On the fit of models implied by unit-weighted scales

Abstract

Unit-weighted scales are often computed in order to estimate the scores of individuals on common factors. Previous work has shown that unit-weighted scales imply a model that can be evaluated. The algebraic framework for this approach was presented here. The relationship between the fit of the model implied by unit-weighted scales, the scale length, and the item inter-correlations was evaluated algebraically and by means of a simulation study. The standardized root mean square residual (SRMR) excluding the elements in the main-diagonal of the item inter-correlation matrix can be used for the fit evaluation of the unit-weighted scale model.

Keywords:

• Factor analysis
• Factor score estimates
• Unit-weighted sum scales

Acknowledgments

We are grateful to William Revelle, who pointed out in his review that an SRMR that excludes the elements in the main-diagonal of the correlation matrix could be a reasonable alternative to an SRMR including the diagonal elements.