I have searched the forum in quest for an answer to why weights above 1 occur for some formative constructs... (even though VIF does not exceed 2 or 3 in my case).
Several users have depicted this problem in this forum, but I have found no replies to this question.
Could somebody please share his/ her experience/ knowledge to help understand this phenomenon and maybe implement an adequate solution.
Thank you,
Roxana
weights higher than 1
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Diogenes
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Some answer about outer weights > 1,
And outer weights with opposite signal of the outer loadings (suppression)
I just finish an article where I conducted a simulation to assess the effect of the multicollinearity between formative indicators in the outer weights and in the path coefficients (available in Portuguese, but I will translate it to English soon).
Some results:
1) The multicollinearity hasn’t effect in the estimated value of the path coefficient.
2) Higher values of multicollinearity cause higher variability in the estimated values of the outer weights (in the same sense of multiple regression – variance inflation).
3) The effect of the multicollinearity in the estimated values of the outer weight is moderated by the value of the path coefficient:
3.1) For the same multicollinearity, the variability of the estimated outer weights are lower with higher values of path coefficient.
3.2) For the same multicollinearity, the variability of the estimated outer weights are higher with lower values of path coefficient.
3.3) For these reasons it is not possible to define a specific cutoff for VIF values (acceptable values). The effect of the multicollinearity depends of the values of the path coefficients.
We could to quote Henseler, Ringle and Sinkovics (2009, p.302): “…any VIF substantially greater than 1 indicates multicollinearity and should alert researchers to the typical problems of multicollinearity.”
4) Some effects of the multicollinearity in the estimated values of the outer weights:
4.1) When 1 < VIF < 1,43, and path coefficient lower or equal than 0,5: some outer weights will have the contrary signal of its outer loading.
4.2) When 1,11 < VIF < 1,43, and path coefficient higher than 0,5: we could have some effect because of the higher variability of the outer weights, like nonsignificant values.
4.3) When VIF > 4, and path coefficient lower than 0,3: some outer weights will be greater than 1.
4.4) In a general way, when the multicollinearity grows we could expect these effects
1st some outer weights will be nonsignificant
2nd some outer weights will have a contrary signal than its outer loading
3rd some outer weights will have a contrary signal than its outer loading and other will be greater than 1.
5) What we should do?
5.1) If you don’t want to interpret the outer weights like a measure of the relative importance of the indicator to the measure of the construct (you are just interested in the structural model – path coefficients), you don’t need to do anything.
5.2) If some assessment of the outer weights is necessary, some options:
- agregate the indicators [simple mean or weighted mean of the standardized values – see Diamantopoulos, Riefler and Roth (2008, p.1212) and Cohen et al. (2003, p.426)] and use it as the indicator of the LV in the SmartPLS.
- run a principal component analysis with Varimax rotation (orthogonal PC), save the factor scores and use them as formative indicator of the LV in the SmartPLS. This recommendation was inspired in the Cohen (2003, p.428-429).
Best regards,
Bido
COHEN, J. Applied multiple regression/correlation analysis for the behavioral sciences. 3rd Ed. New Jersey: Lawrence Erlbaum Associates, Publishers, 2003.
DIAMANTOPOULOS, A.; RIEFLER, P.; ROTH, K. P. Advancing formative measurement models. Journal of Business Research, v.61, n.12, p.1203-1218, dec. 2008.
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. Available at: <http://php.portals.mbs.ac.uk/Portals/49 ... cs-PLS.pdf>.
And outer weights with opposite signal of the outer loadings (suppression)
I just finish an article where I conducted a simulation to assess the effect of the multicollinearity between formative indicators in the outer weights and in the path coefficients (available in Portuguese, but I will translate it to English soon).
Some results:
1) The multicollinearity hasn’t effect in the estimated value of the path coefficient.
2) Higher values of multicollinearity cause higher variability in the estimated values of the outer weights (in the same sense of multiple regression – variance inflation).
