Improved modelling for low-correlated multiple responses by common-subset-of-independent-variables partial-least-squares

In this study, a new approach for PLS modelling for low-correlated multiple responses, called Common-Subset-ofIndependent-Variables Partial-Least-Squares, denoted as CSIV-PLS1, is proposed and evaluated. In CSIV-PLS1, for each response vector, individual PLS1 models with individual model complexities are developed, based on one common set of independent variables, obtained after variable selection by the Final Complexity Adapted Models method, using the absolute values of the PLS regression coefficients, denoted as FCAM-REG. CSIV-PLS1 combines a common variable set for all response vectors, which is a characteristic of PLS2, with the individual model complexity for each response, which is a characteristic of PLS1. These characteristics make CSIV-PLS1 more flexible than PLS2. The selective and predictive abilities of the proposed CSIV-PLS1 method are investigated using one simulated and four real data sets with low-correlated multiple responses from different sources. The simulated data set is used to test the general applicability of the CSIV-PLS1 method. The predictive abilities, measured by the RMSEP values, resulting from CSIV-PLS1 models, are statistically compared with those of the corresponding PLS1 and PLS2 models, using one-tailed paired t-tests. The selective ability of the CSIV-PLS1 method is good, because mostly variables with an informative meaning to the responses are selected. The RMSEP values resulting from the CSIV-PLS1 method are (i) significantly lower at the 95% confidence level than those of the corresponding PLS2 method, and (ii) borderline significantly lower at the 90-95% confidence level than those of the corresponding PLS1 methods. In case of low-correlated multiple responses, the predictive ability of the CSIV-PLS1 method is significantly better than that of the PLS2 method, and borderline significantly better than those of the corresponding PLS1 methods. Therefore, CSIV-PLS1 modelling may be an alternative for PLS1 or PLS2.