Structural equation modelling: Adjudging model fit

For journal editors, reviewers, and readers of research articles, structural equation model (SEM) fit has recently become a confusing and contentious area of evaluative methodology. Proponents of two kinds of approaches to model fit can be identified: those who adhere strictly to the result from a null hypothesis significance test, and those who ignore this and instead index model fit as an approximation function. Both have principled reasons for their respective course of action. This paper argues that the chi-square exact-fit test is the only substantive test of fit for SEM, but, its sensitivity to discrepancies from expected values at increasing sample sizes can be highly problematic if those discrepancies are considered trivial from an explanatory-theory perspective. On the other hand, suitably scaled indices of approximate fit do not possess this sensitivity to sample size, but neither are they “tests” of model fit. The proposed solution to this dilemma is to consider the substantive “consequences” of accepting one explanatory model over another in terms of the predictive accuracy of theory-relevant-criteria. If there are none to be evaluated, then it is proposed that no scientifically worthwhile distinction between “competing” models can thus be made, which of course begs the question as to why such a SEM application was undertaken in the first place.