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Lecture 13   Multiple Classification Analysis (MCA) This Lecture Covers The MCA as the equivalent of a multiple regression analysis MCA adapted to logistic regression Multiple classification analysis (MCA) is used to examine the effect of each independent variable on the dependent variable while controlling for the effects of the other independent variables, when the dependent variable is an quantitative variable and the independent variables are categorical. MCA is most easily explained as multiple regression with dummy variables. Thus, the dependent variable is a quantitative variable, and the independent variables are categorical variables, represented by dummy variables. MCA with one categorical predictor variable is equivalent to one-way analysis of variance; MCA with two categorical predictor variables is equivalent to two-way analysis of variance; and so on. Control variables may be added to the MCA model. When quantitative variables, in addition to categorical variables, are included among the predictor variables, MCA is equivalent to what is commonly called analysis of covariance. MCA can be extended beyond multiple regression, for example, it can be extended to logistic regression and Cox regression. MCA specifies the linear model as follows: MCA is a statistical option with the ANOVA procedure An example To examine the effects of place of residence, ethnicity and education level on women’s age at first marriage If we run multiple regression Multiple classification analysis is an extension of multiple regression that allows us to use regression coefficients to predict the mean value controlling for the effect of other predictors in the model. MCA is simply a way of solving the regression equation. Unadjusted means Unadjusted means can be obtained from simple linear regression: “unadjusted” means “without controls”: Adjusted means Adjusted means are obtained from multiple linear regression: “adjusted” means “with controls”: Adjus