A Survey of Chemometric Methods Used in Spectroscopy

August 1st 2020We provide a scorecard of chemometric techniques used in spectroscopy. The tables and lists of reference sources given here provide an indispensable resource for anyone seeking guidance on understanding chemometric methods or choosing the most suitable approach for a given analysis problem.

Using Reference Materials, Part II: Photometric Standards

October 1st 2019Alignment of the instrument y-axis is a critical step for quantitative and qualitative measurements using spectroscopy. Here, we explain in detail how to use photometric standards for ultraviolet, visible, near infrared, infrared, and Raman spectroscopy.

More About CLS, Part 1: Expanding the Concept

June 1st 2019A newly discovered effect can introduce large errors in many multivariate spectroscopic calibration results. The CLS algorithm can be used to explain this effect. Having found this new effect that can introduce large errors in calibration results, an investigation of the effects of this phenomenon to calibrations using principal component regression (PCR) and partial least squares (PLS) is examined.

Using Reference Materials, Part I: Standards for Aligning the X-Axis

February 1st 2019The use of reference materials to align or test the wavelength–wavenumber axis for optical spectroscopy is essential for quantitative and qualitative methods. This article provides details for using reference materials with ultraviolet, visible, near-infrared, infrared, and Raman spectroscopy methods.

Calibration Transfer Chemometrics, Part II: A Review of the Subject

June 1st 2018Calibration transfer involves several strategies and mathematical techniques for applying a single calibration database consisting of samples, reference data, and calibration equations to two or more instruments. In this installment, we review the chemometric and tactical strategies used for the calibration transfer process.

Calibration Transfer Chemometrics, Part I: Review of the Subject

October 1st 2017Calibration transfer involves multiple strategies and mathematical techniques for applying a single calibration database to two or more instruments. Here, we explain the methods to modify the spectra or regression vectors to correct differences between instruments.

How to Select the Appropriate Degrees of Freedom for Multivariate Calibration

June 1st 2016This column addresses the issue of degrees of freedom (df) for regression models. The use of smaller degrees of freedom (df) (e.g., n or n-1) underestimates the size of the standard error; and possibly the larger df (e.g., n-k-1) overestimates the size of the standard deviation. It seems one should use the same df for both SEE and SECV, but what is a clear statistical explanation for selecting the appropriate df? It is a good time to raise this question once again and it seems there is some confusion among experts about the use of df for the various calibration and prediction situations - the standard error parameters should be comparable and are related to the total independent samples, data channels containing information (i.e., wavelengths or wavenumbers), and number of factors or terms in the regression. By convention everyone could just choose a definition but is there a more correct one that should be verified and discussed for each case? The problem with this subject is in computing the standard deviation using different df without a more rigorous explanation and then putting an over emphasis on the actual number derived for SEE and SECV, rather than on using properly computed confidence intervals. Note that confidence limit computations for standard error have been discussed previously and are routinely derived in standard statistical texts (4).

Statistics, Part I: First Foundation

October 1st 2015We present the first of a short set of columns dealing with the subject of statistics. This current series is organized as a “top down” view of the subject, as opposed to the usual literature (and our own previous) approach of giving “bottom up” description of the multitude of equations that are encountered. We hope this different approach will succeed in giving our readers a more coherent view of the subject, as well as persuading them to undertake further study of the field.

Optimizing the Regression Model: The Challenge of Intercept–Bias and Slope “Correction”

July 1st 2015The archnemesis of calibration modeling and the routine use of multivariate models for quantitative analysis in spectroscopy is the confounded bias or slope adjustments that must be continually implemented to maintain calibration prediction accuracy over time. A perfectly developed calibration model that predicted well on day one suddenly has to be bias adjusted on a regular basis to pass a simple bias test when predicted values are compared to reference values at a later date. Why does this problem continue to plague researchers and users of chemometrics and spectroscopy?

Units of Measure in Spectroscopy, Part III: Summary of Our Findings

February 1st 2015What is it that we thought we knew that we have learned "ain't so" from the work reported in this series of columns?Volume 30 Number 2Pages 24-33What is it that we thought we knew that we have learned "ain't so" from the work reported in this series of columns?

Units of Measure in Spectroscopy, Part II: What Does It Mean?

