latent variable correlations - test of hypotheses

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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Compano
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latent variable correlations - test of hypotheses

Post by Compano »

Dear users,

I have got a big problem at the end of my thesis. I would be very thankful if anybody might help me...

I want to verify some hypotheses about correlations of latent variables. In my specific case there are three latent variables. One of them is measured reflective, the others are formative constructs. The output of PLS gives me information about the absolute correlations of the latent variables. 2 question rise up:

a) I'am searching for an information which helps me to verify the hypotheses. Is there any possibility to test them with a statistical proof?

b) Is there a possibility to model correlations in PLS? When I try to model a correlation between to latent constructs, I get a notice "There must be valid path model for calculation".

Thanks a lot for your help!

Michael
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Post by phenomenon »

Hello Micheal,

did you correctly import your data into PLS? (.csv file, variable names in the first row, only numbers starting with the first column).
You use PLS to test your hypotheses if there are complex relations between the variables. (actually PLS is predicition oriented, Lisrel would be even better suited for complex relations, but it's not a freeware and it needs much bigger sample sizes than a PLS model) If there is only one dependent variable, you can do a simple multiple regression in Spss or Excel.
You have to evaluate the measurement model as well as the structural model (your hypothesized correlations). The path coefficients in PLS are the same as regression coefficients. With the bootstrap method you can calculate t-values for you paths.
See this forum and the working papers by Ringle on the measures that help you determine how well your model fits the data. The site by Prof. W.Chin should also be of good use (just google for "chin pls" )

I hope this helps
Philipp
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Post by Compano »

Hello Philipp,

thanks for your answer. Maybe I have´t been detailled enough... ;-)

Mostly I use PLS for my structural model to interprete different paths from some exogenous vaiables to endogenous variables. This is one side of my thesis and this works already well including the interpretation (weights, loadings, t-test, etc.)

In addition to that I want to check some correlations as I described in my first posting. I have to check three of my endogenous variables (formative and reflective) if they are correlated and if the correlation is significant. Maybei anybody has got an idea...

Thanks a lot

Michael
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Diogenes
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Post by Diogenes »

Hi Michael,

you could copy/paste the LV scores to SPSS and compute the correlations and significances there.
Or to use a resampling software http://www.uvm.edu/~dhowell/StatPages/R ... pling.html
Best regards.
Bido
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Post by Compano »

Hello Prof. Diogenes,

thanks for your answer.

Copy and paste doesn't make sense, does it? As I know, it is only possible to test correlations beetween two variables/indicators, either? Also the link, you have pasted, seems to analyse the correlation beetween two indicators.

In my specific case I have to test the correlation beetween two latent constructs (with several indicators) and find an answer, if the correlation is significant or not.

Best wishes

Michael
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Diogenes
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Post by Diogenes »

Hi Michael,
in the output you have
"Latent Variable Scores"
Then you could copy/paste these scores to compute correlation between LVs.
Best regards.
Bido
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Post by Compano »

Hello Bido,

thanks again for your answer. Now I see your point! It works well.

Best wishes

Michael
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path correlations

Post by viswadatta »

If you want to check correlation significances between constructs, use spss and check out correlation between factor scores of the constructs.

A hypothesis is an arrow in the diagram. Check it out first.
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Post by Diogenes »

Hi Vivek,
just one last remembering.
For instance, If we have two LV without arrows between them:
- in LISREL will be imposed during the estimation that the partial correlation be zero between them(a constrain);
- in PLS, all LV are correlated, even without arrows (no constrain). This is not tested, for this reason Michael asked us.
Best regards.
Bido
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LV correlations

Post by viswadatta »

True Prof Bido. We check the discriminant validity in LISREL by seeing the increase in chi square value after imposing a correlation of 1 between the constructs.

By the way thanks for all your timely help. I have submitted my dissertation on supply chains.

Regards

Vivek
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