On a scale as a sum of manifest variables

The most common approach for a scale construction is to create a scale as a sum of manifest variables (a "sum scale"). When we use the sum scale for analysis, we implicitly assume that there is a one-dimensional latent structure representing the manifest data on a multidimensional space. In this commentary, we review basics of identifying a latent structure using measured variables with a minimum linear algebra. We demonstrate the technique using Fisher's iris data as an illustration. We examine the relationships between resulting latent variables and the sum scale to evaluate goodness of the sum scale. As a practical solution, in general, we could create a sum scale using a set of positively and highly correlated measured variables. More care is needed when the data are not unidimensional.