Abstract
Partial least squares (PLS) regression has become a popular technique within the chemometric community, particularly for dealing with calibration problems. An important aspect of calibration is the implicit requirement to predict values for future samples. The PLS predictor is non-linear with a presently unknown statistical distribution. We consider approaches for providing prediction intervals rather than point predictions based on sample reuse strategies and, by application of an algorithm for calculating the first derivative of the PLS predictor, local linear approximation. We compare these approaches, together with a naive approach which ignores the non-linearities induced by the PLS estimation method, using a simulated example. © 1997 John Wiley & Sons, Ltd.
Keywords
Partial least squares regressionCalibrationComputer scienceLinear regressionStatisticsMathematicsRegressionLeast-squares function approximation
Affiliated Institutions
Related Publications
Partial least squares regression and projection on latent structure regression (PLS Regression)
Abstract Partial least squares (PLS) regression ( a.k.a. projection on latent structures) is a recent technique that combines features from and generalizes principal component a...
Consistent Partial Least Squares for Nonlinear Structural Equation Models
Partial Least Squares as applied to models with latent variables, measured indirectly by indicators, is well-known to be inconsistent. The linear compounds of indicators that PL...
Regression methods for high dimensional multicollinear data
To compare their performance on high dimensional data, several regression methods are applied to data sets in which the number of exploratory variables greatly exceeds the sampl...
A Comparison of Least Squares and Latent Root Regression Estimators
Miilticollinesrity among the columns of regressor variables is known to cause severe distortion of the least squares estimates of the parameters in a multiple linear regression ...
A fast non-negativity-constrained least squares algorithm
In this paper a modification of the standard algorithm for non-negativity-constrained linear least squares regression is proposed. The algorithm is specifically designed for use...
Publication Info
- Year
- 1997
- Type
- article
- Volume
- 11
- Issue
- 1
- Pages
- 39-52
- Citations
- 118
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
118
OpenAlex
Cite This
Michael C. Denham
(1997).
Prediction intervals in partial least squares.
Journal of Chemometrics
, 11
(1)
, 39-52.
https://doi.org/10.1002/(sici)1099-128x(199701)11:1<39::aid-cem433>3.0.co;2-s
Identifiers
- DOI
- 10.1002/(sici)1099-128x(199701)11:1<39::aid-cem433>3.0.co;2-s