Hi
I have modeled and estimated two-way effects in PLS. I would like to seek your views whether the way I have modeled is the correct way to model In PLS. Or is there any other better way to do that.
1. I have four independent LVs (a,b,c,d) and I have linked these four LVs to my dependent LV (e) to show the normal linear effect.
2. Now I want to see the reverse effect of decedent LV (e) on the four independent LVs (as above) in the same model.
Since PLS does not allow me to draw the reverse link (from dependent variable to independent variables), so I have created four more LVs (a,b.c.d, which are exactly same) in the model and have created the reverse link from LV (e) to LVs (a,b,c,d). By doing that situation has reversed and my independent variables as at point 1 has become dependent variables. While doing that the links that I have created at point 1 are also in the model.
So instead of having 5 variables (as per my model on point 1), now I have 9 varaibles.
3. Then I simply run the model.
My questions:
1) Is this the best way to see the reverse effect or two-way effect in PLS. Or is there any other way to do this?
2) Second, is there any thing I need to be careful about when I evaluate measurement model and structural model using above method of modeling?.
Please help.
Cheers
Jiwat
modeling and estimating two-way / reverse effects
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Diogenes
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Hi,
There are some articles that use reciprocal effect, like this:
Cross sectional:
A --> B
B --> A
But, Maruyama (1998, p.100-101), even for LISREL estimation, suggests that we should use longitudinal data:
Lagged (time 0 and time 1):
A_0 --> A_1
A_0 --> B_1
B_0 --> B_1
B_0 --> A_1
MARUYAMA, G. M. Basics of Structural Equation Modeling. Thousand Oaks, CA: Sage Publications, 1998.
In your case, when running the model from 4 LV to LV (e) the results will be influenciated by the multicollinearity.
When running from (e) to the other 4 LV, you will have simple regressions (no multicollinearity), and they will be equal correlations between these LVs.
My personal tendency is not to adopt reciprocal influences, but you could find some references to support your model.
Best regards.
Bido
There are some articles that use reciprocal effect, like this:
Cross sectional:
A --> B
B --> A
But, Maruyama (1998, p.100-101), even for LISREL estimation, suggests that we should use longitudinal data:
Lagged (time 0 and time 1):
A_0 --> A_1
A_0 --> B_1
B_0 --> B_1
B_0 --> A_1
MARUYAMA, G. M. Basics of Structural Equation Modeling. Thousand Oaks, CA: Sage Publications, 1998.
In your case, when running the model from 4 LV to LV (e) the results will be influenciated by the multicollinearity.
When running from (e) to the other 4 LV, you will have simple regressions (no multicollinearity), and they will be equal correlations between these LVs.
My personal tendency is not to adopt reciprocal influences, but you could find some references to support your model.
Best regards.
Bido
Thanks Professor Bido.
1. I am running only one model that has following nine LVs. The 4 LVs i.e. A, B, C, and D are duplicated in the model, that means I have two extaclty same LVs for A, B, C, and D LVs and one E LV. The reason I am creating duplicated 4 LVs is because PLS doesnot allow me to create a reciprocal link. I have following relationships in one model.
A -> E
B -> E
C -> E
D -> E
E -> A
E -> B
E -> C
E -> D
2. Do you think I should run two separate models as follows in PLS to see what I want to see (given at point 3 below):
model 1
A -> E
B -> E
C -> E
D -> E
Model 2
E -> A
E -> B
E -> C
E -> D
3. All I want to see is whether the independent variables have the only effect on dependet variable or whether there is a reciprocal / two-way effect exist. And if it does, which effect is stronger.
By doing that I would know where to focus more. Is it that the effect of independent LV on Dependent LV more important or the effect of Depdent LV on Independent LV more important. Hence it will raise fundamental question on whether indepdent LV is actually is the influencing factor on depdent LV.
Please let me know your thoughts on above.
Regards
Jiwat
1. I am running only one model that has following nine LVs. The 4 LVs i.e. A, B, C, and D are duplicated in the model, that means I have two extaclty same LVs for A, B, C, and D LVs and one E LV. The reason I am creating duplicated 4 LVs is because PLS doesnot allow me to create a reciprocal link. I have following relationships in one model.
A -> E
B -> E
C -> E
D -> E
E -> A
E -> B
E -> C
E -> D
2. Do you think I should run two separate models as follows in PLS to see what I want to see (given at point 3 below):
model 1
A -> E
B -> E
C -> E
D -> E
Model 2
E -> A
E -> B
E -> C
E -> D
3. All I want to see is whether the independent variables have the only effect on dependet variable or whether there is a reciprocal / two-way effect exist. And if it does, which effect is stronger.
