CHOOSING A MULTIVARIATE MODEL - NONCENTRALITY AND GOODNESS OF FIT

A number of goodness-of-fit indices for the evaluation of multivariate structural models are expressed as functions of the noncentrality parameter in order to elucidate their mathematical properties and, in particular, to explain previous numerical findings. Most of the indices considered are shown to vary systematically with sample size. It is suggested that Akaike's information criterion cannot be used for model selection in real applications and that there are problems attending the definition of parsimonious fit indices. A normed function of the noncentrality parameter is recommended as an unbiased absolute goodness-of-fit index, and the Tucker-Lewis index and a new unbiased counterpart of the Bentler-Bonett index are recommended for those investigators who might wish to evaluate fit relative to a null model.