The Form of Structural Equation Models
The Form of Structural Equation Models
Structural equation modeling incorporates several different approaches or frameworks to representing these models. In one well-known framework (popularized by Karl Jöreskog, University of Uppsala), the general structural equation model can be represented by three matrix equations:
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.
Latent Constructs
In structural equation modeling, the key variables of interest are usually "latent constructs"--abstract psychological concepts such as "intelligence" or "attitude." We can observe the behavior of latent variables only indirectly, and imperfectly, through their effects on manifest variables.
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
Structural equation modeling incorporates several different approaches or frameworks to representing these models. In one well-known framework (popularized by Karl Jöreskog, University of Uppsala), the general structural equation model can be represented by three matrix equations:
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.
Latent Constructs
In structural equation modeling, the key variables of interest are usually "latent constructs"--abstract psychological concepts such as "intelligence" or "attitude." We can observe the behavior of latent variables only indirectly, and imperfectly, through their effects on manifest variables.
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