# AN INTRODUCTION TO STRUCTURAL EQUATION MODELING

## John Fox

### 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

 Materials Lectures Notes, R Script file Exercises Questions (Data: Lincoln.R, Rindfuss.R, Wheaton.R), Solutions (Scripts: Lincoln-solution.R, Rindfuss-solution.R, Wheaton-solution.R)