Strong Consistency of Reliability Estimators for Multiple-Component Measuring Instruments

It is shown that the maximum likelihood estimator of the widely used omega coefficient for reliability of multicomponent measuring instruments converges almost surely to the population reliability coefficient for normal congeneric measures with uncorrelated errors as sample size increases indefinitely. This strong consistency implies convergence in probability (consistency) as well as in distribution for the omega estimator. Strong consistency is also demonstrated for the maximal reliability estimator associated with the optimal linear combination of the instrument components. The findings of this note add (i) to the recommendation to use in the general normality case the omega estimator in empirical research, (ii) to the critical literature on the popular coefficient alpha then, and (iii) to the literature on the properties of the optimal linear combination of observed measures and the maximal reliability estimator.