How to “Fit a three-way PLS regression model”

Fit a PLS model to the centered data
[Xfactors,Yfactors,Core,B] = npls(Xcalm,Ycalm,7);

Convert the parameters to scores and loadings
[T,Wj,Wk] = fac2let(Xfactors); 
[U,Q] = fac2let(Yfactors);

Use standard plots to evaluate the model.

Spectral score plot 
plot(T(:,1),T(:,2),'o') 
for i = 1:size(T,1) 
  text(T(i,1),T(i,2),num2str(i)) 
end 
title('SCORE PLOT') 
xlabel('Score 1') 
ylabel('Score 2')

T/U score plot
for j = 1:4
subplot(2,2,j)
plot(T(:,j),U(:,j),'o') 
  for i = 1:size(T,1) 
     text(T(i,j),U(i,j),num2str(i))
end
title('T/U PLOT') 
xlabel('Score 1') 
ylabel('Score 1')
end

Loading plot 
plot(EmAx,Wj(:,1:4)) 
title('Emission loading plot') 
xlabel('Wavelength/nm') 
ylabel('Loading')

Determine the optimal number of components
Ynpls=[]; 
RMSEP=[]; 
for i=1:7 
  yp=npred(Xtestm,i,Xfactors,Yfactors,Core,B)+mean(ColorCal); 
  Ynpls=[Ynpls yp]; 
  RMSEP=[RMSEP sqrt(mean( (yp-ColorVal)'*(yp-ColorVal) ))]; 
end 
plot([1:7],RMSEP) 
title('SCREE PLOT') 
xlabel('Number of components') 
ylabel ('RMSEP')   
plot(ColorCal,Ynpls(:,OptNumb),'o')

where OptNumb is the number you’ve determined as the optimal number of components (minimal RMSEP).

ylabel ('Predicted') 
xlabel ('Reference')