Structural Equations and Path Analysis for Discrete Data

Abstract

This article proposes a solution to the long-standing methodological problem of incorporating discrete variables inoto causal models of social phenomena. Only a subset of the variety of ways in which discrete data arise in empirical social research can be satisfactorily modeled by conventional log-linear or logit approaches. Drawing on the insights of several literatures, this article exposits a general approach to causal models in which some or all variables are discretely measured and shows that path analytic methods are available which permit quantification of causal relationships among variables with the same flexibility and power of interpretation as is feasible in models that include only continous variables. It presents methods of identifying and estimating these models and shows how the direct and indirect effects of independent varibles can be calculated by extensions of usual path analysis methods for continuos variables An important distincion developed here is that discrete variables can play two roles: (1) as measures of inherently discrete phenomena and (2) as indicators of underlying continous variables. The value of this distinction is shown in two empirical examples examined previously by other authors. In examining the effects of social background and parental enouragement on college plans of high school seniors, the article shows that modeling a discrete measure of encouragement as an indicator of a latent continous variable rather than as an inherently discrete variable (as has been done in previous analyses) provides a clearer interpretation and a superior fit to the data. In examining the effects of state Fair-Employment-Practices Legislation on black-white wage differentials, this study shows that two distinct effects on the relative wage can be detected: the direct ameliorative effect of the law itself and the effects of the popular progressive sentiment for racial equality of which the law is an indicator. The methods and models presented here are not only natural generalizations of structural equation and path analysis methods for continuous varibles to include discrete variables but also provide a means of investigating a richer variety of substantive hypotheses than is feasible with methods for discrete data commonly used in the sociological literature to date.