By doing that I would know where to focus more. Is it that the effect of independent LV on Dependent LV more important or the effect of Depdent LV on Independent LV more important. Hence it will raise fundamental question on whether indepdent LV is actually is the influencing factor on depdent LV.
Please let me know your thoughts on above.
Regards
Jiwat
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Diogenes
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Hi,
I think that PLS-PM is not the best way to test reciprocal relations.
1) You should have theory to justify a LV AS independent or dependent.
2) In the LISREL, we have chi-squared tests that could help us to decide if the effect from A to B is bigger from B to A.
3) The PLS-PM algorithm is like regression, and the effect from A to B will be the same as B to A (bivariate case).
4) In your model 1 (multiple regression) the path coefficients, probably, will be lower than the correlations (model 2) because multicollinearity.
From your questions, I understood that you are not sure about which LV is the dependent and which the independent is. Then, it is not possible to justify the hypothesis based on previous theory.
Why don’t you run a confirmatory factor analysis?
- Each LV connected with all others.
- Factor weighting scheme
- Comment just the measurement model (AVE, CC) and the correlations between LV.
Best regards,
Bido
I think that PLS-PM is not the best way to test reciprocal relations.
1) You should have theory to justify a LV AS independent or dependent.
2) In the LISREL, we have chi-squared tests that could help us to decide if the effect from A to B is bigger from B to A.
3) The PLS-PM algorithm is like regression, and the effect from A to B will be the same as B to A (bivariate case).
4) In your model 1 (multiple regression) the path coefficients, probably, will be lower than the correlations (model 2) because multicollinearity.
From your questions, I understood that you are not sure about which LV is the dependent and which the independent is. Then, it is not possible to justify the hypothesis based on previous theory.
Why don’t you run a confirmatory factor analysis?
- Each LV connected with all others.
- Factor weighting scheme
- Comment just the measurement model (AVE, CC) and the correlations between LV.
Best regards,
Bido
Thanks Prof Bido.
I have answered your questions/points to seek your comments as below:
1) You should have theory to justify a LV AS independent or dependent.
I agree that theory should drive the model. But then one should challenge the theory if there is a rationale to challenge. In my variables case, there is a rationale or logical reasons that independent LV and Dependent LV may have reciprocal effect and hence I want to challenge the theory.
And after testing in PLS, I can see it is true for three variables.
2) In the LISREL, we have chi-squared tests that could help us to decide if the effect from A to B is bigger from B to A.
I have never used LISERAL. I tested the model in AMOS. AMOS allows to create reverse links, but once I run the model it does not give estimates poroperly.
3) The PLS-PM algorithm is like regression, and the effect from A to B will be the same as B to A (bivariate case).
Actaully after I created reverse effects, I can see that the effects are not same. For example results for one variable 'A' in PLS are like this
A --> E (say significant positive effect 0.3)
E --> A (say significant positive effect 0.54)
Looking at above example, my argument is that in practice we should focus on the relationship E --> A rather than A-->E. Although both relationships are valid. Hence the results challenges the fundamentals of theory in a way.
4) In your model 1 (multiple regression) the path coefficients, probably, will be lower than the correlations (model 2) because multicollinearity.
So far I have run all relationships as one model. I havent tested relationships as Model 1 and Model 2 yet.
5) From your questions, I understood that you are not sure about which LV is the dependent and which the independent is. Then, it is not possible to justify the hypothesis based on previous theory.
Theoretically I know which are the independet LVs and which one is dependent LV. But there is a reason to belive that otherway round is possible and probably we should focus on that. And that is what I want to argue in my Model results.
6) Why don’t you run a confirmatory factor analysis?
- Each LV connected with all others.
- Factor weighting scheme
- Comment just the measurement model (AVE, CC) and the correlations between LV.
I run CFA in AMOS, but my overall model fit is not good. I also run SEM in AMOS and model fit is not good.
The reason being, of the four independent constructs two constructs are formed of two reflective indiacators. In SEM, at least one needs to have 3 indicator items per construct for model to run properly.
Advantage of PLS is that it gives model output and avoids strict assumptions of AMOS based SEM estimations. Hence I have to use PLS.
Regards
Jiwat
I have answered your questions/points to seek your comments as below:
1) You should have theory to justify a LV AS independent or dependent.
