Correlated Denominators in Multiple Regression and Change Analyses

Abstract

Sociological and demographic research often uses variables computed as ratios.When the denominators are highly correlated, or identical, and the ratios are used in correlation or regression analysis, a statistical dependency is formed. Interpretations and inferences may be difficult to make and misleading. This article has two basic purposes. The first is to show how this problem expands from bivariate correlation and regression to partial correlation and multiple regression. The second purpose is to review advantages and disadvantages of selected alternative change models, focusing on path analysis and the problem of correlated denominators in change and path analyses. It is suggested that, when an identical denominator exists, it can be used as an independent control variable in standard leastsquares regression equations constructed from the numerators. When, however, the denominators are highly correlated but not identical, as is found in most crosssectional research and is virtually inescapable in longitudinal research, the use of residual analysis is suggested as a solution to the problem of correlated denominators. ociological and demographic research often uses variables computed as ratios or rates. Usually, the denominator of the ratio is used for control purposes, as when population size is used in the calculation of per capita income or the birthrate (Schuessler, 1974). When two ratios with highly correlated, or the same, denominators are correlated, a statistical depend-

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