Software for Implementing Partial Least Squares Regression

Partial Least Squares Regression (PLSR) is a statistical technique widely used in multivariate data analysis, particularly effective for handling datasets with multicollinearity issues. MATLAB, as a powerful mathematical computing platform, offers multiple approaches to implement PLSR algorithms.

In MATLAB, PLSR can be implemented using the Statistics and Machine Learning Toolbox. The primary function for this purpose is plsregress, which streamlines the modeling process by accepting predictor and response matrices as inputs. This function returns essential outputs including regression coefficients, score matrices, and loading matrices. The basic syntax follows: [XL,YL,XS,YS,BETA] = plsregress(X,Y,ncomp), where ncomp specifies the number of PLS components.

Key parameter configuration involves determining the optimal number of principal components, which significantly impacts model interpretation and predictive performance. MATLAB provides cross-validation capabilities through functions like crossval and cvpartition to help identify the ideal component count. Implementation typically involves iterative testing with different ncomp values and evaluating performance metrics like RMSE or Q².

Beyond core functionality, MATLAB supports comprehensive visualization of PLSR results through plotting tools. Users can generate variable importance plots (VIP scores), score plots showing sample distribution in latent space, and loading plots illustrating variable contributions. These graphical representations aid in understanding variable relationships and internal model structure using functions like plot, scatter, and biplot with appropriate label customization.