Partial Least Squares regression - confidence interval of the predicted variable (response)

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Gustavo Lunardon
Gustavo Lunardon 2023-1-20
评论： Gustavo Lunardon 2023-1-25
Hello all,
I am interested in obtaining confidence intervals for the response variable of PLS (Partial Least Squares Regression). Can someone help me on that? Here is my attempt at it:
% https://nl.mathworks.com/help/stats/partial-least-squares-regression-and-principal-components-regression.html
load spectra
X = NIR; % independent variables
y = octane; % dependent variables
PLS_comp = 3; % number of PLS components
[XL,yl,XS,YS,beta,PCTVAR,mse,stats] = plsregress(X,y,PLS_comp); % PLS regression
yfit = [ones(size(X,1),1) X]*beta; % Model fit
residuals = y - yfit; % Ordinary residuals vector
alpha_stat = 0.05; % Significance level
dgf = length(y) - PLS_comp - 1; % Degree of freedom
RMSE_model = sqrt(sum(residuals.^2)/dgf); % Degree of freedom corrected root-mean squared error (standard deviation estimator)
t_Student = tinv((1-alpha_stat/2),dgf); % t-value Student distribution
delta = t_Student*RMSE_model*sqrt(1+stats.T2); % CI boundaries
figure()
set(gcf,'color','white','position',[100 100 500 500])
errorbar(y,yfit,delta,'o')
hold on; grid minor;
hline = refline([1 0]);
hline.Color = 'k';
hline.LineStyle = ':';
xlabel('Measured')
ylabel('Predicted')
Questions are:
  • Is there a better (or simpler) way to do it? (maybe even using a MATLAB standard function). I tried to follow the guidelines of this paper here, in case someone is wondering about the degrees of freedom: 10.1016/j.chemolab.2009.11.003
  • Is this approach correct? The confidence intervals look too big to be correct
  • This T2 statistic from the stats struct is not retrievable for data outside the training data. How do I collect it for a new spectra? (if same approach is used). I cannot get confidence intervals of prediction the way I did it.
Kind regards,
Gustavo

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采纳的回答

Torsten
Torsten 2023-1-20
I did not look into your code in detail, but I think you could use the output structure "gof" from MATLAB's "fit" together with "confint" to compare with your statistical parameters.

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