Nominal Association Vector and Matrix

TL;DR

This paper introduces a novel framework using association vectors and matrices to measure and analyze the dependence between nominal response variables and explanatory variables, providing detailed local and global insights.

Contribution

It proposes a new set of measures for nominal association, including a general class of global measures and an association matrix that extends existing concepts like the Goodman-Kruskal measure.

Findings

Defines a nominal association vector and matrix for detailed dependence analysis

Introduces a class of global association measures encompassing Goodman-Kruskal's measure

Connects the association matrix to the generalized confusion matrix in classification

Abstract

When response variables are nominal and populations are cross-classified with respect to multiple polytomies, questions often arise about the degree of association of the responses with explanatory variables. When populations are known, we introduce a nominal association vector and matrix to evaluate the dependence of a response variable with an explanatory variable. These measures provide detailed evaluations of nominal associations at both local and global levels. We also define a general class of global association measures which embraces the well known association measure by Goodman-Kruskal (1954). The proposed association matrix also gives rise to the expected generalized confusion matrix in classification. The hierarchy of equivalence relations defined by the association vector and matrix are also shown.