I agree that theory should drive the model. But then one should challenge the theory if there is a rationale to challenge. In my variables case, there is a rationale or logical reasons that independent LV and Dependent LV may have reciprocal effect and hence I want to challenge the theory.
And after testing in PLS, I can see it is true for three variables.
2) In the LISREL, we have chi-squared tests that could help us to decide if the effect from A to B is bigger from B to A.
I have never used LISERAL. I tested the model in AMOS. AMOS allows to create reverse links, but once I run the model it does not give estimates poroperly.
3) The PLS-PM algorithm is like regression, and the effect from A to B will be the same as B to A (bivariate case).
Actaully after I created reverse effects, I can see that the effects are not same. For example results for one variable 'A' in PLS are like this
A --> E (say significant positive effect 0.3)
E --> A (say significant positive effect 0.54)
Looking at above example, my argument is that in practice we should focus on the relationship E --> A rather than A-->E. Although both relationships are valid. Hence the results challenges the fundamentals of theory in a way.
4) In your model 1 (multiple regression) the path coefficients, probably, will be lower than the correlations (model 2) because multicollinearity.
So far I have run all relationships as one model. I havent tested relationships as Model 1 and Model 2 yet.
5) From your questions, I understood that you are not sure about which LV is the dependent and which the independent is. Then, it is not possible to justify the hypothesis based on previous theory.
Theoretically I know which are the independet LVs and which one is dependent LV. But there is a reason to belive that otherway round is possible and probably we should focus on that. And that is what I want to argue in my Model results.
6) Why don’t you run a confirmatory factor analysis?
- Each LV connected with all others.
- Factor weighting scheme
- Comment just the measurement model (AVE, CC) and the correlations between LV.
I run CFA in AMOS, but my overall model fit is not good. I also run SEM in AMOS and model fit is not good.
The reason being, of the four independent constructs two constructs are formed of two reflective indiacators. In SEM, at least one needs to have 3 indicator items per construct for model to run properly.
Advantage of PLS is that it gives model output and avoids strict assumptions of AMOS based SEM estimations. Hence I have to use PLS.
Regards
Jiwat
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Diogenes
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Hi,
1 and 5) Ok.
2) When I said LISREL is SEM-covariance based (equal to AMOS or EQS).
3 and 4) Your results were:
A --> E (say significant positive effect 0.3)
E --> A (say significant positive effect 0.54)
As I said, these path coefficients were expected (A--> E lower than E-->A), just because in the first case you have four predictors.
6) Ok.
7) Unfortunately, to test theory, SEM-covariance based (AMOS, LISREL, EQS) is the recommended procedure. See Fig.4, p.296 of
HENSELER, J.; RINGLE, C. M.; SINKOVICS, R. R. The use of partial least squares path modeling in international marketing. Advances in International Marketing, v. 20, p. 277-319, 2009.
The evidences given by the PLS-PM are weak to “challenges the fundamentals of theory”.
Best regards,
Bido
1 and 5) Ok.
2) When I said LISREL is SEM-covariance based (equal to AMOS or EQS).
3 and 4) Your results were:
A --> E (say significant positive effect 0.3)
E --> A (say significant positive effect 0.54)
As I said, these path coefficients were expected (A--> E lower than E-->A), just because in the first case you have four predictors.
6) Ok.
7) Unfortunately, to test theory, SEM-covariance based (AMOS, LISREL, EQS) is the recommended procedure. See Fig.4, p.296 of
HENSELER, J.; RINGLE, C. M.; SINKOVICS, R. R. The use of partial least squares path modeling in international marketing. Advances in International Marketing, v. 20, p. 277-319, 2009.
The evidences given by the PLS-PM are weak to “challenges the fundamentals of theory”.
Best regards,
Bido
Thanks Prof Bido
I now fully understand why I am getting stronger results for reverse effects. I also agree that PLS-PM may not be the correct way to challenge the theory.
When I created reverse effects in AMOS, I did not get the proper results in the output. The reason I think was that once I created a link from Dependent LV to independent LVs (to show the reciprocal effect), I needed to provide error term to my independent LVs (since they become dependent LV due to reciprocal link). If I provide error term to independent LVs (to make them dependent LV for reverse effect), it will become an issue. Therefore, I think reverse link estimation will not work in SEM. Is my understanding correct?
