PLS2

PLS2 refers to a variant of Partial Least Squares (PLS) regression that extends the standard, single-output framework to multiple dependent variables. In PLS2, the predictor matrix X is related to a response matrix Y that contains two or more outcome variables. The method seeks latent variables that capture directions of maximum covariance between X and Y, yielding a lower-dimensional representation of the data while preserving predictive information for all responses simultaneously. Computational approaches commonly used with PLS2 include the NIPALS and SIMPLS algorithms, which iteratively extract score vectors and corresponding loadings and then deflate X and Y to reveal subsequent latent components.

Compared with PLS1, which handles one dependent variable, PLS2 exploits potential correlations among the multiple responses. This can improve predictive performance when the outcomes share information or when modeling them jointly reduces noise and redundancy in Y.

Applications of PLS2 are widespread in fields dealing with high-dimensional predictors and multivariate responses. In chemometrics, it is used for forensic spectroscopy, pharmaceutical analytics, and process monitoring. In bioinformatics and metabolomics, PLS2 supports modeling of multiple related phenotypes or metabolite sets from spectral or genomic data. It is also employed in econometrics and environmental science where several related response measures are modeled from common predictor variables.

Software implementations of multivariate PLS regression often label the method as PLS2 or provide multivariate Y support under the umbrella of PLS regression. Users should consult specific package documentation to confirm support for multiple responses and to select appropriate validation procedures.