Multivariate calibration in which a dependent variable is regressed against the scores of a chosen number of factors obtained from principal-component analysis of the predictor variable.
Notes: - PCA decomposes the predictor variable data \(\boldsymbol{X}\) into \(k\) principal component factors \(\boldsymbol{\hat X}_{k} = \boldsymbol{T}_{k}\boldsymbol{P}_{k}^{\rm{T}}\), where \(k\) may be determined by cross validation. The dependent variable \(\boldsymbol{c}\) is then regressed against \(\boldsymbol{\hat X}_{k}\), \(\boldsymbol{c} = \boldsymbol{\hat X}_{k}\boldsymbol{\hat b}\).
- The factorization gives orthogonal factors, but no information about the predicted variable \(\boldsymbol{c}\) is used.
See also: multilinear regression, partial least squares
Source:
PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 435 (https://doi.org/10.1515/pac-2015-0605)