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# AN
INTRODUCTION TO STRUCTURAL EQUATION MODELING

## John Fox

### (Department of Sociology,
McMaster University, Canada)

### Programa de Computação Científica - FIOCRUZ Rio de
Janeiro - Brasil

### November 2008

Structural-equation models (SEMs)
are multiple-equation regression models in which the response variable in one
regression equation can appear as an explanatory variable in another equation.
In "non-recursive" SEMs, two variables in a model can affect one-another
reciprocally, either directly, or indirectly through a "feedback"
loop. Structural-equation models can include "latent" variables --
variables that are not measured directly, but rather indirectly through their
effects (called indicators) or, sometimes, through their observable causes.

This basic introduction to SEMs takes
up several topics: The form and specification of observed-variable SEMs; instrumental-variables
(IV) estimation; determining whether or not an SEM, once specified, can be estimated
(the "identification problem"); estimation of observed-variable SEMs
by IV, two-stage least-squares, and full-information maximum-likelihood; structural-equation
models with latent variables, measurement errors, and multiple indicators; the
"LISREL" model, a general structural-equation model with latent variables;
using the sem package in R to estimate structural-equation models.

A sound background in single-equation
regression models and some knowledge of basic matrix algebra are assumed.

For the "hands-on" part of the course, it would help to have some basic knowledge of the R statistical computing environment. In addition to many books on R, there is an introductory manual available, as well as a variety of contributed documentation.

## Resources

## Readings

J. Fox, "Linear Structural-Equation
Models", Chapter 4, *Linear Statistical Models and Related Methods*
(Wiley, 1984).

J. Fox, "Structural-Equation
Modeling with the sem Package in R", *Structural Equation Modeling*, 2006, 13:465-486.

K. A. Bollen, "Latent
Variables in Psychology and the Social Sciences", *Annual Review
of Psychology*, 2002, 53: 605-634.

Last Modified: 11 October 2008 by J.
Fox <jfox AT mcmaster.ca>