Having your cake and eating it too: Multiple dimensions and a composite

Abstract

This paper first develops a framework for exploring options that one can have in psychometric modeling alternatives for multidimensional measurement situations. In particular, we focus on situations where there is seen to be value in both (i) the individual dimension outcomes (i.e., “having your cake”), and (ii) the summative combination of those multiple dimensions (i.e., ‘eating it too”). We review the literature about this issue, mainly from the perspective of latent variable modeling. There have been three main modeling options used, (a) the Unidimensional and the Multidimensional-Covariance models, (b) the Bifactor model, and (c) the Hierarchical model. We describe a fourth model, the c..