Correlated Errors in True Score Models and Their Effect on Coefficient Alpha

Abstract It is well known that coefficient alpha is an estimate of reliability if its underlying assumptions are met and that it is a lower-bound estimate if the assumption of essential tau equivalency is violated. Very little literature addresses the assumption of uncorrelated errors among items and the effect of violating this assumption on alpha. True score models are proposed that can account for correlated errors. These models allow random measurement errors on earlier items to affect directly or indirectly scores on later items. Coefficient alpha may yield spuriously high estimates of reliability if these true score models reflect item responding. In practice, it is important to differentiate these models from models in which the errors are correlated because 1 or more factors have been left unspecified. If the latter model is an accurate representation of item responding, the assumption of essential tau equivalency is violated and alpha is a lower-bound estimate of reliability.