Hi Jeremy,
To calculate Q residuals and T2 values from the outputs of ‘plsregress’ function in MATLAB and determine if a new observation is an outlier or not, you can go through the following steps and the attached code snippets:
1. Perform the PLS regression and preprocess the new data that you want to observe.
% Perform PLS regression
[XL, YL, XS, YS, BETA, PCTVAR, MSE, STATS] = plsregress(xcal, ycal, ncomp);
2. Project the data onto the latent space using the loading matrix (XL) from the ‘plsregress’ function, which gives the scores for the new observations.
t_val = xval0 * XL;
3. Calculate the T2 statistic by using the scores (XS) and the variance captured by each principal component.
% T² value
T2_val = (t_val ./ sqrt(var(XS))) * t_val';
4. For Q residuals, reconstruct the observation in the original space using the scores and loadings and calculate the residuals as the difference between the original and reconstructed observation.
% Q residuals
xval_pred = t_val * XL';
xval_residual = xval0 - xval_pred;
Q_val = sum(xval_residual.^2);
5. For assessing outliers, you can compare the calculated T2 and Q residual values to the pre-defined thresholds.
To know more about the ‘plsregress’ function in MATLAB, you can go through the following page:
Hope this works for you!
