Chemometrics in Spectroscopy

Revised Second Edition

Howard Mark, Jerry Workman Jr.

• Publisher: Academic Press
• Year: 2021
• eBook ISBN: 9780323911702
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Analytic Chemistry

Chemometrics in Spectroscopy, Revised Second Edition provides the reader with the methodology crucial to apply chemometrics to real world data. The book allows scientists using spectroscopic instruments to find explanations and solutions to their problems when they are confronted with unexpected and unexplained results. Unlike other books on these topics, it explains the root causes of the phenomena that lead to these results. While books on NIR spectroscopy sometimes cover basic chemometrics, they do not mention many of the advanced topics this book discusses. This revised second edition has been expanded with 50% more content on advances in the field that have occurred in the last 10 years, including calibration transfer, units of measure in spectroscopy, principal components, clinical data reporting, classical least squares, regression models, spectral transfer, and more. - Written in the column format of the authors' online magazine - Presents topical and important chapters for those involved in analysis work, both research and routine - Focuses on practical issues in the implementation of chemometrics for NIR Spectroscopy - Includes a companion website with 350 additional color figures that illustrate CLS concepts

Table of contents

• Chemometrics in Spectroscopy
• Chapter 1 A New Beginning …☆
• Chapter 2 Elementary Matrix Algebra: Part 1—Primitive operations: Addition, Subtraction, Multiplication, Division, Inverse, Transpose
• Chapter 3 Elementary Matrix Algebra: Part 2—Elementary Operations, Inverse of a Matrix
• Chapter 4 Matrix Algebra and Multiple Linear Regression: Part 1—Quasi-Algebraic Operations, Multiple Linear Regression, The Least Squares Method
• Chapter 5 Matrix Algebra and Multiple Linear Regression: Part 2—When There Are More Equations Than Unknowns, The Power of Matrix Mathematics
• Chapter 6 Matrix Algebra and Multiple Linear Regression: Part 3—The Concept of Determinants
• Chapter 7 Matrix Algebra and Multiple Linear Regression: Part 4—Concluding Remarks, and A Word of Caution
• Chapter 8 Experimental Designs, Part 1: Introduction
• Chapter 9 Experimental Designs, Part 2: One-Way ANOVA☆
• Chapter 10 Experimental Designs, Part 3: Two-Factor Designs☆
• Chapter 11 Experimental Designs, Part 4: Varying Parameters to Expand the Design☆
• Chapter 12 Experimental Designs, Part 5: One-at-a-Time Designs☆
• Chapter 13 Experimental Designs, Part 6: Sequential Designs☆
• Chapter 14 Experimental Designs, Part 7: β, the Power of a Test☆
• Chapter 15 Experimental Designs, Part 8: β, the Power of a Test (Continued)☆
• Chapter 16 Experimental Designs, Part 9: Sequential Designs (Concluded)☆
• Chapter 17 Analytic Geometry: Part 1—The Basics in Two and Three Dimensions
• Chapter 18 Analytic Geometry: Part 2—Geometric Representation of Vectors and Algebraic Operations
• Chapter 19 Analytic Geometry: Part 3—Reducing Dimensionality
• Chapter 20 Analytic Geometry: Part 4—The Geometry of Vectors and Matrices
• Chapter 21 Calculating the Solution for Regression Techniques: Part 1—Multivariate Regression Made Simple
• Chapter 22 Calculating the Solution for Regression Techniques: Part 2—Principal Component(s) Regression Made Simple
• Chapter 23 Calculating the Solution for Regression Techniques: Part 3—Partial Least Squares Regression Made Simple
• Chapter 24 Calculating the Solution for Regression Techniques: Part 4—Singular Value Decomposition
• Chapter 25 Interlude: Looking Behind and Ahead☆
• Chapter 26 A Simple Question☆
