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

Question

Gustavo Lunardon 2023-1-20

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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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Answer 1

Torsten 2023-1-20

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https://ww2.mathworks.cn/matlabcentral/answers/1897780-partial-least-squares-regression-confidence-interval-of-the-predicted-variable-response#answer_1153065

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.