Partials, Partitions, and Paths

Abstract

In a good deal of recent sociological discussion, published and unpublished, one senses an implicit assumption that the objective of a piece of research is best served by a partitioning of the explained variance or by the calculation of a partial correlation. I wish to argue, to the contrary, that achieving an algebraically consistent partitioning or system of partialing is secondary in importance to setting up an appropriate representation (or model) of the structure of the problem. Much confusion arises because of the protean character of regression and correlation statistics, which permits their algebraic manipulation into a large number of essentially equivalent but apparently distinct forms. Preoccupation with this algebra is not likely to generate anything new, for many capable statisticians have had a go at the subject during the twentieth century. Even worse, it is likely to distract one from the more urgent task of making sure that the regression setup itself is suited to the inferences and interpretations to be attempted. The viewpoint of this paper is that of the analyst seeking a rationally defensible and