# Structural Equation Models

Structural Equation Models (SEMs) are statistical models, used primarily to evaluate whether theoretical models are plausible when compared to observed data. SEMs are very general, so for example regression and factor analysis are both just special cases of SEM.

Theory in the social sciences tends to be rich and complex, where multiple outcomes are seen as the result of multiple interacting factors and chains of mediation. Standard regression analysis cannot represent such theories in a single model, forcing the researcher to evaluate only partial or constrained models. SEMs allow for the representation of complex theory in a single, integrated model.

SEM allows researchers to take seriously the problems of modelling hypothetical constructs. Although sometimes not recognized as such, many of the phenomena of interest in the social sciences are not directly observable, even in principle, but are instead hypothetical constructs, intellectual devices that are used to categorise and give meaning to observed phenomena. Examples include social capital, authoritarianism, trust and social class. SEMs allow the researcher to represent these hypothetical constructs explicitly and to distinguish the measurement of a construct from the key relationships among the constructs.

**Additional Information**

A hub for SEM information: Ed Ridgeon’s SEM FAQ.

An introductory textbook: Kline, R. B. (2004). *Principles and Practice of Structural Equation Modeling* (2nd Ed). New York: Guildford.

An advanced textbook: Skrondal, A. & Rabe-Hesketh, S. (2004). *Generalized Latent Variable Modeling*. Boca Raton, Fla: Chapman.

Key historical references:

Jöreskog, K. G. (1970). A general method for analysis of covariance structures. *Biometrika* 57:239-51.

Wright, S. (1934). The method of path coefficients. *The Annals of Mathematical Statistics*, 5:161-215.