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We discuss an application of Bayesian factor analysis for estimation of the optimal linear combination and associated maximal reliability of a multi-component measuring instrument. The described procedure yields point and credibility interval estimates of this reliability coefficient, which are readily obtained in educational and behavioral measurement research. In addition, the outlined method permits evaluation of the gain in measurement consistency resulting from utilizing the maximal reliability coefficient instead of the traditionally used overall sum score reliability. The discussed Bayesian inference approach is applicable with widely available software in empirical studies, and is illustrated using a data example.
Raykov et al. (Tue,) studied this question.