Linear Regression and Classical Path Analysis

Abstract

In many ways, structural equation modeling (SEM) techniques may be viewed as “fancy” multivariate regression methods. Some models can be understood simply as a set of simultaneous regression equations. If the statistical assumptions of ordinary least squares (OLS) regression are met, standard OLS estimation as available in general-purpose statistical computer programs such as SPSS, SAS, or BMDP can be used to estimate the structural parameters in these models. This chapter serves to set the stage for presenting general structural equation models in Chapter 3, which include as special cases the regression and path analytical models presented in this chapter and the confirmatory factor analysis models introduced in Chapter 2. For now, the two main purposes are (1) to introduce a general SEM notation system by reviewing some important results in univariate simple and multiple regression, and (2) to discuss the multivariate method of path analysis as a way to estimate direct, indirect, and total structural effects within an a priori specified structural model. Throughout the chapter, examples based on data from a sociological study serve as an introduction to the LISREL and EQS programs. The respective manuals (Jöreskog and Sörbom, 1993a,b; Bentler, 1993; Bentler and Wu, 1993) should be consulted for more detailed programming information.