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 and brief 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; general structural-equation models with latent variables, measurement errors, and multiple indicators. The **sem** package in R will be used to estimate structural-equation models.

A sound background in single-equation regression models and some knowledge of basic matrix algebra are assumed, as is familiarity with basic statistical ideas such as the method of maximum likelihood.

I also assume a basic knowledge of the R statistical computing environment. In addition to many books on R, there is a free introductory manual distributed with the software, as well as a variety of free contributed documentation.

Please make sure that R and the **sem** package are installed on your computer prior to the workshop.

- lecture slides
- R script for examples
- J. Fox, "Structural Equation Modeling in R with the sem Package" (An Appendix to
*An R Companion to Applied Regression, Second Edition*,

by J. Fox and S. Weisberg, Sage 2011) - J. Fox, "Linear Structural-Equation
Models" (Chapter 4, of
*Linear Statistical Models and Related Methods,*Wiley, 1984)

K. A. Bollen, "Latent
Variables in Psychology and the Social Sciences", *Annual Review
of Psychology*, 2002, 53: 605-634, provides a good brief overview of latent-variable models; although it is now a bit dated, my favourite book-length treatment of SEMs remains K. A. Bollen, *Structural Equations with Latent Variables* (Wiley, 1989).

*Last Modified: 12 June 2014 by J.
Fox <jfox AT mcmaster.ca>*