Cross correlation of manifest variables with latent scores

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mkiddhome
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Cross correlation of manifest variables with latent scores

Post by mkiddhome » Fri Apr 22, 2016 9:35 am

I have a data set with a specified underlying latent structure. If I do an EFA, the factor loadings support the underlying structure except for two manifest variables which strongly load on a different factor. This made me think whether it is possible to test the appropriateness of manifest variables in PLS-SEM by cross correlating them with the latent variable scores? My strategy would be to fit PLS-SEM without the manifest variable in question, and then calculate correlations of all the latent variables with the manifest variable that was excluded. One would expect the correlation if its own latent variable to be higher than for the other latent variables.

Would this be a valid strategy to follow, and if so, are there any publications referring to this or methods similar?

jmbecker
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Re: Cross correlation of manifest variables with latent scor

Post by jmbecker » Tue May 03, 2016 3:39 pm

I have never seen such an analysis and I would doubt that it is a valid strategy (just by gut feeling).
In addition, if you have a specified latent structure then it is more appropriate to do a CFA than an EFA, because you want to test whether the specified structure is correct and not explore the latent structure that emerges from your data set. EFA should be reserved for exploratory analysis.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
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mkiddhome
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Re: Cross correlation of manifest variables with latent scor

Post by mkiddhome » Tue May 10, 2016 8:17 am

Thanks for your reply. For the specific example I referred to, I did do CFA first which did not provide adequate fit, and then did the EFA.

In many other occasions however, I do not have large enough sample sizes to do proper CFA, so my question really was whether an approach like this could be used in PLS-SEM as a further diagnostic for shedding more light on the latent structure. In a sense similar to the heterotrait-monotrait ratio, but in this case evaluating on an item level.

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