Dear forum,
I have a question regarding the specific level of complexity that means the max. number of arrows pointed at a construct in a PLS path model where HCMs are used (see attachment).
If I look at HOC_E (because this is in my opinion the part of the model with the largest number of predictors) I would say that 10 arrows from the following predictors are pointing at it:
1.SOC_E
2. LOC1_E
3. LOC2_E
4. LOC3_E
5. LOC4_E
6. LOC5_E
7. LOC6_E
8. LOC7_E
9. LOC8_E
10. HOC_P
Or am I wrong because I have to consider all the predictors of the LOC_s (18) and the HOC_P, too?
Thank you very much in advance.
Best regards,
S. Boddien
Specific level of complexity of HCMs / number of predictors
Specific level of complexity of HCMs / number of predictors
 Attachments

 PLS path model including HCMs.png (123.15 KiB) Viewed 866 times

 SmartPLS Developer
 Posts: 971
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: Specific level of complexity of HCMs / number of predictors
Well, yes based on the structural model that you show 10 is the largest number of predictors that point to a construct (HOC_e). However, if you model the HOC with the repeated indicator approach (which seems to be the case in your model) and you have a formative HOC and use Mode B to with the repeated indicators of this HOC you might have more arrows pointing to the HOC in the measurement model. For example, if you have 22 repeated indicators 22 would be the largest number of arrows pointing to a construct.
Nevertheless, this rule of thumb thing with counting the arrows is nowadays usually also discouraged and a power analysis is the better option to determine the sample size. But if gives you an impression of your minimum sample size. However, sample size requirements might be much larger.
Nevertheless, this rule of thumb thing with counting the arrows is nowadays usually also discouraged and a power analysis is the better option to determine the sample size. But if gives you an impression of your minimum sample size. However, sample size requirements might be much larger.
Dr. JanMichael Becker, University of Cologne, SmartPLS Developer
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Re: Specific level of complexity of HCMs / number of predictors
Thank you very much for your reply.
I want to use in the first stage the repeated indicators approach to obtain the LOC´s scores which will serve in the second stage as manifest variables in the HOC´s measurement model (twostage approach).
Do I need to consider now all the repeated indicators of the first stage (3 x 8 = 24 repeated indicators + 2 = 26) or only the LOCs indicators of the second stage (8 + 2 = 10)?
Thank you once again for clearifying!
I want to use in the first stage the repeated indicators approach to obtain the LOC´s scores which will serve in the second stage as manifest variables in the HOC´s measurement model (twostage approach).
Do I need to consider now all the repeated indicators of the first stage (3 x 8 = 24 repeated indicators + 2 = 26) or only the LOCs indicators of the second stage (8 + 2 = 10)?
Thank you once again for clearifying!

 SmartPLS Developer
 Posts: 971
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: Specific level of complexity of HCMs / number of predictors
I would not use the repeated indicator approach in the firststage if you want to do a twostage approach. Either do a repeated indicator approach or a twostage approach where you use a direct effects model in the first stage (as described in Becker, J.M., Klein, K., & Wetzels, M. (2012). Hierarchical latent variable models in PLSSEM: Guidelines for using reflectiveformative type models. Long Range Planning, 45(56), 359394. http://dx.doi.org/10.1016/j.lrp.2012.10.001), where you connect your lowerorder constructs directly with your other constructs. Such an approach is much more robust and gives better results than a repeated indicator approach in the first round.
Dr. JanMichael 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
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Re: Specific level of complexity of HCMs / number of predictors
Thank you for your kind advice. Just to reconfirm if I have understood it correctly:
So I would have in the first stage my direct effect model (without the HOCs) but only the LOCs connecting directly with the other constructs.
Then I would have to run the PLS algorithm and evaluate the results of the reflective LOCs (internal consistency reliability, convergent validity and discriminant validity) and of the formative LOCs (convergent validity, collinearity issues and significance/relevance of the formative indicators).
After that I would have to create the more parsimonious model of the second stage with the HOCs. As their indicators I would use then the latent variable scores of the LOCs of the direct effect model of the first stage.
Again I would run the PLS algorithm and evaluate the results of the two exogenous reflective latent constructs (internal consistency reliability, convergent validity and discriminant validity) and of the 3 formative HOCs (convergent validity, collinearity issues and signifigance and relevance of the formative indicators).
Last but not least I would have to do the general evaluation of the structural model of the second stage (collinearity issues, R2, f2, Q2 etc.)
Is this how you meant it?
So I would have in the first stage my direct effect model (without the HOCs) but only the LOCs connecting directly with the other constructs.
Then I would have to run the PLS algorithm and evaluate the results of the reflective LOCs (internal consistency reliability, convergent validity and discriminant validity) and of the formative LOCs (convergent validity, collinearity issues and significance/relevance of the formative indicators).
After that I would have to create the more parsimonious model of the second stage with the HOCs. As their indicators I would use then the latent variable scores of the LOCs of the direct effect model of the first stage.
Again I would run the PLS algorithm and evaluate the results of the two exogenous reflective latent constructs (internal consistency reliability, convergent validity and discriminant validity) and of the 3 formative HOCs (convergent validity, collinearity issues and signifigance and relevance of the formative indicators).
Last but not least I would have to do the general evaluation of the structural model of the second stage (collinearity issues, R2, f2, Q2 etc.)
Is this how you meant it?

 SmartPLS Developer
 Posts: 971
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: Specific level of complexity of HCMs / number of predictors
Yes.
Dr. JanMichael 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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GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
Re: Specific level of complexity of HCMs / number of predictors
Great! Thank you so much, Dr. Becker!