FAQ  Frequently Asked Questions
Issue:

How are the Qresiduals and Hotelling's T^2 (T^{2}) values calculated for PLS models?
Possible Solutions:

Q and T^2 are done in PLS exactly the as they are for PCA (see the PLS_Toolbox manual for a description) except that the basis that is being used for T^2 is the PLS loads rather than the PCA loads. For Q, we actually calculate the eigenvalues of the residual subspace and it is exactly the same as in PCA.
For T^2, there is an approximation made of the eigenvalues. If Tcal is the column vectors of scores from your calibration model (extract from the model.loads{1,1} field) :
f = diag(Tcal'*Tcal)/size(Tcal,1); f = sqrt(1./f);OR you can use:
f = sum(Tcal.^2)./size(Tcal,1); f = sqrt(1./f);Either method gives you f, a normalized vector of lengths of each of your original scores. Next, you take each of those lengths and divide your new scores (Tnew) by the corresponding length: (again, here are two methods of doing it)
Method 1:
T2 = sum( (Tnew * diag(f)).^2 ,2);Method 2:
for j=1:length(f); Tnew(:,j) = Tnew(:,j)*f(j); end T2 = sum( Tnew.^2 ,2);
Still having problems? Check our documentation Wiki or try writing our helpdesk at helpdesk@eigenvector.com