Hello everyone,
I have some difficulties with the procedure in my empirical evaluation. My structural model consists of seven independent variables and one dependent variable and so far I have evaluated 150 German and 150 American data sets individually. However, since I want to check in which country the significant relationships between IV and DV are stronger, I am unsure how to proceed correctly.
Is it possible to compare just the significant path coefficients to find out if the relationship between IV and DP in country A is stronger than in country B?
Or does this have to be evaluated by means of a multi-group analysis?
Thanks for your help,
Baxmauer
Please look at the following below links which may help you in your analysis:
https://esajournals.onlinelibrary.wiley.com/doi/pdf/10.1890/0012-9623%282005%2986%5B283%3AITRFMR%5D2.0.CO%3B2
http://faculty.cas.usf.edu/mbrannick/regression/Pathan.html
https://jslefche.github.io/sem_book/coefficients.html
Thanks
Hello Michael,
So, you have as many as 300 independent estimates of IV-DV relationship, and you'd like to know whether the resultant values are dependably different based on the country from which data were collected, right?
If the same IV-DV set were used, a simple t-test on the observed correlation (with Fisher-z adjustment) would let you know whether country made any difference.
Note that if you use the unstandardized or standardized coefficients and studies differed with respect to how many of your target IVs they incorporated, then collinearity (and model complexity) could be confounding variables. (Isam's first link, in the response above, is germane to this situation.) That's the reason I suggested going with the observed correlations.
If all 7 IVs and the DV were exactly the same in all samples, then a manova would compare simultaneously the equality of country centroids of path coefficients.
In the SEM framework, a multi-group approach could work (again, presuming exactly the same variables and model for each sample), but I'm not clear how best to go beyond one sample per country, which is how most textbook examples would be presented (multi-level, perhaps? e.g., sample within country).
Good luck with your work.
Hello Michael,
as David has already mentioned, the most effective way would to go to a multigroup SEM. There is a ton of literature on "measurement invariance" that describes such an analysis as a set of tests.
1) You begin by testing the structure. If you have just a regression structure with no effects fixed to zero, there is no real test. But if you have some restrictions (e.g., a full mediation) this would be a good thing, and you can test wether this structure holds in both groups. This step is called "configural invariance". Perhaps you have latent measurement models. These are tested as well (i.e., whether the m.models are equivalent across countries
2) Then you have the option to specify "equality constraints". That means that you tell the algorithm to estimate a certain coefficient but under the premise that this coefficient must be identical in both countries. The empirical question then is, whether this is correct or a serious violation (as the countries differ in the values of the coefficient). Hence this step consists of comparing the fit of the model with the configurally invariant model. If the fit gets a bit worse but not to a significant degree than the H0 of "no difference" holds. If the fit gets significantly worse, than you reject the H0 and assume a difference. The powerful and efficient aspect is that you can apply equality constraints for all parameters of interest at once leading to a strong omnibus test of "all parameters are equal across both countries".
Again, if you have a mmeasurement model, you would usually start by testing for "metric invariance", namely whether the factor loadings are identical followed by a test of "structural invariance" testing your substantial cross-country hypothesis.
I have an introductory book on SEM (in German language) with the lavaan package in R that has a chapter on multigroup models and how you do it (if you forgive me the shameless self-advertisement :)
HTH
--Holger
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