Analysis of Partial Rank Correlation Measures Based on the Product-Moment Model: Part One
Robert H. Somers · Social Forces · 1974
Partial rank correlation coefficients are defined as special cases of a generalized product-moment system. The case of two independent variables is examined in detail, and the coefficient is partitioned into components summarizing information lying between and within conditional distributions. Probability interpretations are given for two basic components. Recent developments identifying the structural assumptions needed for a full probability interpretation and bases for a general theory are briefly summarized. The basic components that do not require structural assumptions but cannot be calculated from bivariate data are suggested as alternative measures of partial rank correlation. One of them is closely related to Kendall's partial tau, another to Davis's partial gamma. The manner in which these methods summarize a triple dichotomy is illustrated. The logic of statistically “partialling out” ordinal covariation is discussed and quantified.