Hi @ all,
I am still struggling with the question, whether I should apply the PLS-approach or stick to a "regular" linear multiple regression...
My model consists of only 1 DV and about 12 IV (I know its a lot for a sample of just n=120). I want to test the direct effects and some interaction effects, which lead to an even more critical ratio sample size / IV. I don't have any mediating effects.
My IV are constructs in the way that I measured them with multiple items (most of the time 3 items each). The majority of them is reflective, but some are formative.
As suggested in this forum, I have computed two models to compare the results: one in smartPLS and one as a multiple regression. For the latter, I used the average of the indicators for each IV.
The results are almost comparable and I also tested the prerequisites of a multiple regression (homoscedasticity, normality of residuals, multicollinearity, etc.). The results seem to be okay, although I found some evidence of multicollinearity (KI max = 38, but VIF <2,6 and variance proportion seems okay). I also get comparable results for interaction effects between both methods.
Now comes finally my question:
What are the main reasons, why I should use PLS instead of multiple regression?
I see the following points here:
1) I don't have to use the average of the items as indicator, instead I have a simultaneously computed measurement model. So I could at least evaluate the importance of the single formative indicators, which I can't do in regression. On the other hand, my formative constructs have some problems with multicollinearity so that interpretation of single indicators is maybe not reliable.
2) Is it true the PLS can handle multicollinearity better then regression? If I copy the LV scores from smartPLS into SPSS, the KI is much better (KI max =5 instead of 37 for multiple regression). Is this a good argument for PLS?
3) Since PLS is regarded as "soft modeling", wouldn't it be better to use multiple regression, where I even (fairly) fulfill all the "hard" assumptions?
I know, I could just apply both methods and compare the results in my thesis, but then one would certainly ask whether I could not decide on the method... Additionally, I kind of fancy PLS and want to use it in future and therefore understand what I am doing...
Sorry for the long entry. I would be glad, if somebody could post his or her opinion on this.
cheers,
Carsten
P.S. One last question: Would you go for group comparisons with 12 IV and n=120/2=60? Probably not, right? (measurement model invariance is not given I think. ..)
PLS vs. multiple Regression
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Diogenes
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Hi Carsten,
About your points:
1) Ok, we could estimate the measurement and the structural model simultaneously.
2) The PLS algorithm is based in regressions and correlations, in your model, when PLS compute the structural step, a multiple regression was used, than the problem with multicollinearity remains.
3) Yes, you are right, and SmartPLS doesn’t compute multicollinearity index.
Some ideas:
a) With 12 IV multicollinearity is almost sure. See if some of these IV have correlations greater than .4 and if it makes sense to use them as 1st order LV of a 2nd order LV, is there some interpretation for a group of IV?
This idea is similar to principal components regression (see COHEN, J.; COHEN, P.; WEST, S. G.; AIKEN, L. S. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. 3rd Ed. New Jersey: Lawrence Erlbaum Associates, Publishers, 2003. p.428-429)
Another advantage is that we will have less IV, and eventually, a higher power.
b) See viewtopic.php?t=507&highlight=vinzi
Tanagra and Vinzi ppt.
Best regards,
Bido
About the last question: You should run, but if no difference were significant, could be a power issue.
About your points:
1) Ok, we could estimate the measurement and the structural model simultaneously.
2) The PLS algorithm is based in regressions and correlations, in your model, when PLS compute the structural step, a multiple regression was used, than the problem with multicollinearity remains.
3) Yes, you are right, and SmartPLS doesn’t compute multicollinearity index.
Some ideas:
a) With 12 IV multicollinearity is almost sure. See if some of these IV have correlations greater than .4 and if it makes sense to use them as 1st order LV of a 2nd order LV, is there some interpretation for a group of IV?
This idea is similar to principal components regression (see COHEN, J.; COHEN, P.; WEST, S. G.; AIKEN, L. S. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. 3rd Ed. New Jersey: Lawrence Erlbaum Associates, Publishers, 2003. p.428-429)
Another advantage is that we will have less IV, and eventually, a higher power.
b) See viewtopic.php?t=507&highlight=vinzi
Tanagra and Vinzi ppt.
Best regards,
Bido
About the last question: You should run, but if no difference were significant, could be a power issue.
Dear Bido, thank you for your suggestions,
well, I maybe could group some of the IV: I am examining joint venture performance and my IV are different critical factors, which I theoretically could group to different stages of the venture or to different aspects like partner-related IV, contract-related factors, etc.
The problem is, that I want to examine interaction effects, which would make sense only on 1st order level. But I will certainly think about that again. A more complex model with 2nd order LV would give me more reason to favour PLS over regression and as you added give me more power in the model, which in turn would be good for group comparisons.
best regards,
Carsten
well, I maybe could group some of the IV: I am examining joint venture performance and my IV are different critical factors, which I theoretically could group to different stages of the venture or to different aspects like partner-related IV, contract-related factors, etc.
The problem is, that I want to examine interaction effects, which would make sense only on 1st order level. But I will certainly think about that again. A more complex model with 2nd order LV would give me more reason to favour PLS over regression and as you added give me more power in the model, which in turn would be good for group comparisons.
best regards,
Carsten