392 – Goodness of Fit
An Extended GFfit Statistic Defined on Orthogonal Components of Pearson's Chi-Square
Mark Reiser
Arizona State University
Silvia Cagnone
University of Bologna
Junfei Zhu
Arizona State University
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 the cross-classification of a large number of variables, the common statistics may have low power and inaccurate Type I error level due to sparseness. 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, and the asymptotic distribution of the GFfit statistic has been previously established. In this paper a new version of the GFfit statistic is proposed 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 a sum of a subset of these components. The new version of the GFfit statistic also extends the diagnostic to higher-order tables so that the GFfit statistics sum to the Pearson statistic. Simulation results and an application of the new GFfit statistic as a diagnostic for a latent variable model are presented.