Misestimation of reliability using coefficient alpha and structural equation modeling when assumptions of tau-equivalence and uncorrelated errors are violated

Coefficient alpha (a) has been described as a lower bound for test reliability. However' previous research indicates that when certain assumptions are violated' a can either overestimate or underestimate reliability. Raykov (1997a) has shown how structural equation modeling (SEM) can be used to estimate reliability. This study has introduced method factors into the model in Raykov (1997a) to avoid a potential limitation of the SEM approach. Monte Carlo simulation shows that when certain assumptions are violated' either method (a or SEM) can show a substantial bias' though in the most extreme circumstances the bias of a estimates are larger than the bias of SEM-based reliability estimates. Circumstances that favor one method or the other are described and explored.