The golden rule is that there are no golden rules: A commentary on Paul Barrett’s recommendations for reporting model fit in structural equation modelling

Paul Barrett offers a challenging and timely call for a re-examination of fit assessment strategies in structural equation modelling (SEM). He points out that widely accepted cutoff values for approximate fit indices have come to be treated as if they were test statistics. Paul cites four recent studies of the behaviour of fit indices under varying data conditions which demonstrate that universal indicative cutoff values cannot be trusted. Based upon these studies, Paul advocates the abandonment of approximate fit indices and greater reliance on the chi square test and a broader assessment strategy that includes predictive accuracy. I share Paul’s concerns about the lax standards often adopted in model testing and I agree with most of his arguments. However, the authors he cites in support of his recommendation to abandon approximate fit indices do not reach the same conclusion as Paul. In my response to Paul’s article, I discuss some conditions under which it could be legitimate to accept a model which has failed the chi square test and I contend that approximate fit indices can play a useful part in a multi-faceted strategy for determining model adequacy, provided they are not elevated to the status of golden rules.