• Chapter 27 Challenges: Unsolved Problems in Chemometrics☆
• Chapter 28 Linearity in Calibration— Act I—A Thought Experiment Carried Out by Computer Simulation☆
• Chapter 29 Linearity in Calibration—Act II Scene I—A Firestorm Erupts and A Theoretical Explanation of Linearity
• Chapter 30 Linearity in Calibration—Act II Scene II—Details of Reader Responses☆
• Chapter 31 Linearity in Calibration—Act II Scene III—Summary of Reader Responses, and Our Commentary on Those Responses☆
• Chapter 32 Linearity in Calibration—Act II Scene IV—A Summary of Findings and Recommendations for Future Explorations☆
• Chapter 33 Linearity in Calibration—Act II Scene V—Effect of (Non) Linearity on PLS Algorithm☆
• Chapter 34 Collaborative Laboratory Studies: Part 1—A Blueprint
• Chapter 35 Collaborative Laboratory Studies: Part 2—Using ANOVA
• Chapter 36 Collaborative Laboratory Studies: Part 3—Testing for Systematic Error
• Chapter 37 Collaborative Laboratory Studies: Part 4—Ranking Test
• Chapter 38 Collaborative Laboratory Studies: Part 5—Efficient Comparison of Two Methods
• Chapter 39 Collaborative Laboratory Studies: Part 6—MathCad Worksheet Text
• Chapter 40 Is Noise Brought by the Stork? Analysis of Noise—Part 1—A Listing of the Sources of Spectroscopic Noise and Their Characteristics☆
• Chapter 41 Analysis of Noise—Part 2—The analysis of the effect of ‘constant’ detector noise on a transmission measurement☆
• Chapter 42 Analysis of Noise—Part 3—The Analysis of the Effect of ‘constant’ Detector Noise on the Absorbance, the Relative Absorbance (ΔA/A) and the Optimum Absorbance Value☆
• Chapter 43 Analysis of Noise—Part 4—The Analysis of the Effect of ‘constant’ Gaussian Detector Noise When the Noise Is Not Negligible Compared to the Signal☆
• Chapter 44 Analysis of Noise—Part 5—The Analysis of the Effect of ‘constant’ Gaussian Detector Noise When the Reference Energy Approaches Zero☆
• Chapter 45 Analysis of Noise—Part 6—The Analysis of the Effect of ‘constant’ Gaussian Detector Noise: Comparing the Effect of Noise in the Sample Channel Versus Noise in the Reference Channel☆
• Chapter 46 Analysis of Noise—Part 7—The Analysis of ‘constant’ Detector Noise on the Kubelka-Munk Function
• Chapter 47 Analysis of Noise—Part 8—Effect of Noise on the Computed Transmittance, Analysis of Uniformly Distributed Noise for Transmittance and Absorbance Values☆
• Chapter 48 Analysis of Noise—Part 9—Analysis of Poisson-Distributed Noise, Effects on Transmittance and Absorbance Values☆
• Chapter 49 Analysis of Noise—Part 10—Analysis of Poisson-Distributed Noise, Effects on Relative Absorbance☆
• Chapter 50 Analysis of Noise—Part 11—Analysis of Poisson-Distributed Noise, When the Noise Is Not Small Compared to the Reference Signal☆
• Chapter 51 Analysis of Noise—Part 12—Analysis of Poisson-Distributed Noise: Computation of the Transmittance Noise☆
• Chapter 52 Analysis of Noise—Part 13—Analysis of Poisson-Distributed Noise: Computation of the Absorbance Noise☆
• Chapter 53 Analysis of Noise—Part 14—Analysis of Noise Proportional to the Signal, Small-Noise Case☆
• Chapter 54 Analysis of Noise—Part 15—Analysis of Noise Proportional to the Signal, Large-Noise Case☆
• Chapter 55 Derivatives in Spectroscopy: Part 1—The Behavior of the Theoretical Derivative☆
• Chapter 56 Derivatives in Spectroscopy: Part 2—The “True” Derivative☆
• Chapter 57 Derivatives in Spectroscopy: Part 3—Computing the Derivative (the Savitzky-Golay Method)☆
• Chapter 58 Derivatives in Spectroscopy: Part 4—Calibrating With Derivatives☆
• Chapter 59 Corrections and Discussion Regarding Derivatives☆
• Chapter 60 Comparison of Goodness of Fit Statistics for Linear Regression: Part 1—Introduction