3) The effect of the multicollinearity in the estimated values of the outer weight is moderated by the value of the path coefficient:
3.1) For the same multicollinearity, the variability of the estimated outer weights are lower with higher values of path coefficient.
3.2) For the same multicollinearity, the variability of the estimated outer weights are higher with lower values of path coefficient.
3.3) For these reasons it is not possible to define a specific cutoff for VIF values (acceptable values). The effect of the multicollinearity depends of the values of the path coefficients.
We could to quote Henseler, Ringle and Sinkovics (2009, p.302): “…any VIF substantially greater than 1 indicates multicollinearity and should alert researchers to the typical problems of multicollinearity.”
4) Some effects of the multicollinearity in the estimated values of the outer weights:
4.1) When 1 < VIF < 1,43, and path coefficient lower or equal than 0,5: some outer weights will have the contrary signal of its outer loading.
4.2) When 1,11 < VIF < 1,43, and path coefficient higher than 0,5: we could have some effect because of the higher variability of the outer weights, like nonsignificant values.
4.3) When VIF > 4, and path coefficient lower than 0,3: some outer weights will be greater than 1.
4.4) In a general way, when the multicollinearity grows we could expect these effects
1st some outer weights will be nonsignificant
2nd some outer weights will have a contrary signal than its outer loading
3rd some outer weights will have a contrary signal than its outer loading and other will be greater than 1.
5) What we should do?
5.1) If you don’t want to interpret the outer weights like a measure of the relative importance of the indicator to the measure of the construct (you are just interested in the structural model – path coefficients), you don’t need to do anything.
5.2) If some assessment of the outer weights is necessary, some options:
- agregate the indicators [simple mean or weighted mean of the standardized values – see Diamantopoulos, Riefler and Roth (2008, p.1212) and Cohen et al. (2003, p.426)] and use it as the indicator of the LV in the SmartPLS.
- run a principal component analysis with Varimax rotation (orthogonal PC), save the factor scores and use them as formative indicator of the LV in the SmartPLS. This recommendation was inspired in the Cohen (2003, p.428-429).
Best regards,
Bido
COHEN, J. Applied multiple regression/correlation analysis for the behavioral sciences. 3rd Ed. New Jersey: Lawrence Erlbaum Associates, Publishers, 2003.
DIAMANTOPOULOS, A.; RIEFLER, P.; ROTH, K. P. Advancing formative measurement models. Journal of Business Research, v.61, n.12, p.1203-1218, dec. 2008.
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. Available at: <http://php.portals.mbs.ac.uk/Portals/49 ... cs-PLS.pdf>.
Thank you for your detailed answer and the great information you provided! I think your research represents a real progress in a more accurate interpretation of PLS results!
I am however not sure that I have understood all the points you made. I would be very grateful to you if you would elaborate on some issues.
1) to which path coefficients do you refer? I associate path coefficients with the structural model, so I am a bit puzzled
2) your solution to aggregate the indicators into a factor refers to all the formative indicators of a variable or just some indicators which may be highly correlated and would make theoretically some sense?
Thanks for your reply. Please let me know whether and how I can eventually quote your work...
have a great day
Roxana
I am however not sure that I have understood all the points you made. I would be very grateful to you if you would elaborate on some issues.
1) to which path coefficients do you refer? I associate path coefficients with the structural model, so I am a bit puzzled
2) your solution to aggregate the indicators into a factor refers to all the formative indicators of a variable or just some indicators which may be highly correlated and would make theoretically some sense?
Thanks for your reply. Please let me know whether and how I can eventually quote your work...
have a great day
Roxana
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Diogenes
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Hi Roxana,
1) Yes, the path coefficients are from the structural model. The structural model (values of the path coefficients) are moderators of the effect of the multicollinearity in the measurement model (variability of the outer weights).
2) Both the solutions are possible:
- considering all indicators, with a simple mean, We will know that all indicators had the same weight in the measurement of the construct (not estimated by SmartPLS).
- Using PC + Varimax, We could try to interpret the orthogonal PC that will be used as formative indicators (substituting the original MV) in the measurement model.
