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Techniques & Tools Microscopy, Spectroscopy

How to Score with Penalties

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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About the Author

John H. Kalivas

John H. Kalivas completed his doctorate in chemistry with analytical chemistry and chemometric focuses at the University of Washington in 1982 under the direction of Professor Bruce R. Kowalski. He joined the Department of Chemistry at Idaho State University in 1985 as an Assistant Professor and was promoted to Professor in 1994. He is author or coauthor of over 100 professional publications including papers, book chapters, and books. He serves as an Editor for the Journal of Chemometrics and an Associate Editor for Applied Spectroscopy. He also serves on the Editorial Boards of Analytical Letters and Talanta.

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