Difference between DEV and Communality?

Frequently asked questions about PLS path modeling.
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bubach
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Difference between DEV and Communality?

Post by bubach »

Hello Community,

does somebody knows, what's the different between DEV and Communality (both are reported in Quality-Criteria Overview)?

Thanks you for your comments.
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cringle
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Post by cringle »

Please check the following article that you already can find in the "PLS Related Literature"-section of this forum

viewforum.php?f=7

author = Tenenhaus, Michel / Vinzi, Vincenzo E. / Chatelin, Yves-Marie / Lauro, Carlo
title = PLS path modeling
journal = Computational Statistics & Data Analysis
year = 2005
volume = 48
pages = 159-205
bubach
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Post by bubach »

Dear Dr. Ringle,

that means that in the reflective way AVE = Communality, right?

Thanks a lot.
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Diogenes
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Post by Diogenes »

Hi,

if we have a LV with 3 reflective MV, with these loads:
x1 ==> 0.6
x2 ==> 0.7
x3 ==> 0.8

The communalities will be:
x1 ==> 0.6^2 = 0.36 = 36% (variance of the MV explained by the LV)
x2 ==> 0.7^2 = 0.49 = 49%
x3 ==> 0.8^2 = 0.64 = 64%

The AVE will be: (0.36+0.49+0.64)/3 = 0.49666 = 40.6% (the LV explain 40.6% of the variance from all MVs).

Best regards.

Bido
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Post by bubach »

Dear Prof. de Souza Bido,

Thank you so much for your explanations. They are very helpful.

You wrote:

The AVE will be: (0.36+0.49+0.64)/3 = 0.49666 = 40.6% (the LV explain 40.6% of the variance from all MVs).

This is exactly the same formula for communality (used in Tenenhaus et al. 2005). For a latent reflective construct, AVE = communality. I am confused, because AVE as well as communality is reported in SmartPLS 2.0M3.

Is there any reason why there are reported twice? I am thinking, communality is enough.

Thanks you so much.
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Diogenes
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Post by Diogenes »

Hi,

We use communality to assess how much one indicator is explained by the LV, there is a recomendation that communality shoud be greater than 0.5 for each indicator (individually).

The AVE is used to assess the LV like we do in factor analysis: if we really have a common factor, it shoud explain more than 50% of the total variance of the indicators.

Eventually, We have one communality by indicator and one AVE by LV.

Best regardss.

Bido
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Diogenes
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Post by Diogenes »

Hi Michael,

I just could understand what was happening now !!

SmartPLS is showing "Commulality" for each LV, but the correct denomination is "Average Comunnality".

Then we have:
1) "communality" ==> one for each MV (load ^2)
2) "average communality" = AVE ==> one for each LV.

Best Regards.

Bido
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