## second order construct need HTMT and/or Fornell - Larcker criterion or not?

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592210373@qq.com
PLS Junior User
Posts: 7
Joined: Mon Oct 29, 2018 9:08 am
Real name and title: Mao Lina

### second order construct need HTMT and/or Fornell - Larcker criterion or not?

Hi,
I am a beginner in statistics and also smartpls... Now the HTMT and/or Fornell - Larcker criterion for the reflective second-order construct, TKI (reflective- reflective type, with 4 first order constructs TKI-1 to TKI-4) in my model are not ok... For the Fornell - Larcker criterion, the correlation for TKI-1 itself is lower than the one between TKI-1 and the second-order construct TKI, while the HTMT value between first level constructs(TKI-X), also between TKI-X (first - order ) and TKI(second - order) are above 0.85, even higher than 1... (I failed to attach my tables at the moment...)

My questions are:
1, for reflective higher order constructs, we need HTMT and Fornell- Larcker criterion, am I right?
2,for formative constructs, no matter first or second order one, these two indicators are not required, right?
3, if 1, is necessary, then what should I do to make it ok?

These may be stupid questions... however, after read several papers and some topics in this forum, I am still confused... Maybe someone can explain a little bit more?

Thank you so much in advance!

Sincersely,

Marina

jmbecker
SmartPLS Developer
Posts: 971
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

### Re: second order construct need HTMT and/or Fornell - Larcker criterion or not?

Discriminant validity in higher-order models depends...

You do not need it between higher- and lower-order constructs (because they are part of one construct).
I would not necessarily expect it between lower-order constructs that are reflectively attached to the higher-order construct, because they should be interchangeable/redundant because they are reflective measures of the same construct.
I would expect it between lower-order constructs that are formatively attached to he higher-order constructs, because they should represent distinct dimensions (that are not highly correlated). Otherwise you would also have multicollinearity problems in your formative higher-order model.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf

592210373@qq.com
PLS Junior User
Posts: 7
Joined: Mon Oct 29, 2018 9:08 am
Real name and title: Mao Lina

### Re: second order construct need HTMT and/or Fornell - Larcker criterion or not?

Dear Dr. Becker,

Thank you so much for your detailed explanation!
As I don't know whether it is correct or not, which really makes me anxiety.

Yes, my results show that for formative second-order construct, the HTMT,Fornell-Larker criterion and cross-loading of its 3 first-order constructs are all good, while the HTMT for the 4 first-order constructs of the reflective second-order construct are within 0.9, which I think is also ok now.

Now I have other questions...
As my model is AMC-TKI-TP, while AMC is a formative second order construct, and TKI is a reflective second order construct.

My question is,
1, as the TKI is a partial mediation and my model only analysis the indirect effect, so when conduct the analysis ( PLS Algorithm and bootstrap), I just follow my model which is without the direct effect, right?
2, if 1 is yes, then, do I also need to analysis mediation effect? As to analysis the mediation effect, following Zhao's (2010) suggestion, I think I should do another analysis to add the direct effect, just to see whether the direct effect is still significant,am I right? Or is it a must that I add direct effect in my original model?...

3, is about control variables. I think we do not need to have controls in CB-SEMs, so can we have controls in PLS-SEM in SmartPLS? I have read many topics in this forum, some have used controls, and you said, its role is just like in regression. But do we have any literature or paper clarify for that, or has had control variables? I have not seen yet...

4, is about model fit... As I'm interested in both repeated-indicator approach and two-stage approach, I do the both analysis. However, the SRMR of estimated model for these two approaches (stage one for two-stage approach) are all around 0.1 to 0.123, only the SRMR of estimated model for stage two is 0.061, which has no problem. In two stage approach, do I need also to report SRMR in stage one ,or only report SRMR in model two is ok? I think I have seen Dr. Ringle said he would report the second stage one, then how about the first stage one? As it is not satisfied.
Although it is said in SmartPLS website that model fit indexes should be used with caution, I still want to have it, in case the reviewer will ask for them...

Sorry for so many questions...But I really have been suspended for many days bcz of above questions.

Thank you again for your time and effort!

Best regards,

Marina from China

jmbecker
SmartPLS Developer
Posts: 971
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

### Re: second order construct need HTMT and/or Fornell - Larcker criterion or not?

592210373@qq.com wrote:
Thu Nov 08, 2018 3:50 pm
My question is,
1, as the TKI is a partial mediation and my model only analysis the indirect effect, so when conduct the analysis ( PLS Algorithm and bootstrap), I just follow my model which is without the direct effect, right?
2, if 1 is yes, then, do I also need to analysis mediation effect? As to analysis the mediation effect, following Zhao's (2010) suggestion, I think I should do another analysis to add the direct effect, just to see whether the direct effect is still significant,am I right? Or is it a must that I add direct effect in my original model?...
If you want to analyze a mediation effect you need the direct path according to Zhao et al.
592210373@qq.com wrote:
Thu Nov 08, 2018 3:50 pm
3, is about control variables. I think we do not need to have controls in CB-SEMs, so can we have controls in PLS-SEM in SmartPLS? I have read many topics in this forum, some have used controls, and you said, its role is just like in regression. But do we have any literature or paper clarify for that, or has had control variables? I have not seen yet...
If you think that the control variables are important then you should include them.
As a good reference would be:
Hult, G. T. M., Hair Jr, J. F., Proksch, D., Sarstedt, M., Pinkwart, A., & Ringle, C. M. (2018). Addressing endogeneity in international marketing applications of partial least squares structural equation modeling. Journal of International Marketing, 26(3), 1-21.
592210373@qq.com wrote:
Thu Nov 08, 2018 3:50 pm
4, is about model fit... As I'm interested in both repeated-indicator approach and two-stage approach, I do the both analysis. However, the SRMR of estimated model for these two approaches (stage one for two-stage approach) are all around 0.1 to 0.123, only the SRMR of estimated model for stage two is 0.061, which has no problem. In two stage approach, do I need also to report SRMR in stage one ,or only report SRMR in model two is ok? I think I have seen Dr. Ringle said he would report the second stage one, then how about the first stage one? As it is not satisfied.
Although it is said in SmartPLS website that model fit indexes should be used with caution, I still want to have it, in case the reviewer will ask for them...
As said in the note of caution, I think there is no literature on this issue, so I cannot say what will be best.
I could imagine that a model might not fit well in the first stage, if you really have a second-order constructs. That would be the idea of having a higher-order construct. If the first stage already fits well, then why using a higher-order constructs?
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf

592210373@qq.com
PLS Junior User
Posts: 7
Joined: Mon Oct 29, 2018 9:08 am
Real name and title: Mao Lina

### Re: second order construct need HTMT and/or Fornell - Larcker criterion or not?

Dear Dr. Becker,

Thank you for your suggestions and references, also for all the patiant answers in this forum! I have learnt a lot.

You also provide a new way for me to look at higher-order construct. My roriginal idea is a second - order one, I will also try whether just in first - order my constructs are ok or not.

Thank you again for the effort you and the SmartPLS team have been done.

Sincerly,

Marina