HTMT discriminant validity

Frequently asked questions about PLS path modeling.
CvdV
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HTMT discriminant validity

Post by CvdV » Mon Apr 13, 2015 2:24 pm

Good afternoon,

I have a question about the discriminant validity.
All of my statistics are right except the discriminant validity.
My Fornell Larcker Criterion is as follows:
Perceived value Satisfaction Loyalty
Perceived value 0.767
Satisfaction 0.876 1.000
Loyalty 0.882 0.846 0.893

All my Cross Loadings are correct but the HTMT is not:
Perceived value Satisfaction Loyalty
Perceived value
Satisfaction 0.875
Loyalty 0.937 0.888

How can I describe this correctly in my thesis and what does this mean for my results?
Because the other statistics are correct.

I will appreciate your help with this situation.

Best Regards,

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cringle
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Re: HTMT discriminant validity

Post by cringle » Tue Apr 14, 2015 7:02 am

Hi

You should focus on HTMT since cross loadings and Fornell-Larcker do not reliably detect discriminant validity problems.

In your case, discriminant validity has not been established und your results are not valid.

Take a look at this paper, Fig. 8., where you find some hints on how to establish discriminant validity.
http://dx.doi.org/10.1007/s11747-014-0403-8

Best regards,
Christian Ringle

CvdV
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Re: HTMT discriminant validity

Post by CvdV » Tue Apr 14, 2015 7:34 pm

Thanks for your response! Yes that's what I thought, I will try to work with the research paper!
But when the discriminant validity is not established, does that imply that all my results are invalid?
Since AVE and VIF are correct (above 0.5 and below 5.0, resp.) in the research.
Besides those values, my Chronbach's Alpha, Composite Reliability, Outer Loadings and Bootstrapping​ are correct.
Can I still use these results to describe the reliability of the model and the validity of the other two tests?

Best Regards,

faresbrini
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Re: HTMT discriminant validity

Post by faresbrini » Thu May 28, 2015 1:54 pm

Hi CvdV and P. Ringle,
If I well understand your comments on discriminant validity, I shall conclude that:
-discriminant validity shall be established if the HTMT value, in respect to the Confidence interval as shown in PLS3 [2.5%, 97.5%], should be between this interval.
-example: HTMT value X>Y=0.383; the CI is set on [0.215, 0.678]

So, do I consider that these two constructs are discriminant from each others?

Thank you for answering me,

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cringle
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Re: HTMT discriminant validity

Post by cringle » Thu May 28, 2015 3:26 pm

Please take a look at this paper:
http://dx.doi.org/10.1007/s11747-014-0403-8

If 1 does not fall into the CI, then things are fine.

Best
CR

faresbrini
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Re: HTMT discriminant validity

Post by faresbrini » Sun May 31, 2015 11:13 am

Dear Professor,

Thanks a lot for your answer.

Regards,

Leho
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HTMT discriminant validity

Post by Leho » Tue Dec 05, 2017 4:44 pm

Dear Forum,

I have a question about discriminant validity. In my model, I would like to investigate different determinants for two dependent variables A and B with 3 items each. From a theoretical perspective, the items x1 to x6 belong to a single concept (sometimes measured as a higher order construct) with different subdimensions (x1-x3 belongs to subdimension 1 of the concept; x4-x6 belongs to the subdimension 2 of the concept).

In the existing literature, the subdimension 1 (x1-x3) was operationalized as a dependent variable and also both subdimensions (x1-x6) were operationalized as a single dependent variable. The aim of the study is to check the importance of identified determinants for the two subdimensions separately (therefore two dependent variables A and B). The results show that there are significant differences but it is not possible to distinguish discriminant validity between these two subdimensions by using HtMt.

My question to you: Is it necessary to create two models to avoid the problem of a lack of discriminant validity or, in spite of a lack of discriminant validity, to capture both dependent variables into one model?

Thank you in advance!

