Hi,
I am a beginner in statistics and also smartpls... Now the HTMT and/or Fornell  Larcker criterion for the reflective secondorder construct, TKI (reflective reflective type, with 4 first order constructs TKI1 to TKI4) in my model are not ok... For the Fornell  Larcker criterion, the correlation for TKI1 itself is lower than the one between TKI1 and the secondorder construct TKI, while the HTMT value between first level constructs(TKIX), also between TKIX (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
second order construct need HTMT and/or Fornell  Larcker criterion or not?

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

 SmartPLS Developer
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 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: second order construct need HTMT and/or Fornell  Larcker criterion or not?
Discriminant validity in higherorder models depends...
You do not need it between higher and lowerorder constructs (because they are part of one construct).
I would not necessarily expect it between lowerorder constructs that are reflectively attached to the higherorder construct, because they should be interchangeable/redundant because they are reflective measures of the same construct.
I would expect it between lowerorder constructs that are formatively attached to he higherorder constructs, because they should represent distinct dimensions (that are not highly correlated). Otherwise you would also have multicollinearity problems in your formative higherorder model.
You do not need it between higher and lowerorder constructs (because they are part of one construct).
I would not necessarily expect it between lowerorder constructs that are reflectively attached to the higherorder construct, because they should be interchangeable/redundant because they are reflective measures of the same construct.
I would expect it between lowerorder constructs that are formatively attached to he higherorder constructs, because they should represent distinct dimensions (that are not highly correlated). Otherwise you would also have multicollinearity problems in your formative higherorder model.
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

 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 secondorder construct, the HTMT,FornellLarker criterion and crossloading of its 3 firstorder constructs are all good, while the HTMT for the 4 firstorder constructs of the reflective secondorder construct are within 0.9, which I think is also ok now.
Now I have other questions...
As my model is AMCTKITP, 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 CBSEMs, so can we have controls in PLSSEM 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 repeatedindicator approach and twostage approach, I do the both analysis. However, the SRMR of estimated model for these two approaches (stage one for twostage 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
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 secondorder construct, the HTMT,FornellLarker criterion and crossloading of its 3 firstorder constructs are all good, while the HTMT for the 4 firstorder constructs of the reflective secondorder construct are within 0.9, which I think is also ok now.
Now I have other questions...
As my model is AMCTKITP, 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 CBSEMs, so can we have controls in PLSSEM 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 repeatedindicator approach and twostage approach, I do the both analysis. However, the SRMR of estimated model for these two approaches (stage one for twostage 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

 SmartPLS Developer
 Posts: 971
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: second order construct need HTMT and/or Fornell  Larcker criterion or not?
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 pmMy 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 think that the control variables are important then you should include them.592210373@qq.com wrote: ↑Thu Nov 08, 2018 3:50 pm3, is about control variables. I think we do not need to have controls in CBSEMs, so can we have controls in PLSSEM 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...
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), 121.
As said in the note of caution, I think there is no literature on this issue, so I cannot say what will be best.592210373@qq.com wrote: ↑Thu Nov 08, 2018 3:50 pm4, is about model fit... As I'm interested in both repeatedindicator approach and twostage approach, I do the both analysis. However, the SRMR of estimated model for these two approaches (stage one for twostage 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...
I could imagine that a model might not fit well in the first stage, if you really have a secondorder constructs. That would be the idea of having a higherorder construct. If the first stage already fits well, then why using a higherorder constructs?
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

 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 higherorder 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
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 higherorder 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