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.
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Beauducel et al. (2019) studied this question.
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