Comparing Fit and Reliability Estimates of a Psychological Instrument using Second-Order CFA, Bifactor, and Essentially Tau-Equivalent (Coefficient Alpha) Models via AMOS 22

Abstract

Estimation of composite reliability within a hierarchical modeling framework has recently become of particular interest given the growing recognition that the underlying assumptions of coefficient alpha are often untenable. Unfortunately, coefficient alpha remains the prominent estimate of reliability when estimating total scores from a scale with a hierarchical structure, in part because there are few published articles that provide a step-by-step demonstration of how to estimate reliability within the context of structural equation modeling. Using AMOS 22 to analyze simulated and Wechsler Adult Intelligence Scale–Fourth Edition (WAIS-IV) summary data, the authors demonstrate how to compare the fit and reliability estimates of a (a) second-order confirmatory factor analytic (CFA) model, (b) bifactor model, and (c) essentially tau-equivalent model, which conforms to the stringent assumptions underlying coefficient alpha. The variance–covariance matrices generated from the simulated data as well as the WAIS-IV data are provided to allow for replication of results.