Calculation of adjusted response frequencies using least squares regression methods

Abstract

The use of general linear regression methods for the analysis of categorical data is recommended. The general linear model analysis of a 0,1 coded response variable produces estimates of the same response probabilities that might otherwise be estimated from frequencies in a multiway contingency table. When factors in the design are correlated, the regression analysis estimates the same response probabilities that would be estimated from the simple marginal frequencies in a balanced orthogonal design. The independent effects that are estimated by the regression analysis are the unweighted means of the response probabilities in various cells of a cross-classification design; however, it is not necessary that all cells in a complex design be filled in order for the estimates to have that interpretation. The advantages of the general linear model analysis include familiarity of most psychologists with the methods, availability of computer programs, and ease of application to problems that are too complex for development of complete multiway contingency tables.