A structural equation model is described that permits estimation of the reliability index and coefficient of a composite test for congeneric measures. The method is also helpful in exploring the factorial structure of an item set, and its use in scale reliability estimation and development is illustrated. The modeling. estimator of composite reliability it yields does not possess the general underestimation property of Cronbach's coefficient a.

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The population discrepancy between Cronbach's Coefficient Alpha and scale reliability with fixed congeneric measures, uncorrelated errors, and sampling of subjects is studied. This difference is expressed in terms of individual component violations of the assumption of essential T-equivalence that is necessary and sufficient for Alpha to equal composite reliability. An upper bound of the discrepancy is obtained and its magnitude assessed in practical contexts of informed scale development. As an alternative when the difference may be considerable, a latent variable model is recommended for estimating scale reliability.

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.

A method of composite reliability estimation using covariance structure analysis with nonlinear constraints is outlined. To motivate the developments, initially a short overview of research is presented, demonstrating that in many cases the widely used coefficient alpha is an unsatisfactory index of scale reliability already at the population level. As an alternative, the proposed covariance structure analysis procedure is based on the theoretical formula of the scale reliability coefficient in terms of parameters pertaining to a given set of congeneric components. The described approach is illustrated with several numerical examples and its performance compared with that of coefficient alpha.

The population discrepancy of coefficient a from the composite reliability coefficient for fixed congeneric measures with correlated errors is studied and expressed in terms of parameters of the measures. Use of structural equation modeling methodology is recommended for identifying cases in which this discrepancy can be large. The findings are demonstrated across several empirical conditions in a scale construction context.