Test of difference maximum likelihood parameters SEM R

Question

I have a structural equation model implemented in R 3.4.4 using lavaan 0.6-1 and estimated on two different subgroups using a robust maximum likelihood estimator. Now I want to compare the parameters by testing if they significantly deviate from one another. The regular multi-group analysis implemented in lavaan does not provide such a test.

My idea was to take the difference between the two parameters and test if this difference significantly deviates from zero, but I find it difficult to construct the test statistic.

Does anyone know if this is possible and how to construct the test statistic?

Answer 1

If you're willing to assume the normal approximation applies to your parameters of interest (i.e. not too small a sample, support over the entire reals or at least not close to boundaries) then the difference would be normally distributed:

$$\hat\beta_1 - \hat\beta_2 \sim N(\beta_1 - \beta_2, \sigma_{\beta_1}^2+\sigma_{\beta_2}^2 - 2 \sigma_{\beta_1 \beta_2}^2)$$

Otherwise, you can always run a bootstrap to approximate the confidence intervals.

EDIT: you can use vcov() on your fitted model in order to retrieve the values for the variances and covariance between your parameters of interest.