An Extended GFfit Statistic Defined on Orthogonal Components of Pearson's Chi-Square

• Activity Number: 392
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Mark Reiser*+ and Silvia Cagnone and Juhfei Zhu
• Companies: Arizona State University and University of Bologna and Arizona State University
• Keywords: goodness of fit ; orthogonal components ; latent variable model ; sparseness ; Pearson statistic ; cross-classified table

Abstract

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.