A Comparison of Confirmatory Factor Analysis and Network Models for Measurement Invariance Assessment When Indicator Residuals are Correlated

Social science research is heavily dependent on the use of standardized assessments of a variety of phenomena, such as mood, executive functioning, and cognitive ability. An important assumption when using these instruments is that they perform similarly for all members of the population. When this assumption is violated, the validity evidence of the scores is called into question. The standard approach for assessing the factorial invariance of the measures across subgroups within the population involves multiple groups confirmatory factor analysis (MGCFA). CFA models typically, but not always, assume that once the latent structure of the model is accounted for, the residual terms for the observed indicators are uncorrelated (local independence). Commonly, correlated residuals are introduced after a baseline model shows inadequate fit and inspection of modification indices ensues to remedy fit. An alternative procedure for fitting latent variable models that may be useful when local independence does not hold is based on network models. In particular, the residual network model (RNM) offers promise with respect to fitting latent variable models in the absence of local independence via an alternative search procedure. This simulation study compared the performances of MGCFA and RNM for measurement invariance assessment when local independence is violated, and residual covariances are themselves not invariant. Results revealed that RNM had better Type I error control and higher power compared to MGCFA when local independence was absent. Implications of the results for statistical practice are discussed.