Adding 2nd-order constructs and directional constraints

[sdrucker]

Would it be possible to add the Chin/hierarchical second-order construct approach discussed previously in the forum to the next release of Smart PLS?

It would be extremely useful to have the ability to define a 2nd-order construct explicitly, as a method of accounting for high collinearity among 1st order LVs (using the approach of having all the 1st order indicators included in the 2nd order LV). This would be much easier to work with than having to physically add a set of duplicate indicators to define the second-order construct and then set the path relationships manually. That's not a lot of fun when you have models with, say, 50 indicators.

Another feature that would be useful for model building would be a way to impose boundary constraints on the structural parameters (specifically GT or LT 0), or alternatively to set a path to 0 or some predefined value.

As the cliche goes, I can ask:-).

Thanks,
Stuart Drucker

[swende]

I think, we could do that but it depends on the support of the community. ;)

Actually I don´t have the corresponding literature at my fingertips. Therefore it would be nice, if someone can answer me the following questions. I think, we will be able then, to implement the basic functionality.

1. What´s about the measurement model? Is it relevant, how the first order constructs are measured (formative, reflective)? Must all first order constructs be measured the same way (all reflective, all formative) ?

2. How should the second order construct be measured? Reflective, formative ? Does it depend on the first order construct measurement models?

Another feature that would be useful for model building would be a way to impose boundary constraints on the structural parameters (specifically GT or LT 0), or alternatively to set a path to 0 or some predefined value.

I didn´t get the idea, yet! Can you please provide a more detailed example?

[Diogenes]

Hi Sven,

This artiche is the answer:
JARVIS, Cheryl Burke; MACKENZIE, Scott B.; PODSAKOFF, Philip M. "A critical Review of construct indicators and measurement model misspecification in marketing and consumer research." Journal of Consumer Research, sep. 2003, v. 30, n. 2, p. 199-218.

We could have both: indicators and first order constructs like formative indicators.

The software Visual-PLS (http://www2.kuas.edu.tw/prof/fred/vpls/index.html) has implemented the 2nd order construct, but it still doesn´t run the bootstrat for models with this kind of construct.

Regards,

Bido

[cringle]

Hi,

the article by Jarvis/Mackenzie/Podsakoff ("A critical Review of construct indicators and measurement model misspecification in marketing and consumer research") is a good source. Regarding (so called) 2nd-order-models, it basically describes what Lohmoeller already laid out in 1989. But he actually gives a statistical foundation that such models can be computed with the PLS algorithm:

Mode A (first order) – Mode A (Second Order) – Spread (inner model)
Mode A (first order) – Mode A (Second Order) – Collect (inner model)

Mode B (first order) – Mode B (Second Order) – Spread (inner model)
Mode B (first order) – Mode B (Second Order) – Collect (inner model)

Mode A (first order) – Mode B (Second Order) – Spread (inner model)
Mode A (first order) – Mode B (Second Order) – Collect (inner model)

Mode B (first order) – Mode B (Second Order) – Spread (inner model)
Mode B (first order) – Mode B (Second Order) – Collect (inner model)

So far so good – Lohmoeller provides some confidence that 2nd-order-models can be properly computed with the basic PLS algorithm. That is an important point, because reusing manifest variables is a special case in PLS path modeling.



However here comes my question (might be better discussed the methodology section of this forum):

Since 2nd-oder-models are a special PLS path model that uses manifest variables twice for model-estimation, would it be appropriate to embedd such a model into a larger (standard) PLS model.

I have seen such applications recently, but doubt their appropriateness. Besides, I have not found a reasonable discussion on that matter (using manifest variables for more than one time in 2nd-order models and to embed such model in a “normal” PLS model) in literature. In case that would be appropriate regarding the statistical grounds of PLS path modeling, would it then be accurate to also compute 3rd, 4th and so on order models. How often could manifest variables be used in PLS path models – could a reuse in “standard” model make sense as well?



These are important implications in order to prevent users from a “misuse” of such functionalities - as published more and more often. In my own research, I always estimated 2nd-order-models as “stand-alone-models…

Best
Christian

[e09356]

Hi,

So far so good – Lohmoeller provides some confidence that 2nd-order-models can be properly computed with the basic PLS algorithm. That is an important point, because reusing manifest variables is a special case in PLS path modeling.

However here comes my question (might be better discussed the methodology section of this forum):

Since 2nd-oder-models are a special PLS path model that uses manifest variables twice for model-estimation, would it be appropriate to embedd such a model into a larger (standard) PLS model.

Besides, I have not found a reasonable discussion on that matter (using manifest variables for more than one time in 2nd-order models and to embed such model in a “normal” PLS model) in literature. In case that would be appropriate regarding the statistical grounds of PLS path modeling, would it then be accurate to also compute 3rd, 4th and so on order models. How often could manifest variables be used in PLS path models – could a reuse in “standard” model make sense as well?

These are important implications in order to prevent users from a “misuse” of such functionalities - as published more and more often. In my own research, I always estimated 2nd-order-models as “stand-alone-models…

Christian

Yes the Lohmoller work is a good foundation. The algorithm can definitely handle it. However, I believe further work is needed here too. Little is known about 2nd order models and if authors are to use it at the moment they should either follow the stand-alone model approach only or if they are embedding it within a broader structural model they should note it appropriately within the study limitations and not over state the relevance/importance of their results. This of course is a risky thing to do as you are identifying possible reasons for study rejection but it is only fair to the reader that you are up front about the process and limitations.
There will be more work on this area in the near future.

[bwilson]

Dear all,

I would agree with the discussion on use of hierarchical or repeated indicators approach. Use in isolation if you can...

But if used in a structural model be upfront about it in study limitation.

Newer monte carlo studies may provide more guidance.
Wilson, B. and Henseler, J. (2007), Modeling Reflective Higher-Order Constructs using Three Approaches with PLS Path Modeling: A Monte Carlo Comparison.Thyne, M.; Deans, K. R., and Gnoth, J. in Australian and New Zealand Marketing Academy Conference. Department of Marketing, School of Business. University of Otago. University of Otago., New Zealand.; 791-800.

Wilson, B. (2005), Using PLS to Investigate Interaction Effects Between Two Second Order Constructs: An Applied Marketing Example.Aluja, T.; Casanovas, J.; Esposito Vinzi, V.; Morineau, A., and Tenenhaus, M., Editors. in 4th International Symposium on PLS and Related Methods., Barcelona, Spain. 183-190.

Happy reading.

brad.

[joseba]

Dear Prof. Wilson,

Great! I would like to know your opinion about this:

Could I justify the use of PLS path modeling with a reflective 2nd-order constructs model in a leding journal?

Could I use to do it your recommended references? How do I get them?

Thank you in advance for yor attention.

Best,

- JB

[bwilson]

first article is available on google.

second article is becoming featured in PLS handbook 2008.

I think that these approaches are gaining in reputation in leading journals.

best regards,

brad