The myth of global fit indices and alternatives for assessing latent variable relations

A common myth among organizational researchers who use structural equations is that adequate fit values from the composite (overall) model speak directly to the adequacy of the proposed theory. However, this is a fallacious assumption, as significant misspecification among the theoretical paths between constructs can occur and be missed when there is an overreliance on global fit indices. To debunk this myth and provide a more valid alternative, the authors begin with an overview of latent variable model estimation procedures, emphasizing how they affect values obtained with fit measures for composite models. The authors next demonstrate problems with these measures, using an algebraic analysis of two popular composite fit indices (CFI, RMSEA) and results from simulation analysis with these indices. They then highlight two alternative indices that focus more on path model relations (NSCI-P, RMSEA-P) and that outperform the composite fit indices in the detection of model misspecification among the latent variables. The authors conclude with recommendations how these latter indices can be incorporated into model evaluation and theory testing.