Rethinking fit assessment in structural equation modelling: A commentary and elaboration on Barrett (2007)

With seemingly few exceptions, current practice in structural equation modelling (SEM) aims at establishing close rather than exact fit between hypothetical models and observed data. This orientation has gone without serious challenge until the appearance of a sharp critique by Barrett (2007), who suggests discontinuing the use of approximate fit indices (AFIs) in SEM. The present article provides a commentary and elaboration on the key aspects of Barrett’s position, and also supplies further practical guidance and methodological references to applied researchers, who may be motivated to significantly alter their modelling practices in order to address the issues he raises. I strongly support his calls for performing more detailed diagnostic examinations of model misfit when confronted with a significant chi-square (χ2) test statistic, rather than simply deferring to AFIs. However, I do not second the recommendation that assessments of a model’s predictive accuracy (e.g., R2 values) can supplant a focused search for the reasons underlying significant global misfit. Accordingly, some misconceptions about the relationship between global model fit and predictive accuracy are pointed out, and modified advice is given to practitioners. Issues surrounding how to properly appraise a model yielding a non-significant χ2 are also discussed, as are concerns raised by Barrett about small sample size and power in SEM. It is concluded that AFIs offer little value-added in SEM practice, given the wide variety of available methods for performing detailed model assessments. However, I leave the issue of whether AFIs should be completely abandoned to future research.