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.
Thank you Prof. Muthen. I will try as per your suggestions.
Tait Medina posted on Thursday, January 23, 2014 - 11:44 am
I am trying to think through the difference between the following two approaches to detecting measurement non-invariance when indicator variables are continuous:
(1) using an ML approach to multiple-group analysis where all measurement parameters are constrained to be invariant across groups and modification indices are used to determine which parameters should be freely estimated.
(2) using a BSEM approach to detecting invariant and non-invariant items as described in Web Note 17.
I am wondering if you know of any work that compares these two approaches and if the same parameters are found to be invariant/non-invariant?
There is hardly any work on this to date. One related article is
van de Schoot, R., Tummers, L., Lugtig, P., Kluytmans, A., Hox, J. & Muthén, B. (2013). Choosing between Scylla and Charybdis? A comparison of scalar, partial and the novel possibility of approximate measurement invariance. Frontiers in Psychology, 4, 1-15. doi: 10.3389/fpsyg.2013.00770.
which is on our website.
Two other approaches suitable for working with many groups are discussed in this paper on our website:
Muthén and Asparouhov (2013). New methods for the study of measurement invariance with many groups. Mplus scripts are available here.
Tait Medina posted on Thursday, January 23, 2014 - 2:24 pm