The plausibility and feasibility of remedies for evaluating structural fit

Various structural fit indices (SFIs) have been proposed to evaluate the structural component of a structural equation model (SEM). Decomposed SFIs treat estimated latent (co)variances from an unrestricted confirmatory factor analysis (CFA) as input data for a path model, from which standard global fit indices are calculated. Conflated SFIs fit a SEM with both measurement and structural components, comparing its fit to orthogonal and unrestricted CFAs. Sensitivity of conflated SFIs to the same structural misspecification depends on standardized factor loadings, but decomposed SFIs have inflated Type-I error rates when compared to rule-of-thumb cutoffs, due to treating estimates as data. We explored whether two alternative approaches avoid either shortcoming by separating the measurement and structural model components while accounting for uncertainty of factor-covariance estimates: (a) plausible values and (b) the Structural-After-Measurement (SAM) approach. We conduct population analyses by varying levels of construct reliability and numbers of indicators per factor, under populations with simple and complex measurement models. Results show SAM is as promising as existing decomposed SFIs. Plausible values provide less accurate estimates, but future research should investigate whether its pooled test statistic has nominal Type I error rates.