Applications and computational strategies for the two-point mixture index of fit

Although numerous descriptive measures have been proposed for assessing model fit when analysing frequency tables, the two-point mixture index of fit proposed by Rudas, Clogg, and Lindsay possesses features that make this index especially appealing in many applied research settings. In particular, the index has an intuitive interpretation that does not depend upon the specific nature of the model being assessed and is not sensitive to sample size. Also, the index can be applied when models are fitted to virtually any frequency table. This paper summarizes the underlying theory and addresses issues of estimation for goodness-of-fit tests for one-way or multi-way frequency tables as well as for certain latent variable models. In addition, a new approach for estimating a lower confidence bound for the index is presented.