How to fit a PLS function with an intercept?

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gsourop 2021-1-29

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https://ww2.mathworks.cn/matlabcentral/answers/730233-how-to-fit-a-pls-function-with-an-intercept

Dear all,

I am using the plsregress function to derive the betas. I want to test a different number of components to see which number fits the model best based on the BIC or another criterion (rather than using the default mse). I would like to use an intercept within my specifications. However, I am not sure if the following is correct

T =100;
x = [ones(T,1) randn(T,10)]; 
y = randn(T,1);
for k = 1 :11
[xl, yl,xs,ys,betapls] = plsregress(x,y,k);
beta_k(k,:) = betapls;
xfitted = xs(:,1:k) * xl(:,1:k)';
yfitted = xs(:,1:k) * yl(:,1:k)';
xresiduals = x - xfitted;
yresiduals = y - yfitted;
N=k+1;
BICCriterionY(k)=log(yresiduals'*yresiduals/T)+N*log(T)/T;
end
[minBIC,k_star]=min(BICCriterionY);

Is the above correct or do I also need to calculate the criterion for the intercept differently? Should I also calculate the BIC for xfitted as well? If yes, I am not quite sure how to do it.

Thank you in advance.