How does SmartPLS3 calculate AVE for 2nd-order constructs

[bmckinley1]

I've seen several articles (PRed) ignore the second-order AVE for reflective-reflective models when using SmartPLS. Instead, they manually calculate the average of squared loadings (normalized) for a repeated indicators approach.
For example, if you have one second-order construct (ignoring it's large nomological net for brevity) with three first-order reflective dimensions (see Edwards or Wetzels et al.), you have a reflective-reflective model.
If you have 5 indicators per first-order construct, then 15 second-order indicators are reused or repeated in the second-order construct. In my situation, the average of squared loadings of the second-order construct is greater than the AVE reported by SmartPLS3. Why the difference? How does SmartPLS3 calculate AVE in the reflective-reflective situation. The difference is substantial in terms of the number of indicators retained in my measurement model.

Here's an MIS Quarterly snippet that refers to the AVE calculation (MacKenzie et al., 2011): Note: Hair's MV statistics texts are often cited in other PRed contexts.

For second-order latent constructs with reflective indicators
(see Figure 3, Panel C), it is also important to examine the
convergent validity of the set of first-order sub-dimensions as
reflective indicators of the second-order construct. As noted
by Edwards (2001, p. 163), this can be assessed using the
multivariate coefficient of determination, R2...(For an equivalent formula for R2
m, see Edwards 2003.)
Alternatively, AVE could be calculated for the second-order
construct by averaging the squared multiple correlations for
the first-order sub-dimensions (or averaging the square of
each sub-dimension’s completely standardized loading on the
second-order construct). In either case, values greater than
.50 mean that, on average, a majority of the variance in the
first-order sub-dimensions is shared with the second-order
latent construct. (p. 313)

MacKenzie, S. B., Podsakoff, P. M., & Podsakoff, N. P. (2011). Construct measurement and validation procedures in MIS and behavioral research: Integrating new and existing techniques. MIS Quarterly, 35(2), 293–334.

[jmbecker]

SmartPLS does not know whether your latent variable is a 2nd-order construct or a normal construct. Hence, the AVE of a 2nd-order construct is based on all repeated indicator variables. This AVE should not be used. Instead, as you have mentioned, you should use the path coefficients from the reflective 2nd-order construct to the lower-order constructs and used these as loading in the AVE formula.
Unfortunately, this has to be done "by-hand" outside of SmartPLS, because at the moment there is no way to distinguish 2nd-order constructs from normal constructs.

We also describe this in our LRP paper:
Becker, J. M., Klein, K., & Wetzels, M. (2012). Hierarchical latent variable models in PLS-SEM: guidelines for using reflective-formative type models. Long Range Planning, 45(5), 359-394.

[bmckinley1]

Now my results make more consistent sense with prior work using the 2nd order construct.
I have your LRP paper. I will have another look there as well. Thank you.

[Man18]

SmartPLS does not know whether your latent variable is a 2nd-order construct or a normal construct. Hence, the AVE of a 2nd-order construct is based on all repeated indicator variables. This AVE should not be used. Instead, as you have mentioned, you should use the path coefficients from the reflective 2nd-order construct to the lower-order constructs and used these as loading in the AVE formula.
Unfortunately, this has to be done "by-hand" outside of SmartPLS, because at the moment there is no way to distinguish 2nd-order constructs from normal constructs.

We also describe this in our LRP paper:
Becker, J. M., Klein, K., & Wetzels, M. (2012). Hierarchical latent variable models in PLS-SEM: guidelines for using reflective-formative type models. Long Range Planning, 45(5), 359-394.

Hi Dr Becker,
I'm facing the same problem with low AVE for HOC (model type reflective-reflective) my question is: the latest version of smartPLS distinguish between LOC and HOC ??
Thank you in advance

[jmbecker]

No. The software cannot distinguish between higher and lower order constructs. If you have a reflective second-order construct you need to calculate AVE, Composite Reliability, etc. yourself based on the path coefficients to the lower order constructs, which serve as loadings.

[Man18]

Ok Dr thank you for your kind reply