A Modified Multiple Regression Approach to the Analysis of Dichotomous Variables

To illustrate the models and methods of the present article, we shall reanalyze those data in the famous study of The American Soldier by Stouffer et al. (1949), subsequently analyzed by Coleman (1964), Zeisel (1968), and Theil (1970). The methods we present reveal how the odds pertaining to a given dichotomized variable (e.g., the odds that a soldier would prefer a Northern to a Southern Camp assignment) are related to other dichotomized variables (e.g., (a) the soldier's race, (b) his region of origin, (c) his present camp location). The usual regression analysis methods do not suit the case considered here, where the dependent variable is the odds pertaining to a given dichotomous variable. Nor do the usual methods suit the case where the dependent variable is a proportion pertaining to the dichotomous variable. This article presents some relatively elementary models and methods suitable for analyzing the odds (or a proportion) pertaining to the given dichotomous dependent variable. Applying these models and methods to the data referred to above, new insights are obtained.