HTMT necessary? Value >1 with Type II construct

Questions about the implementation and application of the PLS-SEM method, that are not related to the usage of the SmartPLS software.
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SHU
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Real name and title: Susanne Hügel
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HTMT necessary? Value >1 with Type II construct

Post by SHU »

Hello all,

the exogenous variable of my model is a first-oder reflective second-order formative construct (type II). I would like to use the HTMT criterion to assess discriminant validity as recommended by Henseler, Ringle & Sarstedt (2015). I detected that the HTMT values between the subconstructs of my second-order formative construct show either values very close to 1.0 or even above 1.0, thus, not meeting the threshold of 0.85 or 0.90.

Also, the inter-item correllations (examined in SPSS) show that the items of the different subconstructs are not clearly delimitable and "somehow" interconnected. This is inline with the theoretical reasoning saying that the subconstructs have (indirect) effects on each other but account for a specific aspect of the overarching construct.

1. Is discriminant validity "within a second-order construct" (in general or in this case?) a necessary requirement?

2. To what extent is a "violated discriminant validity" correlated to (or already indicating potential issues with) multicollinearity?

Further, I only found explicit recommendations for endogenous formative constructs, but not for exogenous formative. I applied the two-stage approach but still wonder which method is best to model an exogenous variable with a formative second-order. Would the mixed approach (i.e., two-stage approach with repeated indicators in the first stage while all other constructs are present in order to generate the latent variable scores for stage two) work too?

Looking forward to your kind reply. Thanks a lot in advance!
jmbecker
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Re: HTMT necessary? Value >1 with Type II construct

Post by jmbecker »

You are raising an important question. However, I don't have a definite answer.

There are two aspects of the discriminant validity problem in higher-order construct (and I think you have already named them both): Conceptual unity and multicollinearity problems.

Lower-order dimensions are part of a more general concept. Hence, it is expected that dimensions are not highly discriminating. Otherwise, it would not make sense to put them under a general concept.
However, as this is definitely true for reflective higher-order constructs, this bears some problems for formative higher-order constructs. For formative measures, the items usually should not highly correlate as it would indicate some sort of redundancy, while we want to have unique aspects of the concept. At the same time the items should have some conceptual unity as they belong to the same concept and therefore might be similar.
Lack of discriminant validity of the lower-order dimensions indicates that the "items" of the higher-order formative model are redundant (more or less the same). Therefore, lack of discriminant validity of the lower-order components (dimensions) is a problem in formative higher-order constructs. You will at least have multicollinearity problems within your model, because your items will be highly correlated.
If you have lack of discriminant validity you might rethink your operationalization as formative and should consider reflective (if theoretically plausible). Sometimes empirical evidence makes us rethink design decisions and this leads to improvements in the theory (dimensions are in fact not different but very closely related and thus reflective and not formative).
Dr. Jan-Michael Becker, BI Norwegian Business School, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
SHU
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Re: HTMT necessary? Value >1 with Type II construct

Post by SHU »

Dear Jan, thank your very much for your reply and recommendation! I really appreciate your timely and detailed answer.

I agree on your explanation regarding the characteristics of second-order formative constructs and I would like to add some additional thoughts to this "hot topic": One of the decision rules whether to specify a model as formative or reflective is that formative indicators need not be interchangeable, but correlation among formative indicators may be possible (Podsakoff, Mackenzie & Jarvis, 2003; Wilcox et al., 2008). As far as I understood the argumentation in literature, the underlying problem of multicollinearity within formative constructs stems from rather "methodological/technical issues" as weighting coefficients become less reliable as they are based on multiple regression (and not from the concept of formative constructs itself).

Further, I found the following paragraph in Diamantopoulos and Winklhofer (2001, p. 274): "If multicollinearity is a serious problem and the study's main concern is the explanation of structural model variance, a formative speculation may still be used, but interpretation should be based on loadings (as in canonical correlation analysis) rather than regression weights (ys); procedures for doing this are described by Bagozzi, Fornell, and Larcker (1981).“

Bagozzi, R. P., Fornell, C., & Larcker, D. F. (1981). Canonical correlation analysis as a special case of a structural relations model. Multivariate Behavioral Research, 16(4), 437-454.

I am not sure if someone has already applied this procedure (and if it has revealed a satisfying solution). What do you think about it as another option to handle multicollinearity in formative construct?

Eliminating items (Bollen & Lennox, 1991; Diamantopoulos & Winklhofer, 2001) and creating an index (Albers & Hildebrandt, 2006; Wilcox et al., 2008) would be other options to reduce multicollinearity, but it may also distort the initial idea of the construct. Thus, the suggestion of Diamantopoulos and Winklhofer sounds quite tempting to overcome the problem anchored in the regression weights.

Also, I agree to your recommendation that rethinking the second-order constructs based on the empirical evidence present may be worth considering as it has the potential to detect an advanced concept of the latent variable (at least based on the specific data set).

Bests, SHU
jmbecker
SmartPLS Developer
Posts: 1282
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

Re: HTMT necessary? Value >1 with Type II construct

Post by jmbecker »

A quick answer to your thoughts:
1) PLS is very similar to canonical correlation analysis. I would doubt that such a procedure adds any value.
2) PLS path coefficients are very robust, when collinearity is present in a formative construct. It is indeed only a problem for estimating the weights within the formative model. If you want to focus only on the path coefficients, then multicollinearity in your formative measurement model is not a problem.
However, in my opinion, multicollinearity in a formative measurement model usually indicates some problem in the measurement design of the formative construct.
Dr. Jan-Michael Becker, BI Norwegian Business School, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
SHU
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Posts: 10
Joined: Tue Jan 03, 2017 5:58 pm
Real name and title: Susanne Hügel
Location: Wiesbaden (Germany)

Re: HTMT necessary? Value >1 with Type II construct

Post by SHU »

Thanks a lot for your opinion!

It has been very helpful for deciding on the next steps of the data analysis:
after merging the three highly correlated subconstructs (of which literature says that they somehow indirectly affect each other) to one more general construct leads to good VIF values (≤ 1.69) in the formative construct (now consisting of three except of five dimensions). Also, discriminant validity is established between the second-order construct and all other dependend variables (between the new three subconstructs it is still above 0.9, but it's acceptable due to the reasoning mentioned above). Nice, thx again!
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