Structural equation modeling made difficult

In his target article (Barrett, 2007), Paul Barrett argues persuasively against continued use of approximate fit indices in SEM in relation to current thresholds for acceptable fit, given recent research that has cast doubt on the generality of these thresholds. He proposes greater use of the chi-square test of exact fit as an alternative, except in special circumstances. Apart from the problems with current fit thresholds, a further problem with fit indices is the lack of any direct relationship between the value of an index and the degree of misspecification in the model. In response to these problems, a procedure for using fit indices in the absence of thresholds is outlined here. The approach requires the investigator to specify acceptable levels of misspecification a priori, and then uses this information in a simulation procedure to develop a decision for retaining versus rejecting the model. It is argued that this approach is preferable to exclusive reliance on the chi-square test of exact fit. Comments on other points made in the target article are given.