title: On congruence and incongruence of measures of fit in structural equation modeling.
abstract: Guidelines to evaluate the fit of structural equation models can only offer meaningful insights to the extent that they apply equally to a wide range of situations. However, a number of previous studies found that statistical power to reject a misspecified model increases and descriptive fit-indices deteriorate when loadings are high, thereby inappropriately panelizing high reliability indicators. Based on both theoretical considerations and empirical simulation studies, we show that previous results only hold for a particular definition and a particular type of model error. At a constant degree of misspecification (as measured through the minimum of the fit-function), statistical power to reject a wrong model and noncentrality based fit-indices (such as the root-mean squared error of approximation; RMSEA) are independent of loading magnitude. If the degree of model error is controlled through the average residuals, higher loadings are associated with increased statistical power and a higher RMSEA when the measurement model is misspecified, but with decreased power and a lower RMSEA when the structural model is misspecified. In effect, inconsistencies among noncentrality and residual based fit-indices can provide information about possible sources of misfit that would be obscured when considering either measure in isolation. (PsycINFO Database Record
authors.affiliation: Research Methods, Institute of Psychology and Education, Ulm University.
authors.forename: Morten
authors.identifier: 0000-0002-2929-7288
authors.initials: M
authors.lastname: Moshagen
authors.affiliation: Research Methods, Institute of Psychology and Education, Ulm University.
authors.forename: Max
authors.initials: M
authors.lastname: Auerswald
mesh_terms: D035843:Biomedical Research / Q000379:methods*; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical