Continuities in Ordinal Path Analysis

Abstract

Aspects of Wilson's (1974a) critique of the interpretations and use of ordinal statistics applied to the regression and path analysis of ordinal variables are clarified and answered. First, the logic of Smith's (1972) technique for the path analysis of ordinals is explicated and various interpretations for the path coefficient based on Kendall's tau-b are presented. Second, as an aid to interpretation, the family of tau-b class ordinal statistics are reconceptualized as special cases of generalized product-moment statistics, rather than as analogs of interval statistics. Third, the virtues of this approach motivate the development of: (1) a generalized regression coefficient in terms of the concepts of generalized pairwise difference, generalized variation, and generalized covariation; (2) a generalized path coefficient in terms of concepts such as the generalized correlation coefficient, the generalized regression coefficient, and the generalized variation; and (3) a generalized residual path coefficient in terms of the generalized correlation coefficient.

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