Hello everyone,
I conducted an experimental study and would like to analyze my data with PLS because of its distribution-free character.
My situation is as follows:
My independent variable (X) was manipulated and consists of three groups, two experimental groups (EG 1 and EG 2) and one control group (CG). The independent variable should affect two mediators (M1 and M2) and one dependent variable (DV).
My model proposes the following relationship: X –> M1 -> M2 -> DV
Before testing the model I want to check if the means in M1, M2, DV differ significantly between groups (CG < EG 1 < EG2). I use two dummy codes to represent my independent variable with the control group as reference group.
Normally, one would conduct an ANOVA with planned contrasts. But as I have a relatively small sample and highly skewed data, a robust approach like PLS seems to be the better solution to me.
My first question is if it is generally possible to check mean differences with PLS in a way that ANOVA would do?
In Bagozzi, Yi and Singh (1991) I read about the following procedure:
“When there is a causal order among the dependent variables, step-down analyses provide useful information as to whether the mean difference in a certain variable is due to the direct effect of the experimental manipulation or its dependence on other variables.” (p. 131)
(Bagozzi, R. F., Yi, Y., & Singh, S. (1991). On the use of structural equation models in experimental designs: Two extensions. International Journal of Research in Marketing, 8, 125-140)
In this sense I implemented a model that only contained direct paths from X to M1, M2, DV. I checked the model twice by switching the two dummies, one as the independent variable the other as the covariate.
My second question is if this procedure is correct?
Thank you very much for your help in advance! If someone knows studies that have implemented PLS in an experimental design like this I would be very thankful!
Best regards,
Corinna
Experimental design - Mean differences
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christian.nitzl
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Hey Corinna,
I have often searched for studies which use PLS in a experimental context. But all what I have found are some studies performing a group comparisons to check the impact of the different experimental groups. That seems reasonable for me. Markus Eberl perform such a procedure very well in his dissertation (only German):
Eberl, M. (2006b): Unternehmensreputation und Kaufverhalten – Methodische Aspekte komplexer Strukturmodelle, Wiesbaden.
Best regards,
Christian
I have often searched for studies which use PLS in a experimental context. But all what I have found are some studies performing a group comparisons to check the impact of the different experimental groups. That seems reasonable for me. Markus Eberl perform such a procedure very well in his dissertation (only German):
Eberl, M. (2006b): Unternehmensreputation und Kaufverhalten – Methodische Aspekte komplexer Strukturmodelle, Wiesbaden.
Best regards,
Christian
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christian.nitzl
- PLS Expert User
- Posts: 248
- Joined: Sat Jul 25, 2009 1:34 pm
- Real name and title:
Hey Christian,
this article sounds quite interesting and comprehensible. Thanks for your hint. I have also found an article from Huang et al. (2010) who approached in the same way.
Huang, R., Kahai, S., & Jestice, R. (2010). The contingent effects of leadership on team collaboration in virtual teams. Computers in Human Behavior, 26, 1098–1110.
I think they solved the "mean difference" problem in an elegant fashion. They manipulated the independent variable, but measured it as well. So they were able to hypothesize that their independent variable should be positively related to their dependent variable.
Unfortunately, my independent variable was just manipulated. I am not sure if I can approach in the same manner. If I want to compare my three groups, how would one arrange the hypothesis so that it fits to the PLS model?
Would it be comprehensible that I first apply analysis of variance and afterwards the test of mediation using PLS?
Thank you so much!
Best regards,
Corinna
this article sounds quite interesting and comprehensible. Thanks for your hint. I have also found an article from Huang et al. (2010) who approached in the same way.
Huang, R., Kahai, S., & Jestice, R. (2010). The contingent effects of leadership on team collaboration in virtual teams. Computers in Human Behavior, 26, 1098–1110.
I think they solved the "mean difference" problem in an elegant fashion. They manipulated the independent variable, but measured it as well. So they were able to hypothesize that their independent variable should be positively related to their dependent variable.
Unfortunately, my independent variable was just manipulated. I am not sure if I can approach in the same manner. If I want to compare my three groups, how would one arrange the hypothesis so that it fits to the PLS model?
Would it be comprehensible that I first apply analysis of variance and afterwards the test of mediation using PLS?
Thank you so much!
Best regards,
Corinna
-
christian.nitzl
- PLS Expert User
- Posts: 248
- Joined: Sat Jul 25, 2009 1:34 pm
- Real name and title:
Hey Corinna,
Thanks a lot for the article!
