How do model second order constructs in PLS

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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JKUB
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How do model second order constructs in PLS

Post by JKUB »

Does anyonw know how to model a formative first order construct that is defined by second order formative components/ dimensions?
While the latter has indicators the former construct does not; ie the former is only defined by the second order constructs. Apparently this is not possible in PLS, since all constructs require a set of indicators. Is there a workaround?

Many thx in advance.
viswadatta
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sexond order constructs

Post by viswadatta »

Second order constructs are done in smartPLS using repeated approach. Reassign all the indicators given to the first order constructs to the second order construct. This way you will have the same indicator twice in the diagram. Proceed with the analysis in the usual way. This approach was suggested by Wold in 1982. The forum has a lot of posts on this topic. If you want to try out without repeating indicators, try another software -visual PLS, but it has some bugs.
JKUB
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second order constructs

Post by JKUB »

Ok. Thx.
Another question: how do you assess the quality of the 2nd order factor? Should all indicator weights be sign. (bootstrap-based t-stats) and the AVE above .5, independent of a high R²? What if this is only the case for the 1st order factors? Does this imply that a second order model is not applicable?
m.stolper
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Same problem

Post by m.stolper »

I have the same problem, are the quality criteria for a reflective/formative second order construct the same as for a reflective/formative first order construct? Aren´t problems with the AVE a logical consequence if indicators are used twice?
chrisblocker
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Instable Estimates in 2nd order model based on # LVs/items

Post by chrisblocker »

I'm working with a 2nd order / 3rd order model (using repeated indicators) where I've got 6 reflective LVs leading to a 2nd order Benefits LV, and 3 reflective LVs leading to a 2nd order Sacrifices LV, both which subsequently lead to a 3rd order Customer Value LV. Measurement is strong.

Problem I'm having is that 2nd order to 3rd order paths are highly dependent and vary significantly based upon the number of LV's/items being used to measure 2nd order LVs when I do sensitivity analysis by adding/removing LVs.

This makes sense from a summative scale standpoint.

I know I've heard that these kinds of models work best when there are 3 LVs on each side (or at least equivalent), but doing so would basically force me to remove some important new constructs or reduce items per construct on the benefit side to 1 or 2.

Any suggestions or literature on this model issue that seems to drive theoretical concessions?

Many thanks!
CPB
viswadatta
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quality factors

Post by viswadatta »

First, second order , third order, etc factors all are assessed in the same way ave, alpha, et al
JKUB
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Higher order factors

Post by JKUB »

Many thx for the feedback.
I have now analyzed two approaches: the repeated indicators approach and the LV score method. My results show that the LV method is superior, more reliable estimates and the quality indicators of the higher factor (AVE, CR, Cronbach, loadings, discriminant validity...) is also superior.

Has anyone obtained similar results or is aware of a reference in the literature?
soumya.ray
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Post by soumya.ray »

I have been trying to create a model where the second order representation of a factor co-exists with its first order elements in a larger model. The reason I want this is that I would like to study the antecedents of the 1st order factors, but would like to study the consequents of the 2nd order factor. I have used the repeating indicator approach suggested earlier, where the 2nd order factor uses ALL the manifest variables of the 1st order factors, and there exist paths from the 1st order factors to the 2nd order factor (I wanted a formative 2nd order factor).

However, the problem that occurs is that while the paths antecedent to the 1st order factors and the paths consequent to the 2nd order factor are all estimated well, the paths from the 1st order factors to the 2nd order factor are not. I believe this is a case of multicollinearity as the 1st order factors are likely quite highly correlated with each other. Reversing the paths between 1st and 2nd order factors does not produce better results.

My question is as follows:

1. Am I trying something infeasible in PLS modelling?

2. If not, is there a better approach to modeling 1st order factors and their 2nd order factor with a larger model? If so, can you provide a little bit of detail as to how to implement it? Particularly,

thank you!
viswadatta
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second order factors

Post by viswadatta »

Yes there is. Find out the factor scores of the first order constructs. Add these scores to the dataset. Redo the model using the scores as indicators for the sec order construct that now becomes a first order construct. Run your model. YOu should not have any problem now.
soumya.ray
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Post by soumya.ray »

Thank you Vivek - I just tried this and your suggestion works very well. Is this approach, representing 2nd order factors as 1st order factors with latent scores as manifest variables, a preferred solution over using the repeated measures approach?

The only thing that is missing using the latent scores approach are the first-order sub-factors which I would like to also include in the model.

To illustrate: lets say that FAC1 FAC2 and FAC3 are all dimensions of a higher order factor called FAC. Using the repeated measures approach, all four of these factors (three 1st order and one 2nd order) are in my model, which is ideal because I want to study the antecedents of FAC1-FAC3 and also make exogenous paths out of the parent FAC factor. However, the paths from FAC1 FAC2 and FAC3 to the parent FAC factor suffer from multicollinearity problems.

Using the latent scores approach that Vivek suggested allows me to keep the FAC factor with 3 manifest variables (the latent scores of its 3 subfactors), but then I lose the FAC1-FAC3 factors from the model. Is there a way to keep those three subfactors in the model (without suffering the multicollinearity problem) or am I just better off doing this in two steps: one model to study the antecedents of FAC1-FAC3, and another model to study the paths from FAC?

thank you for the advice!
viswadatta
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multicolinearity

Post by viswadatta »

Multicolinearity can be tested using discriminant validity check, if there is no discriminant validity, then combine the constructs into one and redo your analysis
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