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How can i validate the modeling step of my dataset with PLS regression?

In other words can i calculate an X_hat and Y_hat using the modeling factors (T,P,Q,U,B,W) and compare it with the original X and Y. I'm using the algorithm PLS2.

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By using the PLS Regression you can follow this steps:

  1. Apply the algorithm by using a validation method (i recommend the full cross validation);
  2. Select the number of latent variables that the validation gives to you;
  3. Re-run the pls algorithm with the number of latent variables in step 2 and re-apply the cross validation.

With this 3 steps you can obtain an $\hat{y}$ but the $X$ now is the result of the combination of the old variables, the Score Matrix. Basically you can only compare the original $y$ with the new $\hat{y}$, because of the nature of the latent variables that you select.

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  • $\begingroup$ I think the original poster wants an answer something like this: X = TP' + error $\endgroup$ – Kevin Wright Dec 10 '17 at 3:48

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