Goodness-of-testing Based on Components of Pearson's Chi-squared Statistic Using Marginal Frequencies of Multinomial Data

• Activity Number: 448
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Mark Reiser*+ and Martin Knott
• Companies: Arizona State University and London School of Economics
• Keywords: smooth test ; chi-squared components ; marginal frequencies ; sparseness ; score statistic

Abstract

The goodness-of-fit test based on Pearson's chi-squared statistic is regarded sometimes as an omnibus test that gives little guidance to the source of poor fit when the null hypothesis is rejected. It also has been recognized that the omnibus test can be frequently outperformed by focused or directional tests of lower order. Furthermore, it is known that p-values obtained by using an asymptotic chi-squared approximation may not be valid when a data table is sparse. In this paper, we consider a Neyman-type smooth test for a model on a k-dimensional data table and employ a score statistic on overlapping cells that correspond to the 1st, 2nd,...,kth-1 order marginal frequencies. We then obtain orthogonal components of Pearson's statistic associated with the marginal frequencies that may be used as test statistics. We investigate the effective order and dilution of these test statistics and the projection of the alternative into the space of the lower-order marginals. We present an example using a latent structure model and demonstrate the advantage of the components in terms of power, resistance to sparseness, and detection of source of poor fit.