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

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 composite model, that we see as having certain advantages over the others. Following a specification of this model, we discuss its estimation, the use of a weighting schemes to create the composite, and the calculation of reliability for the composite. This is followed by an empirical example for which we show results from the different solutions for the models in the framework. In conclusion, we review the results, and issues discussed in the paper, consider the special case of educational and psychological testing, consider future directions for this work, and speculate about the possible uses of the Composite Model. (C) 2019 Elsevier Ltd. All rights reserved.