mediating & interaction effect, standardization, PLS-Lis

[sandra]

Dear All,

I have the variables X1, X2, and X3 in my modell (all influencing Y). X1 also influences X2 and X3 (mediating effects) and I assume an interaction effect between X2 and X3. (All indicators in my model are reflective.)

1. Since X1 affects X2 and X3 do I also have to include a path from X1 to the interaction variable (X2*X3) in my model?

2. I calculated the model with and without standardizing the X2*X3 indicators with different outcomes.
Do I only need to standardize/center the indicators of my interaction effect (X2*X3) or also the other variables in my model?
And, is standardizing or centering better?
(I have 7 point rating scale indicators)

3. Last question: Since I don't have formative construct and my sample is not small other people (maybe reviewers) could argue that I should use Lisrel instead of PLS.
Is it right to argue, that including an interaction term (product term) in a model would violate the variables' multivariate normal distribution and thus PLS has the advantage of not requiring this when an interaction effect is to be considered? However, people do model interaction effects with lisrel ...?

Many thanks for your help
sandra

[viswadatta]

Though PLS uses small samples, it does not exclude the use of large samples. The greatest use of PLS is that it is non parametris, i.e the variables need not have multivariate normality, homoscedasticity, etc. LISREL and AMOS make firm assumptions about the distribution of the variables used.

LISREL also needs a firmly prevalidated theory to work with, while PLS works on any emerging theory

[Diogenes]

Hi Sandra,

About your 1st question, the answer is yes.
In PLS context it is supposed that all LV´s are correlated, even without arrows between them.
In LISREL context, LVs whithout arrows it´s supposed that the correlation between them is zero (a restriction). How it´s expected that this is not the case, the model will be misspecified and will give bad results (GOF).

About the 3rd question:
Why do you want to use PLS instead of LISREL ?
If the sample is large enough, you could use LISREL with Asymptotic Distribuition-free estimation (ADF) = method WLS.
I was not able to think about a way to justify the use of PLS, instead of LISREL, in this case ;-)


I hope this help.

Bido

[sandra]

Hi Bido and ..., thanks a lot.

Q. 2: In case I wanted to model the interaction effect with PLS: Would I have to standardize the indicators for the interaction variable or could I also do it without standardization? Obviously the outcomes are quite different.
If I use standardized (or centered) indicators, my interaction is not significant. If I use the original indicators (not standardized), the interaction term is (of course) quite big and significant. So which result is the "real" one (I found an interaction effect with the traditional regression approach)???

Q. 3: Thus, would you only use PLS (instead of Lisrel or Amos) if there are specific reasons (like a small sample or formative constructs)?
What is the disadvantage of PLS that one would not use it if one can use Lisrel?

many thanks
sandra

[Diogenes]

Hi,

Q2) See CHIN, Wynne W; MARCOLIN, Barbara L; NEWSTED, Peter R. A partial least squares latent variable modeling approach for measuring interaction effests:... Information Systems Research; v. 14, n. 2, Jun 2003.
p.198 = Standardizing or centering the indicators also allows an easier interpretation...
p.199 = .. helps avoid computational errors by lowering the correlation between the product indicators and their individual components.


3a) CHIN, MARCOLIN, NEWSTED (2003, p.198): There is a known bias in PLS that underestimates the structural effects.


3b) R2 values of endogenous LVs of the component-based SEM techniques (PLS) are smaller than that of the covariance-based SEM techniques (LISREL, EQS).
By HSU, Sheng-Hsun; CHEN, Wun-Hwa; HSIEH, Ming-Jyh. Robustness Testing of PLS, LISREL, EQS and ANN-based SEM for Measuring Customer Satisfaction. Total Quality Management; Vol. 17, No. 3, 355–371, April 2006


3c) The biases in R2 and the regression estimates obtained using the PLS approach are appreciably larger than for those obtained using the IV/2SLS and the SEM approaches.
By THOMAS, D. Roland; LU,Irene R.R.; CEDZYNSKI, Marzena. A Critique of Partial Least Squares, and a Preliminary Assessement of an Alternative Estimation Method. Sprott Letters, Working Papers, 2007. Available in: http://busxt03.carleton.ca/index.php?mo ... rs#Working


3d) Reviwers love the gof indexes ..., but see the first article above (CHIN...) maybe it could give you a new idea.

I hope this help.

Bido

[langmach]

Hi,

I followed the interesting discussion and just wanted to share with you a short paragraph from Jaccard/Turrisi (2003), the litle green booklet, on using standardized coefficients in regression analysis:

"Although it is possible to use standardized coefficients in the analysis of interactions, such coefficients have the potential to lead theorists astray and will not exhibit the regularities we have noted. We generally recommend against their use..." (p. 68)

Please note that there is also an article from Echambadi/Hess (2007) on the value of mean-centering variables in moderating regression.
In their opinion "researchers using moderated regression models should not mean-center in a specious attempt to mititgate collinearity between the linear and the interactions terms. Of course, researchers may wish to mean-center for interpretive purposes and other reasons." (p. 438)

Chris

[coupae]

thanks Chris, this is really interesting.

as to Q2, i checked a number of publications on ISR and MISQ and only few of them mentioned the use of standardization. Having said that, it could be true that they all did standardization since they explicitedly sited Chin-isr paper. So, you'd better do it.

[bwilson]

Dear Sandra,

The number of interaction terms at the item level can quickly turn a simple model into a complex one.

Interactions models usually have distributional problems.
It is better to justify is original indicants have distributional problems prior to creating cross-products.

most people standardize and centre cross-product terms.
Use ZumaStat spss add in. It is brilliant.

I would argue for model complexity and non-normality but you are right it is reviewer dependent. They may want to see it has been attempted with CBSEM approach in endnote etc.

Investigating models with CBSEM method have a look at:
Cortina, Jose M.; Chen, Gilad., and Dunlap, William P. (2001), Testing Interaction Effects in LISREL: Examination and Illustration of Available Procedures. Organizational Research Methods. 4 (4), 324-360.

Good luck.