Information Identity in Categorical Data Analysis

• Activity Number: 432
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Philip Cheng*+ and Michelle Liou
• Companies: Institute of Statistical Science and Academia Sinica
• Keywords: Information identity ; logistic regression ; Mantel-Haenszel test

Abstract

We proposed the information identity and partition the mutual information of categorical variables into orthogonal and interpretable components. In this study, we will apply the information identity to a few real empirical examples. In these examples, we show that the information identity presents a few useful aspects. It measures conditional association between three categorical variables, as compared with the conventional and generalized Mantel-Haenszel statistics. And, it models multivariate categorical variables, as a concise alternative to the conventional hierarchical log-linear model and the logistic regression analysis. The data sets in the empirical examples are those reported in Lahkola et al. (2005), Azen & Walker (2011) and item responses on a mathematics achievement examination.