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.

## Literature

- 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.