Respected Prof. Muthen, I am trying to use BSEM to test multigroup (3 groups) invariance - measurement & structural. 1.) I am using Muthén & Asparouhov(2013). BSEM measurement invariance analysis, as the reference to conduct Measurement invariance.However I am not sure how to proceed with structural invariance within BSEM. Kindly guide me on the article for conducting structural invariance in BSEM framework. 2.) I found the following two articles while trying to conduct structural invariance. These articles elaborate on "testing informative hypoheses"; is it the same as testing structural invariance? Also these article refer to R-script? Is it necessary to use the script always for conducting structural invariance? Rens van de Schoot, Marjolein Verhoeven & Herbert Hoijtink (2012): Bayesian evaluation of informative hypotheses in SEM using Mplus: A black bear story, European Journal of Developmental Psychology Van de Schoot, R., Hoijtink, H., Hallquist, M. N., & Boelen, P.A. (2012). Bayesian Evaluation of inequality-constrained Hypotheses in SEM Models using Mplus. Structural Equation Modeling, 19, 593-609 My apologies for an elaborate question. Basically, I am slightly confused with the steps to be taken to conduct structural invariance in a BSEM setup. Please guide me on the steps, & Mplus scripts with examples. Thanking you so very much in advance. Sincerely Arun
you would proceed just like with approximate invariance hypotheses for measurement parameters. So for a particular structural parameter you impose equality with zero-mean, small-variance priors and look to see where you find significant differences across groups. You can use Model Constraint to create a new parameter which is the difference between a structural parameter and its average across groups. This is done automatically and printed in the output for measurement parameters, but you can do it also for structural parameters. I don't have any scripts for doing this.