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cringle
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Re: HTMT discriminant validity

Post by cringle » Sat Dec 09, 2017 11:34 am

Well, we are not so great fans of higher order models but addressed this issue in the advanced PLS-SEM book, Chapter 2: https://www.smartpls.com/documentation/ ... sem-issues

"In the next step, you can assess the discriminant validity between the LOCs COMP and LIKE using the HTMT criterion (Henseler et al., 2015). Exhibit 2.11 shows the HTMT values along with their 95% bias-corrected and accelerated (BCa) bootstrap confidence intervals. The results indicate discriminant validity between COMP and LIKE since the HTMT value of 0.780 is below the (conservative) threshold value of 0.85. Furthermore, the corresponding bootstrap confidence interval does not include the value 1 (i.e., the HTMT value is significantly lower than 1). Also, we establish discriminant validity between LOCs and the reflectively measured construct CUSL as well as with the single item construct CUSA. At the same time, however, we cannot establish discriminant validity between COMP and LIKE and their HOC REPU. This result is expected, however, as the measurement model of the HOC repeats the indicators of its LOCs." (p. 60-61).

Hence, you would like to establish discriminant validity between the LOCs (otherwise it makes probably more sense if you just use the higher order construct without subdimensions).

Best
Christian

Leho
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Re: HTMT discriminant validity

Post by Leho » Wed Dec 13, 2017 12:41 pm

Dear Prof. Ringle,

thank you for your answer!

Best regards
Holger

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Re: HTMT discriminant validity

Post by StevenGregory » Sun Jan 13, 2019 1:18 pm

hi i wanna ask something regarding to this HTMT criterion, im currently doing my Thesis and in my thesis my HTMT is a little bit above 0.9 which is 0.914.
is it still can be accepted or consider as discriminant in some extent even though the value is only a little bit above the requirement?
Thank you very much in advance!

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cringle
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Re: HTMT discriminant validity

Post by cringle » Sun Jan 13, 2019 1:33 pm

Well, it's a little bit high. Can you get it below 0.9? Otherwise, bootstrap the HTMT (use complete bootstrapping in SmartPLS 3) and show that the HTMT is significantly lower than 1 (look at the upper bound of HTMT's bootstrap confidence interval).

Best
Christian

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Re: HTMT discriminant validity

Post by StevenGregory » Sun Jan 13, 2019 2:14 pm

Dear Professor Ringle,

this what i got from the HTMT Confidence Interval after complete bootstrapping Sir

Original Sample Sample Mean 2.5% 97.5%
Latent variable 2 > Latent variable 1 0.914 0.905 0.734 1.018
Latent variable 3 > Latent variable 1 0.762 0.763 0.411 1.023
Latent Variable 3 > Latent variable 2 0.778 0.782 0.449 1.038

is it alright like this Sir?, pardon me Si i'm a beginner regarding to smartpls statistics

Thank you
Regards

Steven
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cringle
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Re: HTMT discriminant validity

Post by cringle » Sun Jan 13, 2019 2:32 pm

You would like to do a one-sided test (or use a 10% probability of error with the 2-sided test) to obtain the upper bound at the 95% point (and not at 97.5%.

StevenGregory
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Re: HTMT discriminant validity

Post by StevenGregory » Sun Jan 13, 2019 2:46 pm

These are what i got Sir, the first one is using one-sided test and the second one is using two-sided test but with 10% probability
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two-sided test with 10% probability of error
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one-sided test
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cringle
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Re: HTMT discriminant validity

Post by cringle » Sun Jan 13, 2019 3:17 pm

Thanks. Use the one or the other approach but with 5,000 bootstrap samples.

However, your upper bound is above 1 which means that discriminant validity has not been established. Your confidence intervals are very wide. I suppose that you use a small sample (which would be a data problem) and/or a fuzzy dataset (which would also be a data problem).

There is no straightforward recommendation and solution which we can offer.

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