Issues in Multiple Regression

Abstract

Controlling for variables implies conceptual distinctness between the control and zero-order variables. However, there are different levels of distinctness, some more subtle than others. These levels are determined by the theoretical context of the research. Failure to specify the theoretical context creates ambiguity as to the level of distinctness, and leads to the partialling fallacy, in which one controls for variables that are distinct in terms of appropriate theory. Although this can occur in using any control procedure, it is especially likely to occur in multiple regression, where high-order partial regression coefficients are routinely obtained in order to determine the relative importance of variables. Four major ways in which these regression coefficients can be seriously misleading are discussed. Although warnings concerning multicollinearity are to be found in statistics texts, they are insufficiently informative to prevent the mistakes described here. This is because the problem is essentially one of substantive interpretation rather than one of mathematical statistics per se.