Considerations in Measuring Partial Association for Ordinal Categorical Data

Some of the measures commonly used to describe association between two ordinal categorical variables, controlling for the effects of other ordinal categorical variables, are compared in their closeness to a corresponding conditional measure for an underlying jointly continuous distribution. Partial gamma and Kendall's partial tau are observed to be poorer than a weighted average of the Kendall's τ b 's from separate control levels, according to this criterion. The asymptotic sampling distribution of a particular weighted average measure is derived, and the behavior of the mean and asymptotic variance of such a measure is analyzed as the categorical variables are more finely measured.