A Simple Method for Constructing Multidimensional Distributions of Correlated Categorical Data

Abstract

We suggest a method for constructing a multidimensional distribution of correlated categorical data with fixed marginal distributions and specified degrees of association based on the log-linear models. A convex combination approach by Lee (1997) is applied to get a joint distribution with fixed Pearson chi-square coefficient. By using the suggested method, we can generate three-dimensional distributions which have a fixed association among three variables. Therefore, the suggested method could be extended to higher dimensions.

Keywords:

• Multidimensional contingency tables
• Pearson chi-square coefficient
• Random number

Mathematics Subject Classification:

• Primary 62H17
• Secondary 62H10