Scaling Variances of Latent Variables by Standardizing Loadings: Applications to Working Memory and the Position Effect

Abstract

The standardization of loadings gives a metric to the corresponding latent variable and thus scales the variance of this latent variable. By assigning an appropriately estimated weight to all the loadings on the same latent variable it can be achieved that the average squared loading is 1 as the result of standardization. As a consequence, there is comparability of the variances of the latent variables of a confirmatory factor model. A precondition of comparability is that the latent variables must have loadings of the same manifest variables and that the variances are estimated with respect to the same covariance matrix. The usefulness of this standardization method is demonstrated by applying it for the evaluation of the sources of performance in a working memory task and for the evaluation of the impact of the position effect on performance in completing a reasoning measure. In these examples the scaled variances of the latent variables provided useful information.