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This question was asked here but no one gave a good answer. So I think it's a good idea to bring it up again and also I would like to add some more comments/questions.

  • The first question is what is the difference between "PLS path modeling" and "PLS regression"? To make it more general, what are structural equation modeling (SEM), path modeling and regression? To my understanding regression focuses more on prediction while SEM focus is on the relationship between response and predictors and path modeling is a special case of SEM?

  • My second question is how trustworthy is PLS? Recently it's been subject to many criticisms as highlighted in Rönkkö et al. 2016 and Rönkkö et al. 2015 which leads to the rejection of papers based on PLS in high tier journals such as Journal of Operations Management (here is the note from the journal editor):

    We are desk rejecting practically all PLS-based manuscripts, because we have concluded that PLS has been without exception the wrong modeling approach in the kinds of models OM researchers use.

    I should note my field is spectroscopy, neither management/psychology nor statistics. In the papers linked above the authors are talking more about PLS as a SEM method, but to me, their criticism looks applicable to PLS regression as well.

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  • $\begingroup$ Your links are all behind paywalls. $\endgroup$
    – Jeremy Miles
    Commented Jan 11, 2018 at 0:57
  • $\begingroup$ you are absolutely right! and I'm sorry, I have the PDFs but I'm not sure if I can upload or share. Science should be free:) $\endgroup$
    – Ress
    Commented Jan 11, 2018 at 4:27
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    $\begingroup$ PLS regression is explained and discussed in quite some detail in stats.stackexchange.com/questions/179733. Unfortunately I know next to nothing about "path modeling". $\endgroup$
    – amoeba
    Commented Feb 13, 2018 at 15:54
  • $\begingroup$ I think "path modeling" is just another name for SEM $\endgroup$
    – rep_ho
    Commented Feb 14, 2018 at 0:00
  • $\begingroup$ From the 2016 paper: "Most introductory texts on PLS gloss over the purposes of the weights, arguing that PLS is SEM and therefore it must provide an advantage over regression with composites (e.g., Gefen et al., 2011); however, such works often do not explicitly point out that PLS itself is also simply regression with composites." is misleading. The main thrust of the argument I can see if that the authors assert that SEM must be a pure theoretical construct and they have disdain for empirically derived structural equations. But PLS does derived 'structured' equations through covariance. $\endgroup$
    – ReneBt
    Commented Feb 21, 2018 at 9:13

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The first question is what is the difference between "PLS path modeling" and "PLS regression"?

None, they are synonyms.

To make it more general, what are structural equation modeling (SEM), path modeling and regression? To my understanding regression focuses more on prediction while SEM focus is on the relationship between response and predictors and path modeling is a special case of SEM?

SEM is a form of regression. Regression is any method that correlates independent and dependent variables and includes methods that use multiple variables handled as separate entities. SEM specifically uses mathematical relationships between the variables to constrain the final model, in the case of PLS this is the covariance. My understanding is that path modeling is a domain- (not mine, I'm a spectroscopist like you) specific term.

My second question is how trustworthy is PLS? Recently it's been subject to many criticisms as highlighted in Rönkkö et al. 2016 and Rönkkö et al. 2015

An excellent rebuttal is found in Henseler et al. 2013 Common Beliefs and Reality About PLS. A main concern for Rönkkö et al. is that PLS didn't perform great in some situations that assume a common latent factor. PLS is in fact designed to handle multiple latent factors, a situation that is much more common in the real world.

How trustworthy? For spectroscopy it is an excellent tool but does have its limitations. It does run the risk of overfitting as it can build complex models that capture contributions from multiple underlying factors. For this reason it does need to be used with care and appropriate external validation are essential, but then these caveats apply to all model building tools. I work mainly on real world datasets for 2 decades and I have not encountered any experimental dataset that had only one common factor underpinning the dependent variable (neither based on data nor on scientific theory).

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    $\begingroup$ +1 even though I wish this answer had more details on the Ronkko et al. vs Henseler et al. disagreement. I am not at all a spectroscopist but I have a relatively good understanding of PLS as a regularization method for linear regression (that's how it's presented in The Elements of Statistical Learning by Hastie et al.). I think it's called PLS1 in chemometrics. Here "performance" relates to reconstruction error, one can use cross-validation to choose regularization strength, etc. This is a very familiar setting to anybody who encountered ridge regression or PCR or anything like that. $\endgroup$
    – amoeba
    Commented Feb 19, 2018 at 20:26
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    $\begingroup$ [cont.] I am also aware of PLS2 with multiple dependent variables, but I am not sure how often this is used. At the same time, from trying to understand what Ronkko et al. mean, it seems that the focus of "SEM" is exclusively on relating multiple X to multiple Y (is it PLS2 then?) and perhaps more on interpreting the relationship between X and Y rather than prediction of Y as such. I am not even sure what they mean by "performance", and I have no idea what they prefer to use instead of PLS when they criticize PLS. $\endgroup$
    – amoeba
    Commented Feb 19, 2018 at 20:28
  • $\begingroup$ Thanks both ReneBT and amoeba. I posted this question on Reddit here and someone (soumya_ray) answered that the regression and SEM are fundamentally different. She did not explain the technical differences. Btw, her answer is against what you said (your answer make sense to me). $\endgroup$
    – Ress
    Commented Feb 20, 2018 at 20:38
  • $\begingroup$ Btw, I do band selection using PLS. I confirm your point on PLS performance, while it might result in good predictions (both on test and calibration) but the model can be fundamentally wrong or at least very hard to interpret since it selects predictors as important variables that has nothing to do with the response variable. $\endgroup$
    – Ress
    Commented Feb 20, 2018 at 20:45
  • $\begingroup$ A further comment on the key issues raised by the authors is "The PLS algorithm thus produces weights that increase the correlation between the adjacent composites compared to the unit-weighted composites used as the starting point by using any correlations in the data, but this does not guarantee achievement of any global optimum". Is a valid concern, in a nutshell what it means is the model will only apply to populations with the same underlying covariance structure, this does not make PLS invalid, but means that one must build and use a model with care. $\endgroup$
    – ReneBt
    Commented Feb 21, 2018 at 9:20

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