Principal component regression, ridge regression and ridge principal component regression in spectroscopy calibration

Abstract

SUMMARYRidge regression (RR) and principal component regression (PCR) are two popular methods intended to overcome the problem of multicollinearity which arises with spectral data. The present study compares the performances of RR and PCR in addition to ordinary least squares (OLS) and partial least squares (PLS) on the basis of two data sets. An alternative procedure that combines both PCR and RR is also introduced and is shown to perform well. Furthermore, the performance of the combination of RR and PCR is stable in so far as sufficient information is taken into account. This result suggests discarding those components that are unquestionably identified as noise, when the ridge constant tackles the degeneracy caused by components with small variances.

Interpretation of non-linear empirical data-based process models using global sensitivity analysis

“…Hence, the least-squares solution becomes ill-conditioned. This problem can be resolved by using ridge regression [25], partial least squares [26], or stepwise variable selection [27]. The major issue with polynomial regression is the prediction accuracy.…”

Bayesian linear regression and variable selection for spectroscopic calibration

“…M > N . There are a number of techniques to address this issue in the chemometric literature, including PCR [3], PLS [2], ridge regression [5] and variable selection [1].…”

“…Ridge regression [5] addresses the collinearity issue in ordinary least squares by introducing a regularization term λ ≥ 0 to penalize the magnitude of the regression parameters:…”

“…For the development of calibration models, a variety of techniques have been proposed to address the collinearity issue as a result of the large number of spectral wavelengths, including partial least squares (PLS) [2], principal component regression (PCR) [3], and ridge regression [5]. These models have become standard approaches to spectroscopic calibration, and they are available in most chemometric software packages.…”

Simultaneous determination of furosemide and spironolactone in pharmaceutical formulations by spectrophotometric method using principal component regression

“…Recently, multivariate calibration methods appear to be the proper techniques that show the best performance for complex mixture resolution (Vigneau et al, 1997;Massart et al, 1998;Lavine 2000;Haaland et al, 2000;Fearn, 2001;Brereton, 2003;Geladi, 2003;Ragno et al, 2004 One major use of PCR lies in overcoming the multicollinearity problem which arises when two or more of the explanatory variables are close to being collinear. PCR can aptly deal with such situations by excluding some of the lowvariance principal components in the regression step.…”