Structural equation modeling and the latent linearity hypothesis in social and behavioral research

The issue of sensitivity of the structural equation modeling (SEM) methodology to violations of the underlying hypothesis of linear latent relationships is the focus of this paper. The identity of overall goodness-of-fit indices of an initially considered linear latent pattern model and of an equivalent model not making this assumption exemplifies the lack of routinely available global means within the methodology to evaluate the linearity assumption. It is next focused on the sensitivity of SEM to violations of presumed linearity for a general, nonlinear pattern of true relationship. The results of a simulation study are then presented which demonstrate that latent correlations and percentage explained variance as well as parameter standard errors and model residuals can provide critical information about violation of latent linearity, and should therefore also be focused on when examining departures from linear relationships at the latent level in applications of the SEM methodology in social and behavioral research.