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Department of Statistics, UCLA

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Maximal Reliability for Unit-weighted Composites


Although coefficient alpha is the most widely used measure of internal consistency, it does not optimally describe the unidimensional internal consistency of a composite. Coefficients based on a one-factor model have been suggested as improved estimators of internal consistency reliability. When the 1-factor model does not fit the data, however, the meaning of such a coefficient is unclear. A new identification condition for factor analytic models is proposed that assures the composite can be modeled with only one common factor. The associated 1-factor reliability is the maximal internal consistency coefficient for a unit-weighted composite. The coefficient also describes k-factor reliability, the greatest lower bound to reliability, and reliability for any composite from a latent variable model with additive errors.

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