latent interaction question(s)/ moderation analysis

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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floriank
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latent interaction question(s)/ moderation analysis

Post by floriank »

I am estimating a model with a continuous moderator using SmartPLS using the product-indicator approach and when I tried each of the 3 options for generation the interaction terms (mean-center, original metric, standardization) and I found that while the estimates for the interaction effect are the same for the mean-centering and standardization option, they are different for the original metric (original indicator values) option. Now, I understand of course that the path coefficients for the simple effects (from independent variable to outcome variable and from moderator to outcome variable) should/can be different, the path coefficient for the interaction effect should always be the same. Can anyone explain to me why this should be different in (Smart)PLS? BTW, this happens whether I use the data metric option "original" or "mean=0, variance=1" in the settings for the PLS algorithm. Or does PLS standardize the solutions in the end anyways and that`s why the estimates differ?

I also have some more general as well as one more specific questions:
1) it is inappropriate to standardize the coefficients for an interaction term and this is why in multiple regression we always only look at the unstandardized results; but PLS seems to produce only standardized coefficients. As far as I can tell, Henseler and Chin 2010 in Structural Equation Modeling is the only paper to ever mention this problem in PLS.
a) are there any more recent papers on interaction effects/ moderation in PLS?
b) is there any PLS software package that deals with this problem? (e.g. by applying the adjustment described in Henseler and Chin 2010)?

2) mean-centering is sometimes helpful to be able to interpret the simple effects at meaningful values of the moderator; but sometimes you may want to use other values than the mean. I guess you would then have to create the centered indicator variables manually and then read them into your PLS software. I`d be curious to see any published examples, if there are any.

3) related to 2), testing for the simple effects at just one value (spotlight test) often does not reveal a complete picture. To get a more complete picture, we test for reasons of significance (floodlight tests or Johnson-Neyman tests) in multiple regression. Again, I assume one would have to do this manually in PLS, but I`d be curious to see examples, if this has ever been done in a PLS context.

4) In the Hair et al. Primer on PLS-SEM (Sage, 2013), page 260 it says: "...one needs to mean-center the moderator variable. This is done by subtracting the latent variable`s mean from each observation".
I fail to understand this. For the product-indicator approach, we are centering the indicator variables before multiplication not the latent scores, right? And for the 2-stage-approach, centering doesn`t seem to be necessary (because the latent scores are standardized anyway, I assume, even though the book doesn`t offer an explanation). Or did I miss anything?

Thank you,


Florian
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