September 1st 2014Now that we have shown the relationships between different units for concentration, we continue by demonstrating their effects on the data we collected and used for our examples. What are the ramifications and consequences of these findings?

Calibration Transfer, Part V: The Mathematics of Wavelength Standards Used for Spectroscopy

June 1st 2014What are the techniques and mathematics used to compute uncertainty, and the optimum methods for maintaining wavelength accuracy within instrumentation over time, when considering measurement condition changes?

Units of Measure in Spectroscopy, Part I: It's the Volume, Folks!

February 14th 2014The data show that different units of measurement have different relationships to the spectral values, for reasons having nothing to do with the spectroscopy. This finding disproves the assumption that different measures of concentration are equivalent except, perhaps, for a constant scaling factor.

Calibration Transfer, Part III: The Mathematical Aspects

June 1st 2013Calibration transfer is a series of techniques used to apply a single spectral database, and the calibration model developed using that database, to two or more instruments. Here, we review the mathematical approaches and issues related to the calibration transfer process.

Statistics and Chemometrics for Clinical Data Reporting, Part II: Using Excel for Computations

October 1st 2009In this installment, columnists Jerome Workman and Howard Mark describe the statistical underpinnings related to computation and interpretation of chemometric methods and statistics for reporting clinical quantitative measurement methods.

Statistics and Chemometrics for Clinical Data Reporting, Part I

June 1st 2009This article describes the application of chemometric methods and statistics for reporting clinical quantitative measurement methods. The equations and terminology are consistent with the Clinical and Laboratory Standards Institute (CLSI) guidelines. These chemometric and statistical methods describe the accuracy and precision of a test method compared to a reference method for a single analyte determination. Part I will introduce these concepts and Part II will discuss the statistical underpinnings in greater detail.

The Long, Complicated, Tedious, and Difficult Route to Principal Components: Part VI

February 1st 2009This column is a continuation of the set we have been working on to explain and derive the equations behind principal components (1–5). As we usually do, when we continue the discussion of a topic through more than one column, we continue the numbering of equations from where we left off.

Addendum to Chemometrics in Spectroscopy

June 1st 2007This column is the continuation of a series (1-5) dealing with the rigorous derivation of the expressions relating the effect of instrument (and other) noise to its effects on the spectra we observe. Our first column in this series was an overview. While subsequent columns dealt with other types of noise sources, the ones listed analyzed the effect of noise on spectra when the noise is constant detector noise (that is, noise that is independent of the strength of the optical signal). Inasmuch as we are dealing with a continuous series of columns, on this branch in the thread of the discussion, we again continue the equation numbering and use of symbols as though there were no break. The immediately previous column (5) was the first part of this set of updates of the original columns.

Linearity in Calibration: Quantifying Nonlinearity, Part II

January 1st 2006At this point in our series dealing with linearity, we have determined that the data under investigation do indeed show a statistically significant amount of nonlinearity, and we have developed a way of characterizing that nonlinearity. Our task now is to come up with a way to quantify the amount of nonlinearity, independent of the scale of either variable, and even independent of the data itself.

Chemometrics in Spectroscopy ? Linearity in Calibration: Quantifying Nonlinearity, Part II (PDF)

January 1st 2006At this point in our series dealing with linearity, we have determined that the data under investigation do indeed show a statistically significant amount of nonlinearity, and we have developed a way of characterizing that nonlinearity. Our task now is to come up with a way to quantify the amount of nonlinearity, independent of the scale of either variable, and even independent of the data itself.

Chemometrics in Spectroscopy Linearity in Calibration: Quantifying Non-linearity

December 1st 2005This column presents results from some computer experiments designed to assess a method of quantifying the amount of non-linearity present in a dataset, assuming that the test for the presence of non-linearity already has been applied and found that a measurable, statistically significant degree of non-linearity exists.

Chemometrics and PAT: What Does It All Mean? (PDF)

January 2nd 2005A paradigm shift is required for chemists and engineers to best utilize chemometrics in their processes. This change demands that one not be too fixated upon ideal textbook thermodynamic models but instead continually check these models using real-time data input and chemometric analysis. The author discusses implementation strategies and the benefits that chemometrics can bring to the process environment.