Type II Second-Order Factor Model Questions

Questions about the implementation and application of the PLS-SEM method, that are not related to the usage of the SmartPLS software.
lzelazny
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Type II Second-Order Factor Model Questions

Post by lzelazny »

Based on my theory I have a type II model (reflective first-order LVs with formative second-order LVs). Some of the second order factors are exogenous and some are endogenous. The structural model mostly contains links between second order factors. This structure leads to my questions. Any references you can suggest to support your suggestions would be greatly appreciated.

I realize that if I test the entire model as is, the paths leading to an endogenous 2nd order LV will most likely be insignificant and the R2 of the endogenous 2nd order LV will be approximately 1.0 due to the variance being explained by the formative nature of the construct.

Q1) My thought to test the structural model with the paths between the 2nd order factors was to treat the 2nd order factors as 1st order factors and use calculated LV scores for the 1st order factors as indicator items. Is this ok?

Q2) I assume the calculated scores would be connected to the 2nd order LVs in mode B. Is this correct?

Based on my research I believe that there are three ways to create LV scores for my first order LVs to use as indicator items for my second order LVs: 1) factor analysis, 2) create a composite (say the mean of the items), or 3) use PLS to create LV scores.

Q3) I was planning on using the mean of the items to create my LV scores. However, if I decided to let PLS create the LV scores, how is that done?

Q4) How do I test the measurement model? Can I test the measurement model with both the 1st order and 2nd order LVs or do I only test the measurement model with the structure from Q1?

Note: I didn’t consider the repeating indicators approach since I do not have equal number of indicator items for the first-order LVs.

Thank you in advance.
mw025134
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in addition

Post by mw025134 »

Dear Expert,

This is a good question and similar to what I have in mind, could you also please explain what happen if we have a third order formative construct.

I have a similar problem:
first order I guess should be reflective, by reflective I mean made from three statement that represent it and by taking one of the statement it will not effect the first order construct.

now this first order construct feed in to a formtive second order construct.
How do we test its validity and evaluate the contribution of the first order construct.

Then what happend if this 2nd order construct is actually part of a third order formative construct. How do we test its validity and evaluate the contribution of the third order formative construct.

of course the third order formative construct is considered to be independent variable that is tested against the dependent variable (LV)

Many thanks for your help.
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Re: Type II Second-Order Factor Model Questions

Post by saddas »

lzelazny wrote:Based on my theory I have a type II model (reflective first-order LVs with formative second-order LVs). Some of the second order factors are exogenous and some are endogenous. The structural model mostly contains links between second order factors. This structure leads to my questions. Any references you can suggest to support your suggestions would be greatly appreciated.

I realize that if I test the entire model as is, the paths leading to an endogenous 2nd order LV will most likely be insignificant and the R2 of the endogenous 2nd order LV will be approximately 1.0 due to the variance being explained by the formative nature of the construct.

Q1) My thought to test the structural model with the paths between the 2nd order factors was to treat the 2nd order factors as 1st order factors and use calculated LV scores for the 1st order factors as indicator items. Is this ok?

Q2) I assume the calculated scores would be connected to the 2nd order LVs in mode B. Is this correct?

Based on my research I believe that there are three ways to create LV scores for my first order LVs to use as indicator items for my second order LVs: 1) factor analysis, 2) create a composite (say the mean of the items), or 3) use PLS to create LV scores.

Q3) I was planning on using the mean of the items to create my LV scores. However, if I decided to let PLS create the LV scores, how is that done?

Q4) How do I test the measurement model? Can I test the measurement model with both the 1st order and 2nd order LVs or do I only test the measurement model with the structure from Q1?

Note: I didn’t consider the repeating indicators approach since I do not have equal number of indicator items for the first-order LVs.

Thank you in advance.

Answer to Q1) Yes

Answer to Q2) Yes, the LV scores should connect to the second order factors (which now become first-order in the second stage of the 2-step approach) in mode B.

Answer to Q3) To estimate the LV scores via PLS, you need to run the PLS algorithm in the first stage by modeling your Type II construct and other constructs in the model. For the second-order construct you can model it using the repeated indicator approach in the first stage (to address the unequal number of indicator issue, one idea is to use item parceling). After running the algorithm, you will find the "Latent variable scores" in the output report under PLS - Calculation results. In the second stage, use those scores as the indicators for all constructs and run the algorithm again to test the structural model.

