Moderation approach 1st order reflective 2nd order formative

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stephan.kramer
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Moderation approach 1st order reflective 2nd order formative

Post by stephan.kramer »

Hi everybody,

I am struggling with a tough question: I have a second order construct where the first level (=indicators) is measured reflective, and the second level is formative (three independent phases building one composite measure). I modelled this with the repeated indicator approach. I am assuming a moderation effect of this second-order variable with another reflective one.

My BIG question now is whether you can model this interaction effect with a product-indicator-approach or whether you have to use the two-step approach? I am not sure who to handle this situation because on the first level my indicators are reflective, but on the other hand the second level is formative (and because these dimensions are quite independent from each other, the indicator loadings from the repeated indicator approach on the top-level are quite low).

The problem is that I am losing statistical power when using 2-step, turning some of my interaction effects insignificant :(

Any answers would be highly appreciated!!!!

Thanks & best regards,

Stephan
christian.nitzl
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Post by christian.nitzl »

Hey Stephan

Henseler and Chin are arguing that the product indicator approach is only for reflective variable applicable, because for formative indicators are not assumed to reflect the same underlying construct. Therefore the product indicator between two sets of formative indicators will not necessarily tap into the same underlying interaction effect. If you follow the argumentation of Henseler and Chin, you have to use the two-stage approach for your model. In the mentioned article two more approaches are presented (hyprid approach and orthogonalizing approach). Maybe one of this both will help you, but I am not sure.

Here comes the cited article:
Henseler, J./Chin, W. (2010): A Comparison of Approaches for the Analysis of Interaction Effects Between Latent Variables Using Partial Least Squares Path Modeling, in: Structural Equation Modeling: A Multidisciplinary Journal, Vol. 17, No. 1, S. 82-109.

Best regards,

Christian
stephan.kramer
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Post by stephan.kramer »

Hi Christian,

Thanks, I know the article and the argumentation. But this was not my question because Henseler and Chin argue for formative indicators and they do not mention second order constructs. However, as outlined, I have reflective indicators and a formative second order (please note that on the second order, the individual reflective indicators of the formative dimensions are connected to the construct through the repeated indicator approach). Thus, the question still remains.

But anyway, thanks for sharing your thoughts with me!!! If anybody has another opinion about my problem, I would be very happy.

Best regards,

Stephan
christian.nitzl
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Post by christian.nitzl »

Hey Stephan,

I recognized that your question is how to handle a second order construct typ II as moderation variable. In my opinion the used procedure to test the effect of a moderator should nevertheless be the same. The repeated use of your reflective construct for a second order construct is only for technical matters. Therefore I would calculate the LV scores for the first order construct with the procedure of wold and thereafter I would take these scores as measurement for my formative second order construct. Is that not the way how you handle that problem? I really ask for my own interest, how you handle a second order construct as moderator.

But I am with you; maybe there is a better procedure to test it.

Kind regards,

Christian
stephan.kramer
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Post by stephan.kramer »

Hi Christian,

Yes, I tend to agree with your argumentation. It was also my first thought that the 2nd order formative dimensions do not necessarily covariate and thus, the reflective indicators of these dimensions do not tap on the same underlying construct (and I tried 2-stage, but its downside is that you lose statistical power which in my case turns the interaction insignificant). BUT, as I wrote, I do not really know for sure and there is nothing in the literature to draw upon. That's why I was asking and maybe if Bido or anybody else knows something please give us a hint.

In general it's a pitty that when models are becoming a little bit more complext than just the usual mediation or 'standard'-moderation, there is just so few established knowledge about PLS that is also based on solid literature... :(

Kind regards, Stephan
jmbecker
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Post by jmbecker »

Hi,
just to comment on the statistical power issue: In the Henseler and Chin Paper the Two-Stage approach is recommended for situations in which we are interested in the significance of the interaction, because it has a high level of statistical power.
Now you’re finding the interaction insignificant with the Two-Stage approach which seems to be more appropriate from the methodological view as you have a formative second order construct (I would agree with Christian at this point); so maybe the interaction is simply not significant??
I find it hard to follow the argument, that the two-stage approach reduces statistical power, because it is actually known for high statistical power.
stephan.kramer
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Post by stephan.kramer »

Hi,

Uf, you're right! Looking up the literature again confirms your claim. Sorry for the confusion! Well in this case I guess it is at it is and I will have to think about a theoretical refinement of my model.

Thank you!!!

Best, Stephan
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