Overview of more complex models

The versatility of structural equation modeling is reflected in the wide variety of models that can be developed using this methodology. To make the material easier to understand, we will start with the simplest types of model, those that only involve the use of observed variables. In later chapters we will introduce abstract variables into our models. The inclusion of these other types of variable greatly expands the variety of problems that can be addressed. As a preview of things to come later, here I present an example of a more complex type of model (Figure 3.1).

The model in Figure 3.1 includes four types of variables. Observed variables (represented by boxes) represent things that have been directly measured. Examples of observed variables include the recorded sex of animals in a sample, or the estimated plant biomass in a plot. Observed variables can also be used to represent experimental treatments (e.g., predators excluded, yes or no?), spatial locations (e.g., different sample sites), or interactions among other variables. Latent variables (represented by circles) represent unmeasured variables, which are often used to represent underlying causes. In the earliest example of a latent variable path model, Wright (1918) hypothesized that the relationships amongst bone dimensions in rabbits could be explained by a number of latent growth factors. While these latent factors could not be directly measured, their effects on bone dimensions could be inferred from the pattern of correlations amongst observed variables.