Communality X AVE = Average Communality

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Diogenes
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Communality X AVE = Average Communality

Post by Diogenes »

Hi,

please see viewtopic.php?p=832#832

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

Thanks.

Bido
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cringle
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Post by cringle »

Hi,

this is not really a bug!

All computations for communality are fine.

I understand that the term "Average Communality" is the precise naming (but that should be pretty much clear if computed for a latent variable and not on the manifest variable level). However, we keep this on our to-do-list.

Best regards
Christian
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Post by ruchi »

Dear Sir

How can i compute AVE by hand for my second order construct?
Sir if you have any excel sheet (template) please let me know.

Thanks
Ruchi
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Diogenes
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Post by Diogenes »

Hi,

if we have the LV_2nd with 3 reflective LV_1st, with these loadings:
LV1 ==> 0.6
LV2 ==> 0.7
LV3 ==> 0.8

The communalities will be:
LV1 ==> 0.6^2 = 0.36 = 36% (variance of the LV1 explained by the LV_2nd)
LV2 ==> 0.7^2 = 0.49 = 49%
LV3 ==> 0.8^2 = 0.64 = 64%

The AVE will be: (0.36+0.49+0.64)/3 = 0.49666 = 40.6%

The composite reliability of the second order also must be computed by hand.

Best regards,

Bido
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Post by Mrs Tourky »

Dear Prof. Bido,

Would you please let me know hoe to compute the composite reliabiluty by hand (for second order construct)? Thanks
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Post by Mrs Tourky »

Hi all,

I found the formula for calculating Composite reliability:
Henseler et al. (2009) p.300

I checked using various examples in published papers; i.e. Wetzels et al. 2009, p: 188; and it worked for calculating Cr for second, third and fourth order constructs.

However, AVE for second, third, fourth order constructs works as suggested by Prof. Bido.

Hope this helps others :)

Best
Marwa
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Post by ckleine »

Dear Prof. Bido,

Could you recommend any literature to your approach to compute the AVE by hand, i.e., any literature that says to do so?

Many thanks in advance.
Christian
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Post by Eins »

Hi Christian,

Did Prof Bido provide you the reference?

Eins
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Diogenes
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Post by Diogenes »

Hi,

if we have the LV_2nd with 3 reflective LV_1st, with these loadings:
LV1 ==> 0.6
LV2 ==> 0.7
LV3 ==> 0.8

The variance of error terms will be:
LV1 ==> 1 – 0.6^2 = 0.36 = 0.64
LV2 ==> 1 – 0.7^2 = 0.49 = 0.51
LV3 ==> 1 – 0.8^2 = 0.64 = 0.36

The CR will be: (0.6 + 0.7 + 0.8)^2/[(0.6 + 0.7 + 0.8)^2 + (0.64 + 0.51 + 0.36)] = 0.745

The composite reliability of the second order is computed in the same way that we compute the CR for the first order LV.

The problem with SmartPLS when computing the AVE and CR for the higher order LV is that it uses the loadings of the repeated indicators, not the loading from the second order LV to its first order LV (these loadings are reported as path coefficients).

Some references about AVE and CR:

FORNELL, C.; LARCKER, D. F. Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, v. 18, p. 39-50, 1981.

HAIR JR., J. F.; BLACK, W. C.; BABIN, B. J.; ANDERSON, R. E. Multivariate Data Analysis. 7th ed. Upper Side River, NJ: Prentice Hall, 2010.

TENENHAUS, M.; ESPOSITO VINZI, V.; CHATELIN, Y.-M.; LAURO, C. PLS path modeling. Computational Statistics & Data Analysis, v. 48, n. 1, p. 159-205, 2005.


Best regards,

Bido
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