Answer to Q4) You can test the measurement model in stage 1 by inspecting the reliability and convergent/ discriminant validity for the reflective constructs. For the formative constructs, you can examine the weights and test for multicollinearity.
lailakasem
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Clarification Please

Post by lailakasem »

I just have a question about the repeated indicator approach? In the first stage, do I only connect the first order constructs to the second order construct, i.e. without including the remaining constructs in the model?

Thanks
Laila
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Post by saddas »

I think you should include the other constructs in the model as well so that you obtain their scores which you subsequently use as indicators in the second step.
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Post by lailakasem »

Thanks Shamel, in this case do I need to go to the second step? In other words, can I keep the first order constructs (not indicators) and report the results?

Thanks,
Laila
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Hengkov
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Post by Hengkov »

Hi Laila,
Stage 1: connect all construct in model (before evaluation outer model) and save latent variable score.
Stage 2: input LVS with mode B and evaluation inner model.
You report analysis Stage 1 and 2. :-)
Regards,
Hengky
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Post by samaro »

How do I check for multicolinearity between the 1st order constructs of a 2nd order formative construct? I understand how to do this between indicators, but how do you do it for Latent Variables(constructs)? Thank You!
Suzanne Amaro
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Post by Hengkov »

Hi,

Using WarpPLS very easy for it or compute by hand 1/1-R-square.

Regards,
Hengky
jwanuis
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Additional Type II question

Post by jwanuis »

Thanks for the informative replies on this topic. I do have two questions considering the repeated approach method I hope you're willing to answer.

1) I have theorized a Type II model with two first-order constructs using reflective indicators. To calculate the LVS for the second-order construct, I use the same indicators as for the first-order construct. Should these indicators be of a formative or reflective nature in order to obtain the correct LVS?

2) Using this LVS in mode B (formative) in the second stage I can estimate the complete model. Is that correct?

Thanks!
samaro
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Post by samaro »

If your 2nd order construct is reflective, formative, than this paper

Hierarchical Latent Variable Models in PLS-SEM: Guidelines for Using Reflective-Formative Type Models
Jan-Michael Becker, Kristina Klein, Martin Wetzels

reccomends considereing the repeated indicators as mode B.

Hope this helps!
Suzanne Amaro
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Post by fnkmstr »

Hengkov wrote:Hi Laila,
Stage 1: connect all construct in model (before evaluation outer model) and save latent variable score.
Should I use original or standardized (mean=0, var=1) data metric to calculate the lvs?

What is the standard reference for this 2nd order model approach?

Thank you very much.
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Hengkov
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Post by Hengkov »

Hi,
Used Mean 0 Var 1.
For reference 2nd order approach, check:

Ringle et al. 2012 in MISQ (see appendix).

Kock, N. 2012. User manual WarpPLS.

Latan, H., and Ghozali, I. 2013. Partial Least Squares: Concept Application Path Modeling with XLSTAT (www.pls-pm.blogspot.com).

Regards,
Hengky
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Post by bwilson »

samaro wrote:If your 2nd order construct is reflective, formative, than this paper

Hierarchical Latent Variable Models in PLS-SEM: Guidelines for Using Reflective-Formative Type Models Jan-Michael Becker, Kristina Klein, Martin Wetzels
This is a good suggestion.
For type I contrast see:
Handbook of Partial Least Squares. http://www.springer.com/statistics/comp ... 40-32825-4

Chapter by Wilson.
Using PLS to Investigate Interaction Effects Between Higher Order Branding Constructs.

Best regards

Brad
Bradley Wilson. Ph.D.
Senior Lecturer in Advertising.
RMIT University.
School of Media and Communication.
GPO Box 2476V
Location. 9.5.20
Melbourne. Victoria.
Australia.

SEE FOR PUBLICATIONS
www.rmit.edu.au/staff/bradleywilson
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Re: Type II Second-Order Factor Model Questions

Post by bradley7680 »

this chapter and my thesis work which is extensive features on Researchgate

best regards brad
Bradley Wilson. Ph.D. Senior Lecturer in Advertising. School of Media and Communication. RMIT University. Melbourne, Australia.
SEE: http://www.researchgate.net/profile/Bradley_Wilson2 http://scholar.google.com.au/citations? ... AAAJ&hl=en
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