A comparison of Cronbach's coefficient alpha and latent variable model estimates of composite reliability for congeneric measures
A Monte Carlo simulation study contrasted two methods of estimating the reliability of composites with fixed, continuous, congeneric components with uncorrelated measurement errors. The two methods were Raykov's (1997a) latent variable model (LVM) reliability estimator and Cronbach's (1951) coefficient α. The present study examined the sample bias and variability of the two reliability estimators across 81 combinations of test length, mean construct loading, dispersion of construct loadings, and sample size. The sample bias of both reliability estimators, as well as the root mean squared errors (RMSE) of sample α estimates (relative to the population reliability), tended to increase with decreasing test length, decreasing population mean construct loading, increasing population range of construct loadings, and decreasing sample size. However, the RMSE and standard errors of both reliability estimators (relative to population estimator values and sample estimates of the population estimator values, respectively) tended to increase with decreasing test length, decreasing population mean construct loading, and decreasing sample size, but not increasing dispersion of construct loadings. Estimates from Raykov's LVM reliability estimator tended to be less biased, and had lower RMSE and standard errors, than estimates of Cronbach's α.
Boyd, Jeremy Kenton, "A comparison of Cronbach's coefficient alpha and latent variable model estimates of composite reliability for congeneric measures" (2002). ETD Collection for Fordham University. AAI3045120.