Validation of modeling step of PLS

Question

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

In other words can I calculate an $\hat{X}$ and $\hat{Y}$ 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.

Answer 1

By using the PLS Regression, you can follow these 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 these 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.