I am constrained by the two constructs in my model which are formed of two indicators each. I don’t see any way my AMOS results are going to come good, as strictly speaking I must check each construct separately (recommended way of checking the constructs in AMOS based SEM) for model fit. Once I do that, for these two constructs model will not be identified hence I don’t meet the basic assumptions to check my constructs, before including them in structural model.
I have read through Hensler's paper, but I will go through once again.
Any other ideas?
Regards
Jiwat
I now fully understand why I am getting stronger results for reverse effects. I also agree that PLS-PM may not be the correct way to challenge the theory.
When I created reverse effects in AMOS, I did not get the proper results in the output. The reason I think was that once I created a link from Dependent LV to independent LVs (to show the reciprocal effect), I needed to provide error term to my independent LVs (since they become dependent LV due to reciprocal link). If I provide error term to independent LVs (to make them dependent LV for reverse effect), it will become an issue. Therefore, I think reverse link estimation will not work in SEM. Is my understanding correct?
I am constrained by the two constructs in my model which are formed of two indicators each. I don’t see any way my AMOS results are going to come good, as strictly speaking I must check each construct separately (recommended way of checking the constructs in AMOS based SEM) for model fit. Once I do that, for these two constructs model will not be identified hence I don’t meet the basic assumptions to check my constructs, before including them in structural model.
I have read through Hensler's paper, but I will go through once again.
Any other ideas?
Regards
Jiwat
Last edited by jiwatr on Sun Jun 17, 2012 12:48 pm, edited 1 time in total.
Thanks Hengky.
In CB-SEM, dependent latent variable need to have error term. So if you create reciprocal links in CB-SEM, you are actually giving error terms to both indepdent and dependent latent varaibles (I am taking about unobserved varaibles) which I think is not correct. Therefore, I think the estimates will not be correct.
I am not very clear about the 'another option' as suggested in the post.
regards
jiwat
In CB-SEM, dependent latent variable need to have error term. So if you create reciprocal links in CB-SEM, you are actually giving error terms to both indepdent and dependent latent varaibles (I am taking about unobserved varaibles) which I think is not correct. Therefore, I think the estimates will not be correct.
I am not very clear about the 'another option' as suggested in the post.
regards
jiwat
Thanks Hengky.
One question from Prof Bido. Going back to the post of June 12 wherein it was discussed as follows (in quotes).
"3 and 4) Your results were:
A --> E (say significant positive effect 0.3)
E --> A (say significant positive effect 0.54)
As I said, these path coefficients were expected (A--> E lower than E-->A), just because in the first case you have four predictors. "
My question is having reciprocal link or adding / deleting predictors should only affect the R-square value of the model or the varaince explained by the predictors in the dependent variable. But it should not affect the co-efficient values for the effects.
So for example when I include reciprocal links A- E and E-A in my model, my co-efficients are 0.3 and 0.54 respectively.
Now I change it and just have A - E effect in my model, I can see my co-efficient is still 0.3.
Or when I have just have E-A effect (and dont have A-E in the model), my co-efficient is still 0.54. So no change in co-efficients.
So it seems to me that PLS still calculates the correct co-efficients for reciprocal links and is not affected by inclusion or removal of the links (I agree that it does affect the R-square value of the model though).
Could you pls comment. Given the above explanation, do you think PLS-PM is giving defective estimates?
Regards
Jiwat
I think
One question from Prof Bido. Going back to the post of June 12 wherein it was discussed as follows (in quotes).
"3 and 4) Your results were:
A --> E (say significant positive effect 0.3)
E --> A (say significant positive effect 0.54)
As I said, these path coefficients were expected (A--> E lower than E-->A), just because in the first case you have four predictors. "
My question is having reciprocal link or adding / deleting predictors should only affect the R-square value of the model or the varaince explained by the predictors in the dependent variable. But it should not affect the co-efficient values for the effects.
So for example when I include reciprocal links A- E and E-A in my model, my co-efficients are 0.3 and 0.54 respectively.
Now I change it and just have A - E effect in my model, I can see my co-efficient is still 0.3.
Or when I have just have E-A effect (and dont have A-E in the model), my co-efficient is still 0.54. So no change in co-efficients.
So it seems to me that PLS still calculates the correct co-efficients for reciprocal links and is not affected by inclusion or removal of the links (I agree that it does affect the R-square value of the model though).
Could you pls comment. Given the above explanation, do you think PLS-PM is giving defective estimates?
Regards
Jiwat
I think
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Hengkov
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Hi Jiwat,
According to Wold (1985, p. 236) "The first stage of the PLS algorithm remains the same, expect that in two of the weight relations the interdependency brings a factor 2 to one of the sign-weighted LV estimates".
