A Power Study of the GFfit Statistic as a Lack-of-Fit Diagnostic

The Pearson and likelihood ratio statistics are commonly used to test goodness-of-fit for models applied to data from a multinomial distribution. When data are from a table formed by cross-classification of a large number of variables, the common statistics may have low power and inaccurate Type I error level due to sparseness in the cells of the table. For the cross-classification of a large number of ordinal manifest variables, it has been proposed to assess model fit by using the GFfit statistic as a diagnostic to examine the fit on two-way subtables. A new version of the GFfit statistic has been developed by decomposing the Pearson statistic from the full table into orthogonal components defined on lower-order marginal distributions and then defining the GFfit statistic as an orthogonal component. An omnibus fit statistic can be obtained as a sum of a subset of these components. In this paper, the individual components are being studied for statistical power as diagnostics to detect the source of lack of fit when the model does not fit the observed data. Simulation results for power of components to detect lack of fit along with comparisons to other diagnostics are presented