However, in applied work, structural equation models are most often represented **graphically**. Here is a graphical example of a structural equation model:

For more information, click on an element of this diagram, or choose from this list:

Latent Constructs |
Structural Model |
Structural Error |
Manifest Variables |
Measurement Model |
Measurement Error |

This diagram uses the dominant symbolic language in the SEM world. However, there are alternate forms, including the " RAM," reticular action model.

A structural equation model may include two types of latent constructs--exogenous and endogenous. In the most traditional system, exogenous constructs are indicated by the Greek character "ksi" (`at left`)

and endogenous constructs are indicated by the Greek character "eta" (`at right`). These two types of constructs are distinguished on the basis of whether or not they are dependent variables in any equation in the system of equations represented by the model. Exogenous constructs are independent variables in all equations in which they appear, while endogenous constructs are dependent variables in at least one equation--although they may be independent variables in other equations in the system. In graphical terms, each endogenous construct is the target of at least one one-headed arrow, while exogenous constructs are only targeted by two-headed arrows.

Parameters representing regression relations between latent constructs are typically labeled with the Greek character "gamma" (*at left*) for the regression of an endogenous construct on an exogenous construct, or with the Greek character "beta" (*at right*) for the regression of one endogenous construct on another endogenous construct.

Typically in SEM, exogenous constructs are allowed to covary freely. Parameters labeled with the Greek character "phi" (*at left*) represent these covariances. This covariance comes from common predictors of the exogenous constructs which lie outside the model under consideration.

(Sometimes, however, it makes more sense to model a latent construct as the result or
**consequence** of its measures. This is the
causal indicators model. This alternative measurement model is also central to Partial Least Squares, a methodology related to SEM.)

However, when a construct is associated with only a single measure, it is usually impossible (due to the limits of identification) to estimate the amount of measurement error within the model. In such cases, the researcher must prespecify the amount of measurement error before attempting to estimate model parameters. In this situation, researchers may be tempted to simply assume that there is no measurement error. However, if this assumption is false, then model parameter estimates will be biased.

http://www.gsu.edu/~mkteer/sem2.html Return to the SEMNET FAQ home page.

Return to Ed Rigdon's home page.

Last updated: April 11, 1996