Covariance Structure Analysis
FROM PATH ANALYSIS
TO STRUCTURAL EQUATION MODELING
MARGARET K. KEILEY
Covariance structure analysis (CSA) has become one of the most useful and powerful tools for answering the complex questions that arise within the field of family research. Does family economic health have an influence on a parent's levels of depression, and ultimately on an adolescent's behavior in school? Do the 40 items on an instrument developed to measure family cohesion and conflict resolution actually measure these two constructs? As with most methodologies that are available to address complicated research questions, the method itself has been somewhat difficult to understand and to apply. The objective of this chapter is to provide a comprehensive, yet coherent, overview of the types of analyses that can be conducted via CSA.
In general, CSA is an extension of regression analysis and path analysis that includes components from factor analysis and classical test theory. In order to facilitate the reader's understanding of both the theoretical and practical aspects of CSA, we present the various “tools” in the CSA “toolkit,” from the most basic (path analysis) to the more advanced (multiple-group CSA). We also illustrate confirmatory factor analysis (CFA) and structural equation modeling (SEM). However, in order to begin this journey into CSA, we first need to define covariance, since CSA (as its full name indicates) is the analysis of covariance structures.
In data analysis, we usually summarize the relationship between two variables by estimating a correlation. To summarize the relationship among all of the variables in any