In assessing the difference between two structural equation models, conventionally one tests the null hypothesis of no difference in fit of two models in the population. As pointed out by MacCallum et al. (2006), this null hypotheses is essentially never true in practice as it can´t be expected, that two nested models would ever fit exactly the same.
To overcome this limitation of conventional tests for model comparison, MacCallum et al. (2006) propose a test of a small difference in fit of two nested models.
The attached code implements this test in R and SPSS. It´s a simple translation of the SAS syntax published by the authors into the R and SPSS language.
- MacCallum, R. C., Browne, M. W. & Cai, L. (2006). Testing differences between nested covariance structure models: Power analysis and null hypotheses. Psychological Methods, 11, 19-35. doi: 10.1037/1082-989X.11.1.19.