The Impact of Scaling Methods on the Properties and Interpretation of Parameter Estimates in Structural Equation Models with Latent Variables

Latent variables in structural equation models do not have an observable scale. Hence researchers resort to scaling methods, such as fixed marker, effects coding, or fixed factor, to assign scales to the latent variables. The use of such procedures results in numerically different estimates, in spite of a single underlying population model. In this paper, we provide a framework which not only allows for a translation between estimates obtained under different scaling methods, but also helps to explore the relation between the underlying population parameters and their estimates, thus providing a basis for the interpretation of estimated parameters. Addition- ally, the framework proves useful for demonstrating that the choice of scaling method affects the power of the Wald test for testing parameters’ significance.