Do you have any experience in integrating a non-linear, i.e. a curvilinear, relationship into a PLS model? More specifically, I'm thinking about a structural model with several latent variables. One relationship is assumed to take on an inverted U shape, indicating that there is some kind of optimum. The exogenous latent variable in this relation is measured by only one manifest variable. Is it feasible to square that manifest variable and enter it into the model (as single formative or reflective variable)? If yes, how to interpret the results? If no, what would you suggest as an alternative? I thought about exporting the latent variable scores (after PLS was run at least once) into SPSS and do a non-linear regression. However, an integrated solution within PLS would be much more desirable.
Best regards,
Christoph Grimpe
Non-linear relationships with PLS
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cringle
- SmartPLS Developer
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- Joined: Tue Sep 20, 2005 9:13 am
- Real name and title: Prof. Dr. Christian M. Ringle
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Hi,
your approach to mix linear and non-linear methods seems practical. However, we will definitely not implement such approaches into SmartPLS for convenience reason. At the moment, I do not fully understand the statistical implications of your proposed procedure and, thus, I am not convinced that this is reasonable. If you are able to clearly and completely lay out the statistical implications (and soundness) of this procedure and if you can provide a “cooking recipe” (matrix presentation) how to partially or fully perform a non-linear PLS approach step-by-step (at best with an EXCEL + Visual Basic Macro example), this might be an implementation for the future development of SmartPLS.
Kind regards
Christian Ringle
your approach to mix linear and non-linear methods seems practical. However, we will definitely not implement such approaches into SmartPLS for convenience reason. At the moment, I do not fully understand the statistical implications of your proposed procedure and, thus, I am not convinced that this is reasonable. If you are able to clearly and completely lay out the statistical implications (and soundness) of this procedure and if you can provide a “cooking recipe” (matrix presentation) how to partially or fully perform a non-linear PLS approach step-by-step (at best with an EXCEL + Visual Basic Macro example), this might be an implementation for the future development of SmartPLS.
Kind regards
Christian Ringle
Prof. Dr. Christian M. Ringle, Hamburg University of Technology (TUHH), SmartPLS
- Literature on PLS-SEM: https://www.smartpls.com/documentation
- Google Scholar: https://scholar.google.de/citations?use ... AAAJ&hl=de
- Literature on PLS-SEM: https://www.smartpls.com/documentation
- Google Scholar: https://scholar.google.de/citations?use ... AAAJ&hl=de
Hi,
It was not my intention to suggest an implementation into SmartPLS (which - of course - would be nice) but to get an understanding of the underlying statistical rationale. Normally, when you enter a squared term into a multiple regression you test for a curvilinear relationship. That's why I thought it would also work within a PLS model as I haven't seen any implementation of non-linear relationships into PLS models yet. Strictly linear relationships are always an approximation. Would you consider it reasonable to run a linear PLS model first and afterwards test selected relationships between latent variables for a curvilinear shape by exporting the LV scores? (Just to appease the reviewers?)
Kind regards,
Christoph Grimpe
It was not my intention to suggest an implementation into SmartPLS (which - of course - would be nice) but to get an understanding of the underlying statistical rationale. Normally, when you enter a squared term into a multiple regression you test for a curvilinear relationship. That's why I thought it would also work within a PLS model as I haven't seen any implementation of non-linear relationships into PLS models yet. Strictly linear relationships are always an approximation. Would you consider it reasonable to run a linear PLS model first and afterwards test selected relationships between latent variables for a curvilinear shape by exporting the LV scores? (Just to appease the reviewers?)
Kind regards,
Christoph Grimpe
-
cringle
- SmartPLS Developer
- Posts: 818
- Joined: Tue Sep 20, 2005 9:13 am
- Real name and title: Prof. Dr. Christian M. Ringle
- Location: Hamburg (Germany)
- Contact:
Well,
I would strictly stick to linear model estimations when using SmartPLS and the basic PLS algorithm. However, if you like to head towards nonlinear relationships, I suggest to search for applications of the NIPALS algorithm. I have seen some articles (but unfortunately do not have the sources on my hands) with some reasonable results considering non-linearity…
Best regards
Christian
I would strictly stick to linear model estimations when using SmartPLS and the basic PLS algorithm. However, if you like to head towards nonlinear relationships, I suggest to search for applications of the NIPALS algorithm. I have seen some articles (but unfortunately do not have the sources on my hands) with some reasonable results considering non-linearity…
Best regards
Christian
Prof. Dr. Christian M. Ringle, Hamburg University of Technology (TUHH), SmartPLS
- Literature on PLS-SEM: https://www.smartpls.com/documentation
- Google Scholar: https://scholar.google.de/citations?use ... AAAJ&hl=de
- Literature on PLS-SEM: https://www.smartpls.com/documentation
- Google Scholar: https://scholar.google.de/citations?use ... AAAJ&hl=de