t the same numerical results as for bootstrap methods. AMS 1980 subjec t classifications: 60F05, 62C05