# Structural Equation Modeling - Introductory Overview

Structural Equation Modeling is a very general, very powerful multivariate analysis technique that includes specialized versions of a number of other analysis methods as special cases. We will assume that you are familiar with the basic logic of statistical reasoning as described in Elementary Concepts. Moreover, we will also assume that you are familiar with the concepts of variance, covariance, and correlation; if not, we advise that you read the Basic Statistics Overview at this point. Although it is not absolutely necessary, it is highly desirable that you have some background in factor analysis before attempting to use structural modeling.

Major applications of structural equation modeling include:

1. Causal modeling, or path analysis, which hypothesizes causal relationships among variables and tests the causal models with a linear equation system. Causal models can involve either manifest variables, latent variables, or both;

2. Confirmatory factor analysis, an extension of factor analysis in which specific hypotheses about the structure of the factor loadings and intercorrelations are tested;

3. Second order factor analysis, a variation of factor analysis in which the correlation matrix of the common factors is itself factor analyzed to provide second order factors;

4. Regression models, an extension of linear regression analysis in which regression weights may be constrained to be equal to each other, or to specified numerical values;

5. Covariance structure models, which hypothesize that a covariance matrix has a particular form. For example, you can test the hypothesis that a set of variables all have equal variances with this procedure;

6. Correlation structure models, which hypothesize that a correlation matrix has a particular form. A classic example is the hypothesis that the correlation matrix has the structure of a circumplex (Guttman, 1954; Wiggins, Steiger, & Gaelick, 1981).

Many different kinds of models fall into each of the above categories, so structural modeling as an enterprise is very difficult to characterize.

Most structural equation models can be expressed as path diagrams. This program uses a command language (PATH1) that looks very much like a path diagram. Consequently even beginners to structural modeling can perform complicated analyses with a minimum of training.