Criteria for longitudinal data model selection based on Kullback’s symmetric divergence

International audience Recently, Azari et al (2006) showed that (AIC) criterion and its corrected versions cannot be directly applied to model selection for longitudinal data with correlated errors. They proposed two model selection criteria, AICc and RICc, by applying likelihood and residual likelihood approaches. These two criteria are estimators of the Kullback-Leibler's divergence distance which is asymmetric. In this work, we apply the likelihood and residual likelihood approaches to propose two new criteria, suitable for small samples longitudinal data, based on the Kullback's symmetric divergence. Their performance relative to others criteria is examined in a large simulation study

The distributions of certain factors occurring in discriminant analysis

Significance tests for several hypothetical discriminant functions have been developed by Williams (7,8) and considered further by the author (6). The test criteria consist of the factors in certain factorizations of the residual likelihood criterion, when the effect of the hypothetical discriminant functions has been eliminated. The independence and distributions of the factors can be seen by geometrical considerations, to be a consequence of the manner in which the factors are constructed in the sample space. In the case of a single hypothetical discriminant function Kshirsagar (5) has produced analytic proofs, by means of matrix transformations, of the independence and distributions of the factors. In this paper we shall give analytic proofs of the independence and distributions of the factors, given in sections 4 and 5 of the authors' paper (6), by extending Kshirsagar's proof to the case of several hypothetical discriminant functions.