Multidimensional measuring instruments are often used in behavioral, social, educational, marketing, and biomedical research. For these scales, the paper discusses how to find the optimal score based on their components that is associated with the highest possible reliability. Within the framework of structural equation modeling, an approach to point and interval estimation of the maximal reliability coefficient of general structure measuring instruments is outlined. The procedure allows obtaining in addition the linear combination of all scale components that possesses maximal reliability. The described method is applicable in empirical research with popular statistical software, and is illustrated using an example.
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Raykov et al. (2024) studied this question.
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