How to Score with Penalties
Could ridge regression and other penalty models be the future of spectroscopy calibration?
John H. Kalivas |
Calibration for an analyte using spectroscopic techniques requires a model: the mathematical relationship between the analyte concentration, for example, and the instrumental signal. Once a model is obtained, it can be used to predict future samples. A spectral calibration model can be obtained by univariate regression, if an appropriate sensor (for example, wavelength) can be identified, or by multivariate regression. The univariate model is based on the common least squares (LS) criterion, minimizing the sum of the squares of residuals or the degree of fit. This is the trendline command in Excel many are familiar with. It is also the same measure used in multivariate regression methods, such as partial least squares (PLS); however, with PLS, projections of the measured data are used instead of the actual measured data. An upshot of the PLS projections is that the size of the regression vector shrinks to lower the variance relative to the ordinary LS (OLS) solution. The regression vector magnitude depends on the number of latent variables (LVs) used in a projection, which can be considered the PLS discrete tuning parameter.
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