Fornell-Larcker criterion

Frequently asked questions about PLS path modeling.
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Prince#9
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Fornell-Larcker criterion

Post by Prince#9 » Sat Aug 07, 2010 5:33 am

Probably a really silly question but i would like to confirm that i am on the right path.

In order to assess the Fornell-Larcker criterion due i use the results presented in the table "Latent Variable Correlations" then square them and compare them to the AVE?

christian.nitzl
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Post by christian.nitzl » Sat Aug 07, 2010 8:46 am

Hey,

yes, you can do it this way or you can do it also the other way around which I prefer.

You root the AVE and compare them with the absolute values in the table "Latent Variable Correlations".

Best regards,

Christian

Prince#9
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Post by Prince#9 » Sat Aug 07, 2010 9:16 am

Hey Christian,

Thank you very much for your quick reply.

In the meanwhile i had already compute based on your way.

Another question arises though. Just found out that in one case the AVE is smaller than a latent variable correlation by 0.05.

The two latents are significantly distant in terms of meaning.

What do you think that i should do?

thank you very much for all your help.

christian.nitzl
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Post by christian.nitzl » Sat Aug 07, 2010 10:08 am

Hey Thomas,

As far as I know there is no rule, how to handle such problem.

But here comes my proposals :-)

The problem is that a latent variable explane more of an other latent variable as the direct measurements (items) of it.

Therefore the next step should be to check your measurements loadings. Are they high enough (>0,7)?

You should also check your "cross loadings". The correlation between the direct measurement of a latent variable and latent variable should always the highest one.

Should the one or other mesurement not fulfill this criteria I would delete it.

I hope this will help you.

Christian

Loopie
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Post by Loopie » Sat Aug 07, 2010 2:20 pm

I would agree with Christian's proposal, a lot of people forget to check the crossloadings as well as a measure of discriminant validity.
I would follow Christian's method and see how your discriminant vailidy looks when examining the cross-loadings.

Kind regards,
Michel

Prince#9
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Post by Prince#9 » Sat Aug 07, 2010 2:52 pm

Christian and Michel thank you very much.

I have checked cross-loadings and they are ok.

The loadings are also very good (above .80 for most of the cases and 0.75 for a couple of indicators).

So you would suggest that according to this there is discriminant validity although the Fornell-Larcker criterion is not met?

thanks

christian.nitzl
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Post by christian.nitzl » Sat Aug 07, 2010 4:24 pm

Hey,

an other 'technical' solution would be to build a second-order construct with the latent constructs which are not met the Fornell-Larcker criteria.

Best regards,

Christian

Prince#9
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Post by Prince#9 » Sat Aug 07, 2010 10:02 pm

Dear Christian,

My model is already a second order formative one.

The criterion is not met for two 1st order latent variables.

StevenGregory
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Re: Fornell-Larcker criterion

Post by StevenGregory » Tue Jan 15, 2019 12:35 pm

hey guys i wanna ask something,
is it alright if i only using the cross loading test for the discriminant validity test?
because my cross loading test values are ok/valid as required
Thank you in advance

jmbecker
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Re: Fornell-Larcker criterion

Post by jmbecker » Fri Jan 18, 2019 8:51 am

No it is usually not ok. The cross-loadings are only a weak test of discriminant validity. There can be severe problems with discriminant validity and the cross-loadings would not indicate it. Therefore, you should also use the Fornell-Larker and HTMT test.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

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