Recursive Path Models when Both Predictor and Response Variables are Categorical

Recursive path analysis is a useful tool for inference on a sequence of three or more response variables in which the causal effects of variables, if any, are in one direction. The primary objective in such analysis is to decompose the total effect of each variable into its direct and indirect components. Methods for recursive analysis of a chain of continuous variables are well developed but there is a lack of uniform methodology when the variables are categorical. In this paper we propose an approach for categorical response variables that is based on generalized linear models. The proposed method has the flexibility of allowing the use of common categorical data models such as the Poisson, Probit and logistic regression models, along with definitions of direct and indirect effects in terms of relative risks and odds ratios. The method can be implemented easily using standard statistical software such as the GENMOD procedure of SAS. This proposed method is illustrated using real data. AMS Subject Classification: 62J12; 62F10. Key-words: Categorical data; Direct effect; Generalized linear models; Indirect effect; Odds ratio; Path analysis; Relative risk; Total effect.