The basic design of PLS is linear, which are interdependent systems with LV, respectively (p.224).
Wold,H. 1985. "Systems Analysis by Partial Least Squares" In Nijkamp et al (Ed.), Lancaster, pp. 221-251. All literature PLS no support
reciprocal model (ML and LS is different).
Regards,
Hengky
According to Wold (1985, p. 236) "The first stage of the PLS algorithm remains the same, expect that in two of the weight relations the interdependency brings a factor 2 to one of the sign-weighted LV estimates".
The basic design of PLS is linear, which are interdependent systems with LV, respectively (p.224).
Wold,H. 1985. "Systems Analysis by Partial Least Squares" In Nijkamp et al (Ed.), Lancaster, pp. 221-251. All literature PLS no support
reciprocal model (ML and LS is different).
Regards,
Hengky
Thanks Hengky.
To my understanding, PLS software will create a regression equation for each relationship that we may have in the model and simultaneously estimate the model to produce R-square, co-efficients for each relationships, and other estimates. No matter there is a reverse link or not.
In PLS, if you have to create reverse link, it seems you can only do that by creating a duplicated LV with an opposite (uni-directional) link. So essentially all the links are linear in the model, no matter how you model them.
But the most important thing to me is the co-efficients values. I know R-square will get affected by the number of predictors to dependet LV.
So for example, I have a relationship A-E and E-A. If I keep both relationships my co-efficients are lets say 0.3 and 0.54 respectively. But if I keep either of the two relationships in my model, my co-efficients are still same, no change at all. That measns, if I just keep A-E relationship in my model (no reverse link), the co-efficient is 0.3. Or if I just keep E-A relationship in the model, the coefficient is 0.54. So having reverse link is not affecting the co-efficients.
To my understanding the reason for above behaviour is because reverse link is still a linear link. My be I am wrong but I wonder why that is happening?
Regards
Jiwat
To my understanding, PLS software will create a regression equation for each relationship that we may have in the model and simultaneously estimate the model to produce R-square, co-efficients for each relationships, and other estimates. No matter there is a reverse link or not.
In PLS, if you have to create reverse link, it seems you can only do that by creating a duplicated LV with an opposite (uni-directional) link. So essentially all the links are linear in the model, no matter how you model them.
But the most important thing to me is the co-efficients values. I know R-square will get affected by the number of predictors to dependet LV.
So for example, I have a relationship A-E and E-A. If I keep both relationships my co-efficients are lets say 0.3 and 0.54 respectively. But if I keep either of the two relationships in my model, my co-efficients are still same, no change at all. That measns, if I just keep A-E relationship in my model (no reverse link), the co-efficient is 0.3. Or if I just keep E-A relationship in the model, the coefficient is 0.54. So having reverse link is not affecting the co-efficients.
To my understanding the reason for above behaviour is because reverse link is still a linear link. My be I am wrong but I wonder why that is happening?
Regards
Jiwat
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Hengkov
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Hi Jiwat,
1. Not justify and not support theory for latent variable and latent score in same model.
2. Latent variable and latent score not identical.
3. Reciprocal develop in CB-SEM using Maximum Likelihood (ML) by Joreskog and PLS develop using Least Squares (LS) estimation by Wold. ML and LS is different.
4. In CB-SEM, I think your experiment delete reverse link A=>E = 0.3, E=>A = 0.54, not still same but change.
Regards,
Hengky
1. Not justify and not support theory for latent variable and latent score in same model.
2. Latent variable and latent score not identical.
3. Reciprocal develop in CB-SEM using Maximum Likelihood (ML) by Joreskog and PLS develop using Least Squares (LS) estimation by Wold. ML and LS is different.
4. In CB-SEM, I think your experiment delete reverse link A=>E = 0.3, E=>A = 0.54, not still same but change.
Regards,
Hengky
Thanks Hengky.
I am not clear what exactly you mean by point 1 and 2 and how that is related in anyway to my questions.
Point 3, you must be right. But I cant say how that is affecting the reslts I am getting.
Point 4, I can only say that when I am able to test the same model in PLS and CB-SEM.
Regards
Jiwat
I am not clear what exactly you mean by point 1 and 2 and how that is related in anyway to my questions.
Point 3, you must be right. But I cant say how that is affecting the reslts I am getting.
Point 4, I can only say that when I am able to test the same model in PLS and CB-SEM.
Regards
Jiwat