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A general approach to obtaining weights and reliability coefficients of maximally reliable composites is offered for a variety of test theoretic models which assume a single common underlying dimension. The reliability maximizing weights are related to the theoretically specified true score scaling weights to show there is a constant relationship between them that is invariant under separate linear transformations on each variable in the system. Furthermore, an argument is made that test theoretic relations should be derived for the most general model available and not for unnecessarily constrained models.
Anthony J. Conger (Tue,) studied this question.