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GAT
May 18, 2020, 4:44:38 PM5/18/20
to lavaan
**Apologies if this is not a good place to ask - if so please let me know and I'll delete the question.
I have a question concerning good practices when testing invariance in multi-sample structural equation models.
I am currently working with a questionnaire which has been administered to three different groups (three countries, in fact).
I am currently working with a questionnaire which has been administered to three different groups (three countries, in fact).
This study includes some single-item measures and some latent variables with 3 or 6 items each. I have tested for invariance using confirmatory factor analyses for the latent variables (each construct separately), obtaining partial scalar invariance in all cases. Ok, good.
Now I am proceeding to test the structural equation models to examine my hypotheses pertaining relationships among variables. Do I keep the loadings and intercepts constrained across groups in this last model? (except for those couple of items that are non-invariant, naturally). Or do I start fresh so to say and keep everything free to vary?
Thank you
Now I am proceeding to test the structural equation models to examine my hypotheses pertaining relationships among variables. Do I keep the loadings and intercepts constrained across groups in this last model? (except for those couple of items that are non-invariant, naturally). Or do I start fresh so to say and keep everything free to vary?
Thank you
Nickname
May 19, 2020, 10:14:30 AM5/19/20
to lavaan
GAT,
I can tell you what I think would be a good practice but cannot assure you that this is common or accepted practice.
I would fit the structural model both ways and compare with a chi-square difference test. You can also compare the fit of each structural model to the corresponding CFA (with or without equality constraints). If the structural model with equality constraints fits as well as the models in which it is nested, then that bodes well. You can then do the rest of the things that you would ordinarily do to critically evaluate the constrained structural model solution. If the constrained model does not fit, then at least you have an a priori test of the more general model before you switch from confirmatory to exploratory mode.
If the structural model is well specified, it should reproduce the same covariance structure among the latent variables that you saw in the CFA. As a result, you should expect the parameter estimates for the parameters in the measurement part of the full structural model to closely reproduce the estimates that you obtained in the CFA. If not, that could be a sign if mis-specification in the structural portion of the model.
Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/
I can tell you what I think would be a good practice but cannot assure you that this is common or accepted practice.
I would fit the structural model both ways and compare with a chi-square difference test. You can also compare the fit of each structural model to the corresponding CFA (with or without equality constraints). If the structural model with equality constraints fits as well as the models in which it is nested, then that bodes well. You can then do the rest of the things that you would ordinarily do to critically evaluate the constrained structural model solution. If the constrained model does not fit, then at least you have an a priori test of the more general model before you switch from confirmatory to exploratory mode.
If the structural model is well specified, it should reproduce the same covariance structure among the latent variables that you saw in the CFA. As a result, you should expect the parameter estimates for the parameters in the measurement part of the full structural model to closely reproduce the estimates that you obtained in the CFA. If not, that could be a sign if mis-specification in the structural portion of the model.
Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/
GAT
May 19, 2020, 11:44:33 AM5/19/20
to lavaan
Thank you for the insightful answer.
Giovanni
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