# How does the $\chi^2$ test tests the overall fit of a structural equation model?

I understand the $\chi^2$ test tests the model fit based on the comparison between the observed and null covariance matrices. Can someone explain to me how to compute the null matrix?

Second, the $\chi^2$ test does not compare the observed and null matrices, it compares the observed and saturated matrices. It is the multivariate test that all of the residuals (i.e. the difference between the fitted and observed matrices) is equal to zero.