I would perform a three group comparison in that way, that I would define a reference group (control group) and compare the other groups to this reference group. I would check, if there is a significant differences in their path coefficients (see also Eberl, Markus (2010): An Application of PLS in Multi-Group Analysis, in: Esposito Vinzi, V./Chin, W./Henseler J./Wang, H. (Hrsg.): Handbook of Partial Least Squares: Concepts, Methods and Applications, Berlin, S. 487-514).
I know, that some authors use paralle to PLS an ANOVA. But Henseler et al. (2009) wrote on page 283 about that:
“Our review further more discloses that some studies use PLS path modeling in combination with other analysis techniques such as t-tests, ANOVA , and CBSEM. Yet, these methods are not always a suitable choice. If, for instance , PLS was selected because of its distribution-free character, it would be inconsequent to introduce distributional assumptions in another analysis such as t-test or ANOVA, or to rely on criteria derived from CBSEM’schi-square statistic. This finding provides evidence that either PLS path modeling lacks important features, which makes the use of additional analyses necessary, or that researchers are not aware of the respective extensions of PLS path modeling. In particular, the findings underpin the strong need for a PLS-based approach to multi group analysis (MGA) in international marketing in order to compare model parameters across groups such as countries or cultures.”
I hope that helps!
Best regards,
Christian
Thanks a lot for the article!
I would perform a three group comparison in that way, that I would define a reference group (control group) and compare the other groups to this reference group. I would check, if there is a significant differences in their path coefficients (see also Eberl, Markus (2010): An Application of PLS in Multi-Group Analysis, in: Esposito Vinzi, V./Chin, W./Henseler J./Wang, H. (Hrsg.): Handbook of Partial Least Squares: Concepts, Methods and Applications, Berlin, S. 487-514).
I know, that some authors use paralle to PLS an ANOVA. But Henseler et al. (2009) wrote on page 283 about that:
“Our review further more discloses that some studies use PLS path modeling in combination with other analysis techniques such as t-tests, ANOVA , and CBSEM. Yet, these methods are not always a suitable choice. If, for instance , PLS was selected because of its distribution-free character, it would be inconsequent to introduce distributional assumptions in another analysis such as t-test or ANOVA, or to rely on criteria derived from CBSEM’schi-square statistic. This finding provides evidence that either PLS path modeling lacks important features, which makes the use of additional analyses necessary, or that researchers are not aware of the respective extensions of PLS path modeling. In particular, the findings underpin the strong need for a PLS-based approach to multi group analysis (MGA) in international marketing in order to compare model parameters across groups such as countries or cultures.”
I hope that helps!
Best regards,
Christian
Hi Christian,
thank you so much for your assistance.
First, I thought of using the multiple group comparison approach, too.
But as I proceeded like Taylor et al. (2008) propose for the three-path mediated effect, I was wondering if I still have comparable results to the ANOVA situation. They say on page 242:
"Estimating the model requires that the following three regression equations be estimated:
(1) M1 = Intercept + b1X + Residual
(2) M2 = Intercept + b2M1 + b5X + Residual
(3) Y = Intercept + b4X + b3M2 + b6M1 + Residual"
Taylor, A.B., MacKinnon, D.P., & Tein, J-Y. (2008). Tests of three-path mediated effect. Organizational Research Methods, 11, 241-269.
As far as I understood, b5 represents the effect of X on M2, controlling for the effect of X on M1. This is for testing the mediation.
But if I first want to check if the groups differ significantly on M1 and M2, how would one test the paths? In the ANOVA situation one would not control for the effect of X on M1 when testing for mean differences on M2. How would this path be tested in the PLS model?
I hope my thoughts are comprehensible.
Thanks so much!
Best wishes,
Corinna
thank you so much for your assistance.
First, I thought of using the multiple group comparison approach, too.
But as I proceeded like Taylor et al. (2008) propose for the three-path mediated effect, I was wondering if I still have comparable results to the ANOVA situation. They say on page 242:
"Estimating the model requires that the following three regression equations be estimated:
(1) M1 = Intercept + b1X + Residual
(2) M2 = Intercept + b2M1 + b5X + Residual
(3) Y = Intercept + b4X + b3M2 + b6M1 + Residual"
Taylor, A.B., MacKinnon, D.P., & Tein, J-Y. (2008). Tests of three-path mediated effect. Organizational Research Methods, 11, 241-269.
As far as I understood, b5 represents the effect of X on M2, controlling for the effect of X on M1. This is for testing the mediation.
But if I first want to check if the groups differ significantly on M1 and M2, how would one test the paths? In the ANOVA situation one would not control for the effect of X on M1 when testing for mean differences on M2. How would this path be tested in the PLS model?
I hope my thoughts are comprehensible.
Thanks so much!
Best wishes,
Corinna