One important article that I didn´t quote, and will be useful to answer this, is:
LITTLE, T. D.; CUNNINGHAM, W. A.; SHAHAR, G.; WIDAMAN, K.F. (2002). To Parcel or Not to Parcel: Exploring the Question, Weighing the Merits. Structural Equation Modeling, (9)2, p.151-173.
Another one that could improve the discussion (I didn´t do this) is:
LITTLE, T.D.; LINDENBERGER, U.; NESSELROADE, J.R. (1999). On selecting indicators for multivariate measurement and modeling with latent variable: when “good” indicators are bad and “bad” indicators are good. Psychological Methods, (4)2, p.192-211.
Best regards,
Bido
1) Yes, the path coefficients are from the structural model. The structural model (values of the path coefficients) are moderators of the effect of the multicollinearity in the measurement model (variability of the outer weights).
2) Both the solutions are possible:
- considering all indicators, with a simple mean, We will know that all indicators had the same weight in the measurement of the construct (not estimated by SmartPLS).
- Using PC + Varimax, We could try to interpret the orthogonal PC that will be used as formative indicators (substituting the original MV) in the measurement model.
One important article that I didn´t quote, and will be useful to answer this, is:
LITTLE, T. D.; CUNNINGHAM, W. A.; SHAHAR, G.; WIDAMAN, K.F. (2002). To Parcel or Not to Parcel: Exploring the Question, Weighing the Merits. Structural Equation Modeling, (9)2, p.151-173.
Another one that could improve the discussion (I didn´t do this) is:
LITTLE, T.D.; LINDENBERGER, U.; NESSELROADE, J.R. (1999). On selecting indicators for multivariate measurement and modeling with latent variable: when “good” indicators are bad and “bad” indicators are good. Psychological Methods, (4)2, p.192-211.
Best regards,
Bido
Hello Prof. Bido,
I am trying to implement the solution of using PC + Varimax.
I am not sure, how many factors to extract. Using the eigenvalue >1 criterium gets me in many cases just one factor. Making eigenvalue > 0 gets me n-1 factors (n variables -1). Extract k factors from k variables (like Cohen suggests)?
How do you proceed with PCA? and then do you interpret the factors using the indicator loadings (provided there are no significant cross-loadings)?
Thanks for your reply!
Best regards
Roxana
I am trying to implement the solution of using PC + Varimax.
I am not sure, how many factors to extract. Using the eigenvalue >1 criterium gets me in many cases just one factor. Making eigenvalue > 0 gets me n-1 factors (n variables -1). Extract k factors from k variables (like Cohen suggests)?
How do you proceed with PCA? and then do you interpret the factors using the indicator loadings (provided there are no significant cross-loadings)?
Thanks for your reply!
Best regards
Roxana
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PaHeinecke
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Hi Professor Bido,
I have a question regarding this comment in the SmartPLS forum (viewtopic.php?t=1106&highlight=cases).
I have a exogenous second order construct in my SEM involving a total of 13 formative indicators for 4 first-order latent variables in this exogenous multidimensional construct. However I am only having 58 or 37 cases, depending on which performance data I am using in the endogenous construct. Both are below the minimum of 65 required cases, if assuming a factor 5 on the 13 formative indicators (under normal conditions).
This leads to problems in the bootstrapping, e.g. the t-values of the path coefficients of this second-order construct are not significant in comparison to those of another second-order latent variable (which is specified in a reflective manner). This is not logical, as the former path coefficients of the formative measured construct (-0.4) have a greater distance to zero than the path coefficients of the later (reflective) construct (+0.3).
Consequently, I calculated the PLS algorithm and extracted the resulting factor values of the formative first-order LVs, thereby reducing the number of required cases to 4 times the factor 5 = 20 cases; without changing the reflective measured second-order construct. This leads to good path coefficients / t-values.
Is this procedure fine? Or, in other words, is it ok to assume that the PLS algorithm calculates fine the factor values of the formative first-order constructs, so that I can use them as "indexed values" in the subsequent bootstrapping.
