Structural equation models with latent variables

Consider the relationship between the following variables:

• Self-esteem and job satisfaction
• Customer satisfaction and repurchase intention

The assumption that these variables are somehow related makes sense, but unfortunately they are not directly observable; they are latent variables. Nevertheless, imagine that we wish to build a model expressing the dependence between latent variables. For instance, we may consider the structural equation

where ζ and ξ are latent variables, ν is an error term, and γ is an unknown parameter. If we want to estimate the parameter, we need to relate the latent variables to observable variables, which play the role of measurements. Imagine that the latent variable ξ can be related to observable variables X₁ and X₂ by the following measurement model:

where α₁ and α₂ are unknown parameters, and  and  are errors. This is an interdependence model, quite similar to factor analysis. By the same token, the measurement model for ζ can be something like

The overall model can be depicted as in Fig. 15.4. We stress again that a structural model with latent variables includes both dependence and interdependence components. Methods have been proposed to estimate the unknown parameters, combining ideas from regression and factor analysis.

Fig. 15.4 Schematic illustration of a structural model with latent variables.

Fig. 15.5 Schematic illustration of multidimensional scaling.