Incorporating Distance Information in Comparing Categorical Data

• Activity Number: 468
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Hao Chen*+ and Nancy Zhang
• Companies: Stanford University and Stanford University
• Keywords: compare categorical data ; distance ; high-dimensional ; minimum spanning tree

Abstract

When testing the equivalence of two multinomial distributions, the existing tests, such as Pearson's Chi-square test and the likelihood ratio test, do not work well when the number of observations is proportional to the number of categories. The $\chi^2$ approximation to the existing tests with standard degree of freedom calculations is inaccurate, and the tests have low power even using permutation tests under this situation. To improve the power of the test, we use the implicit information of similarity between categories, which is usually naturally embedded in the data. We construct a graph on the observations based on several criteria - minimum spanning tree, cross-match and nearest neighbor - and count the edges connecting points from two different groups. An averaged statistic is used to deal with ties in the distance matrix due to the intrinsic property of categorical data. Simulation results show that the test based on minimum spanning trees works best because it makes fully use of the distance information. A Gaussian approximation to the permutation distribution of this test is also derived.