Or does the number of cases also restrict the application of the PLS algorithm? Or does the numer of cases only restrict the application of bootstrapping, meaning that the above described procedure is
fine?
Thank you very much.
Best regards
Patrick
I have a question regarding this comment in the SmartPLS forum (viewtopic.php?t=1106&highlight=cases).
I have a exogenous second order construct in my SEM involving a total of 13 formative indicators for 4 first-order latent variables in this exogenous multidimensional construct. However I am only having 58 or 37 cases, depending on which performance data I am using in the endogenous construct. Both are below the minimum of 65 required cases, if assuming a factor 5 on the 13 formative indicators (under normal conditions).
This leads to problems in the bootstrapping, e.g. the t-values of the path coefficients of this second-order construct are not significant in comparison to those of another second-order latent variable (which is specified in a reflective manner). This is not logical, as the former path coefficients of the formative measured construct (-0.4) have a greater distance to zero than the path coefficients of the later (reflective) construct (+0.3).
Consequently, I calculated the PLS algorithm and extracted the resulting factor values of the formative first-order LVs, thereby reducing the number of required cases to 4 times the factor 5 = 20 cases; without changing the reflective measured second-order construct. This leads to good path coefficients / t-values.
Is this procedure fine? Or, in other words, is it ok to assume that the PLS algorithm calculates fine the factor values of the formative first-order constructs, so that I can use them as "indexed values" in the subsequent bootstrapping.
Or does the number of cases also restrict the application of the PLS algorithm? Or does the numer of cases only restrict the application of bootstrapping, meaning that the above described procedure is
fine?
Thank you very much.
Best regards
Patrick
Dear Professor Bido,
Thanks for sharing the results of your simulation study. If the (Portuguese) article is already published, could you please share the citation?
Thanks much,
Christoph
Thanks for sharing the results of your simulation study. If the (Portuguese) article is already published, could you please share the citation?
Thanks much,
Christoph
Diogenes wrote:Some answer about outer weights > 1,
And outer weights with opposite signal of the outer loadings (suppression)
I just finish an article where I conducted a simulation to assess the effect of the multicollinearity between formative indicators in the outer weights and in the path coefficients (available in Portuguese, but I will translate it to English soon).
Some results:
1) The multicollinearity hasn’t effect in the estimated value of the path coefficient.
2) Higher values of multicollinearity cause higher variability in the estimated values of the outer weights (in the same sense of multiple regression – variance inflation).
3) The effect of the multicollinearity in the estimated values of the outer weight is moderated by the value of the path coefficient:
3.1) For the same multicollinearity, the variability of the estimated outer weights are lower with higher values of path coefficient.
3.2) For the same multicollinearity, the variability of the estimated outer weights are higher with lower values of path coefficient.
3.3) For these reasons it is not possible to define a specific cutoff for VIF values (acceptable values). The effect of the multicollinearity depends of the values of the path coefficients.
We could to quote Henseler, Ringle and Sinkovics (2009, p.302): “…any VIF substantially greater than 1 indicates multicollinearity and should alert researchers to the typical problems of multicollinearity.”
4) Some effects of the multicollinearity in the estimated values of the outer weights:
4.1) When 1 < VIF < 1,43, and path coefficient lower or equal than 0,5: some outer weights will have the contrary signal of its outer loading.
4.2) When 1,11 < VIF < 1,43, and path coefficient higher than 0,5: we could have some effect because of the higher variability of the outer weights, like nonsignificant values.
4.3) When VIF > 4, and path coefficient lower than 0,3: some outer weights will be greater than 1.
4.4) In a general way, when the multicollinearity grows we could expect these effects
1st some outer weights will be nonsignificant
2nd some outer weights will have a contrary signal than its outer loading
3rd some outer weights will have a contrary signal than its outer loading and other will be greater than 1.
5) What we should do?
5.1) If you don’t want to interpret the outer weights like a measure of the relative importance of the indicator to the measure of the construct (you are just interested in the structural model – path coefficients), you don’t need to do anything.
