Confusiing Post on Problematic indicator weights

[AndrewG]

Hi, I'm finding this post confusing: "Formative constructs with problematic indicator weights".

The various contributions seem to be saying that all indicators in PLS are formative, whether the outer, "measurement" model is specified as being inner or outer directed. And that ALL latent variables in PLS are weighted sums of their indicators, no matter how the weights are determined. And that the problem is really one of how we diagram PLS models, not a conceptual problem.
The advice seems to be that to eliminate or lessen the problem of negative weights in formative models, all you have to do is reverse the arrows in the diagram. However, when this is done, the magnitude of many of the path coefficients changes markedly. Can someone please explain why this occurs? I get the impression from the post that reflective models or a combination of reflective and formative models can't be effectively analysed in Smart-PLS. Can someone also please confirm this?

[mariaemaus]

Hi Andrew,

Did you get a reply at all, or did you find the answer yourself? I constructed a 2nd order model fully formatively measured in which I repeated the indicators for the 2nd order construct, and I came across the same advice (and outcome). On top of that, I have negative negative loadings, no matter how I construct the model (in mode A or B).

Kind regards,
Magdelijn

[AndrewG]

Hi Magdelijn,

I didn't receive a response but I read the Temme, Kreis and Hildebrandt (2006) article (p.13-15) which mentions that the SPAD-PLS, and PLS-GUI software programs are the only PLS software that don't have this negative signs problem because they use different sets of starting values to the others (Also VisualPLS but it has another issue). It might be impolitic to say this on this forum, but I think XL-STAT is the latest version of SPAD and I don't have the same negative coefficient paths problem with XL-STAT (with formative indicators). However, Temme et al also report that SPAD-PLS does not consistently produce the lowest t-ratios. I get the impression that each software program has its pros and cons. e.g. a big pro with SmartPLS is the FIMIX function, and a big plus of WarpPLS is its nonlinear capability. Therefore, I think we probably need to become capable users of several PLS programs.
cheers
Andrew

[sdrucker]

Hi Magdelijn,

I didn't receive a response but I read the Temme, Kreis and Hildebrandt (2006) article (p.13-15) which mentions that the SPAD-PLS, and PLS-GUI software programs are the only PLS software that don't have this negative signs problem because they use different sets of starting values to the others (Also VisualPLS but it has another issue). It might be impolitic to say this on this forum, but I think XL-STAT is the latest version of SPAD and I don't have the same negative coefficient paths problem with XL-STAT (with formative indicators). However, Temme et al also report that SPAD-PLS does not consistently produce the lowest t-ratios. I get the impression that each software program has its pros and cons. e.g. a big pro with SmartPLS is the FIMIX function, and a big plus of WarpPLS is its nonlinear capability. Therefore, I think we probably need to become capable users of several PLS programs.
cheers
Andrew

Andrew,
I've used both SmartPLS and XLSTAT's PLS-PM, and it's not completely true that the XLSTAT version eliminates the negative coefficient weight issue with formative indicators of the LV. Yes, you can use Mode PLS, which is essentially a PLS regression for the MVs defining the LV rather than an OLS regression, for obtaining the factor scoring weights of that latent variable. This can be a middle ground between a "reflective" model (which is the case where you select one component for estimating the LV in question with Mode PLS) and the "formative" model (where there are as many components as MVs for that LV). Whether such a middle ground is theoretically justified is a different question.

However, while Mode PLS it can allieviate some aspects of severe collinearity within the LV, it does NOT eliminate them. I've used Mode PLS a few times, and it really depends on the dimensionality of the data as to whether it makes a practical difference or not. You still have to be careful that you're not retaining components that are simply adding in aspects of MV collinearity, manifesting itself as discrimination in the scoring weights.

The XLSTAT folks recommend inspecting the eigenvalue breakdown of the components within each LV to see if multiple dimensions within the scoring of the LVs are justified or not, based on the notion of retaining components with eigenvalues>1. In practice, they're actually quite conservative about it, meaning that a reflective model fits the MV/LV relationship far more on survey data than occasions where Mode PLS allows you to "have your cake and eat it too" with the indicators. At least that's what Professor Vinzi et al recommended at their Paris seminar earlier this year.

What I think you're seeing in XLSTAT is Mode PLS with a single component retained in defining a particular LV, on the measurement model side, which really is a reflective model, but with the arrows in the "wrong" direction. And if that's the case, how the arrows are drawn is subjective. Whether you have a Mode PLS model of MVs to a particular LV that has single component for that part of the measurement model, or a reflective model for the MVs to that LV, the results are the same.

Also, I will mention that even if you implement the Mode PLS approach on the strutural model with a single component (dimension), you won't neccessarily have a model that forces the path relationships in the inner model to be exactly in the same direction as you would expect from bivariate correlations. At least not in the data I've seen, in models that have more than a single series of path relationships predicted (i.e. only one engogenous LV).

[AndrewG]

Hi Stuart,
thanks for your informative post.
Actually I used OLS, with treatment of the MVs : raw MV.