Using Multiple Regression with Dichotomous Dependent Variables

A dichotomous dependent variable is used to determine a combination of variables that will predict group membership. Dichotomous variables are frequently encountered in multiple regression analysis. However, several textbooks question the appropriateness of using multiple regression analysis when analyzing dichotomous dependent variables. The critics state that in addition to the predictions made by the regression equation with a dichotomous dependent variable, the statistical tests are also invalid. This paper assesses the meaning of the charges against multiple regression and deals with some logical extensions of them. Data from the A3 data set in Gunst and Mason is used to examine the criticisms by comparing results of cases viewed as appropriate by critics with cases viewed as inappropriate for one predictor and two predictor examples. As the tests of significance are identical whether the dichotomous variable is independent or dependent, critics must deal with all significance testing with t-tests, analysis of variance, analysis of covariance, discriminant analysis, and any use of dummy variables in multiple regression if they are to be taken seriously. (BS)