5.2) If some assessment of the outer weights is necessary, some options:
- agregate the indicators [simple mean or weighted mean of the standardized values – see Diamantopoulos, Riefler and Roth (2008, p.1212) and Cohen et al. (2003, p.426)] and use it as the indicator of the LV in the SmartPLS.
- run a principal component analysis with Varimax rotation (orthogonal PC), save the factor scores and use them as formative indicator of the LV in the SmartPLS. This recommendation was inspired in the Cohen (2003, p.428-429).
Best regards,
Bido
COHEN, J. Applied multiple regression/correlation analysis for the behavioral sciences. 3rd Ed. New Jersey: Lawrence Erlbaum Associates, Publishers, 2003.
DIAMANTOPOULOS, A.; RIEFLER, P.; ROTH, K. P. Advancing formative measurement models. Journal of Business Research, v.61, n.12, p.1203-1218, dec. 2008.
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. Available at: <http://php.portals.mbs.ac.uk/Portals/49 ... cs-PLS.pdf>.
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Diogenes
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Hi,
it was presented in a Brazilian encounter (EnEPQ - Encounter for Teaching and Research in Administration and Accounting):
BIDO, D. S.; SILVA, D.; SOUZA, C. A.; GODOY, A. S. Indicadores Formativos na Modelagem em Equações Estruturais com Estimação via PLS-PM: Como Lidar com a Multicolinearidade Entre Eles? II Encontro de Ensino e Pesquisa em Administração e Contabilidade – EnEPQ, Anais... Curitiba/PR: ANPAD, 2009.
http://www.anpad.org.br/evento.php?acao ... alho=11330
It was submited to a Brazilian periodical, but I am still waiting.
Best regards,
Bido
it was presented in a Brazilian encounter (EnEPQ - Encounter for Teaching and Research in Administration and Accounting):
BIDO, D. S.; SILVA, D.; SOUZA, C. A.; GODOY, A. S. Indicadores Formativos na Modelagem em Equações Estruturais com Estimação via PLS-PM: Como Lidar com a Multicolinearidade Entre Eles? II Encontro de Ensino e Pesquisa em Administração e Contabilidade – EnEPQ, Anais... Curitiba/PR: ANPAD, 2009.
http://www.anpad.org.br/evento.php?acao ... alho=11330
It was submited to a Brazilian periodical, but I am still waiting.
Best regards,
Bido
Great, thank you very much! Good luck with the submission to the periodical.... this paper will be very helpful for many researchers.
Christoph
Christoph
Diogenes wrote:Hi,
it was presented in a Brazilian encounter (EnEPQ - Encounter for Teaching and Research in Administration and Accounting):
BIDO, D. S.; SILVA, D.; SOUZA, C. A.; GODOY, A. S. Indicadores Formativos na Modelagem em Equações Estruturais com Estimação via PLS-PM: Como Lidar com a Multicolinearidade Entre Eles? II Encontro de Ensino e Pesquisa em Administração e Contabilidade – EnEPQ, Anais... Curitiba/PR: ANPAD, 2009.
http://www.anpad.org.br/evento.php?acao ... alho=11330
It was submited to a Brazilian periodical, but I am still waiting.
Best regards,
Bido
-
stefanperras
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Dear Prof. Bido,
I face some multicollinearity in my formative measurement models (VIF between 1 and 3 for each indicator).
I wanted to apply your approach to conduct a principal component analysis in SPSS to combine the correlating indicators. You mentioned that you should then use the factor scores from SPSS and include them in SmartPLS.
Can you kindly explain in more detail how to do this? My SPSS output does not show any "combined" score for the components. And how to include the new scores in SmartPLS?
Many thanks in advance
Stefan
I face some multicollinearity in my formative measurement models (VIF between 1 and 3 for each indicator).
I wanted to apply your approach to conduct a principal component analysis in SPSS to combine the correlating indicators. You mentioned that you should then use the factor scores from SPSS and include them in SmartPLS.
