Pair-wise association measures for categorical and mixed data

We introduce two measures for the strength of the association between two categorical variables. The measures, denoted by η1 and η2, take values in the interval [0, 1]. A value of zero means there is no association between the two categorical variables, while a value of 1 means there is a perfect association (e.g., when we associate a variable with itself, we obtain η=1η=1). The measures are symmetric with respect to the order of variables, invariant with respect to permutations of the categories of the variables, and scalable for large number of observations. In addition, extensions of the proposed measures are presented for measuring the strength of association between pair of mixed variables, one quantitative and the other is categorical. The performance of the proposed measures compared to other association measures is investigated using simulated as well as real data.