Hi Shi

It is possible to get an equation in PLS analysis as you are looking for. I wonder which statistical program you are using. If option is open for you, try XLSTAT, you will get decent figures and statistical outputs including equation that you are looking for.

Cheers

Hi Shi

In a standard regression equation with a single predictor and a single criterion, a linear relationship is denoted as in equation 1, where criterion y is expressed as a function of constant a, regression slope b of predictor x and error ε. This equation is central in the classic validation model.

(1) y = a + bx + ε

with 4 LVs in your case, that should be:

y = a + bx1 + cx2 + dx3 + dx4 + ε

b, c and d are the beta values (regression slopes) for each LV. You should get the beta values from PLS results. 

Hope this is helpful. Cheers.

Hi Shi

It is possible to get an equation in PLS analysis as you are looking for. I wonder which statistical program you are using. If option is open for you, try XLSTAT, you will get decent figures and statistical outputs including equation that you are looking for.

Cheers

Hi, 

With PROC pls in SAS, you'll find all you asked.

http://www.ats.ucla.edu/stat/sas/library/pls.pdf

Of course it is possible to get PLS equation as other colleagues have indicated. It depends on what software you are using. With library (pls) in R for example, after you select the optimal number of the components (in your case is 4), then you get the loading values (PLS coefficients for each variable) together with the intercept and you can then easily come up with PLS model (equation). I hope that helps

also check out Neusrel software which may have the benefit of exploring possible non linear relationship

it gives the model equations in regression style form.

enjoy

brad

Thank you, guys. Your suggestions are very useful for me.

I'm using SmartPLS and VisualPLs, from the results,  where can I find the intercept or the constant for my PLS Model Equation ?

thanks in advance.

Hadi

The product you are looking for is called B-coefficients. It is the direct PLS model with the regression model coefficient applied on the factors. This product is very good for variable selection and spectral assignment as well.

Thanks for your answer Nimrod; the use of the VIP is the simplest method to select relevant variables for a PLSR; The B-coefficients is another method that indicates to me that it is good for the selection of variables and I will take it into account; In any case, whether it is the use of VIPs or B-coefficients, I am interested in finding paper or bibliography for PLSR2, that is, PLSR with more than one dependent variable, and I have found little or no bibliography for this case (PLRS2 ).

https://help.xlstat.com/customer/en/portal/articles/2062244-partial-least-squares-pls-regression-in-excel?b_id=9283

How to get the regression equation using the PLS model for a variable?