Correlated Denominators in Multiple Regression and Change Analyses

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. Interpre tations 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 denomi nators in change and path analyses. It is suggested that, when an identical denomi nator exists, it can be used as an independent control variable in standard least- squares regression equations constructed from the numerators. When, however, the denominators are highly correlated but not identical, as is found in most cross- sectional research and is virtually inescapable in longitudinal research, the use of residual analysis is suggested as a solution to the problem of correlated denomi nators.