Can you kindly explain in more detail how to do this? My SPSS output does not show any "combined" score for the components. And how to include the new scores in SmartPLS?
Many thanks in advance
Stefan
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Diogenes
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Hi
In the SPSS:
Analyze / dimension reduction / Factor / ... / Scores / Save as variables / Continue / Ok.
The standardized scores will be saved in the data set.
You could paste them to your original data set and use them as indicators.
I think that you could try “Varimax” rotation, to keep the scores noncorrelated one with another and to try find some interpretation (if it will be possible) of the factors or components.
Best regards,
Bido
My article (in Portuguese): http://www.angrad.org.br/_resources/_ci ... le_465.pdf
In the SPSS:
Analyze / dimension reduction / Factor / ... / Scores / Save as variables / Continue / Ok.
The standardized scores will be saved in the data set.
You could paste them to your original data set and use them as indicators.
I think that you could try “Varimax” rotation, to keep the scores noncorrelated one with another and to try find some interpretation (if it will be possible) of the factors or components.
Best regards,
Bido
My article (in Portuguese): http://www.angrad.org.br/_resources/_ci ... le_465.pdf
-
stefanperras
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Dear Prof. Bido,
I applied your approach with seven formative indicators (objective measures such as completion time etc.) and PCA in SPSS resulted with only two additional factors. How can I integrate them with an inital indicators in order to obtain their weights in second order model (Type IV according to Jarvis et al. 2003; first- and second-order formative) in SmartPLS? Thank you very much in advance!!
Kind regards,
Tihomir
I applied your approach with seven formative indicators (objective measures such as completion time etc.) and PCA in SPSS resulted with only two additional factors. How can I integrate them with an inital indicators in order to obtain their weights in second order model (Type IV according to Jarvis et al. 2003; first- and second-order formative) in SmartPLS? Thank you very much in advance!!
Kind regards,
Tihomir
Dear Professor Bido,
I would like to know if your simulation study is available in english. In my study I might have some suppressor effects in my LVs even though VIFs for the indicators are not too high (e.g. two formative LVs, one with all VIFs < 3,5 (7 indicators), the other with all VIFs < 2 (5 indicators)). So I'm interested in reading more about the results of your study.
Best regards
Stephan
I would like to know if your simulation study is available in english. In my study I might have some suppressor effects in my LVs even though VIFs for the indicators are not too high (e.g. two formative LVs, one with all VIFs < 3,5 (7 indicators), the other with all VIFs < 2 (5 indicators)). So I'm interested in reading more about the results of your study.
Best regards
Stephan
Re: weights higher than 1
Hey everyone! I could really need some help!
What are the steps in SPSS to test for a possible suppression effect in the formative indicators?
"Negative weights are the result of the pattern of correlations among the formatively measured construct indicators. Suppression occurs when an indicator shares more variance with another indicator than with the formatively measured construct." (Cenfetelli & Bassellier, 2009)
To test suppression I need
* the semi-partial correlations of each indicator
* the zero-order correlation of each indicator with the formative construct
Therefore I use SPSS
* Linear Regression
* formative indicators as independent variables
* formative construct as dependent variable (????)
Suppression exists when
* the semi-partial correlation of an indicator is larger than the zero-order correlation with the formative construct
But how do I determine the value of the formative construct to use it as a dependent variable in the linear regression?
What are the steps in SPSS to test for a possible suppression effect in the formative indicators?
"Negative weights are the result of the pattern of correlations among the formatively measured construct indicators. Suppression occurs when an indicator shares more variance with another indicator than with the formatively measured construct." (Cenfetelli & Bassellier, 2009)
To test suppression I need
* the semi-partial correlations of each indicator
* the zero-order correlation of each indicator with the formative construct
Therefore I use SPSS
* Linear Regression
* formative indicators as independent variables
* formative construct as dependent variable (????)
Suppression exists when
* the semi-partial correlation of an indicator is larger than the zero-order correlation with the formative construct
But how do I determine the value of the formative construct to use it as a dependent variable in the linear regression?