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Coefficient Alpha and Composite Reliability With Interrelated Nonhomogeneous Items

The relationship between Cronbach's coefficient alpha (a) and the reliability of a composite of a prespecified set of interrelated nonhomogeneous components is examined. It is shown that a can over- or underestimate scale reliability at the population level. The bias is expressed in terms of structural parameters and illustrated on simulated data. The relevance of substantive considerations about, and examination of, the latent structure of an item set prior to estimation of composite reliability using at is emphasized and demonstrated using a structural equation modeling approach.