• Chapter 61 Comparison of Goodness of Fit Statistics for Linear Regression: Part 2—The Correlation Coefficient
• Chapter 62 Comparison of Goodness of Fit Statistics for Linear Regression: Part 3—Computing Confidence Limits for the Correlation Coefficient
• Chapter 63 Comparison of Goodness of Fit Statistics for Linear Regression: Part 4—Confidence Limits for Slope and Intercept
• Chapter 64 Linearity in Calibration, Act III Scene I: Importance of (Non)linearity☆
• Chapter 65 Linearity in Calibration, Act III Scene II: A Discussion of the Durbin-Watson Statistic, a Step in the Right Direction☆
• Chapter 66 Linearity in Calibration, Act III Scene III: Other Tests for Nonlinearity☆
• Chapter 67 Linearity in Calibration, Act III Scene IV: How Test for Nonlinearity☆
• Chapter 68 Linearity in Calibration, Act III Scene V: Quantifying Nonlinearity☆
• Chapter 69 Linearity in Calibration, Act III, Scene VI: Quantifying Nonlinearity, Part II: A Calculus-Based Approach, and A News Flash☆
• Chapter 70 Connecting Chemometrics to Statistics: Part 1—The Chemometrics Side☆
• Chapter 71 Connecting Chemometrics to Statistics: Part 2—The Statistics Side☆
• Chapter 72 Limitations in Analytical Accuracy: Part 1—Horwitz’s Trumpet
• Chapter 73 Limitations in Analytical Accuracy: Part 2—Theories to Describe the Limits in Analytical Accuracy
• Chapter 74 Limitations in Analytical Accuracy: Part 3—Comparing Test Results for Analytical Uncertainty
• Chapter 75 The Statistics of Spectral Searches
• Chapter 76 The Chemometrics of Imaging Spectroscopy
• Chapter 77 Corrections to Analysis of Noise—Part 1: Alternate Analysis of Transmittance Noise in the ‘large noise’ Regime☆
• Chapter 78 Corrections to Analysis of Noise—Part 2: Alternate Analysis of Absorbance noise in the ‘large noise’ Regime☆
• Chapter 79 What Can NIR Predict?☆
• Chapter 80 The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When You’re Through Reading This Set You’ll Know Why It's Always Done With Matrices)—Part 1: Introduction and Review
• Chapter 81 The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When You’re Through Reading This Set You’ll Know Why It's Always Done With Matrices)—Part 2: Our First Attempt☆
• Chapter 82 The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When You’re Through Reading This Set You’ll Know Why It's Always Done With Matrices)—Part 3: Multivariate Curve Fitting☆
• Chapter 83 The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When you’re Through Reading This Set You’ll Know Why It's Always Done With Matrices)—Part 4: The Lagrange Multiplier☆
• Chapter 84 The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When you’re Through Reading This Set You’ll Know Why It's Always Done With Matrices)—Part 5: Solving the Equations With Determinants☆
• Chapter 85 The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When You’re Through Reading This Set You’ll Know Why It's Always Done With Matrices)—Part 6: Solving the Equations Without Determinants☆
• Chapter 86 The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When You’re Through Reading This Set You’ll Know Why It's Always Done With Matrices)—Coda: Applying Constrained Univariate Calculations☆
• Chapter 87 Statistics and Chemometrics for Clinical Data Reporting, Part 1—Fundamentals
• Chapter 88 Statistics and Chemometrics for Clinical Data Reporting, Part 2 (Using Excel for Computations)
• Chapter 89 Statistics and Chemometrics for Clinical Data Reporting, Part 3 (Using Excel for Data Plotting)
• Chapter 90 Classical Least Squares, Part 1: MathematicalTheory☆
• Chapter 91 Classical Least Squares, Part 2: Mathematical Theory Continued☆
• Chapter 92 Classical Least Squares, Part 3: Spectroscopic Theory☆
• Chapter 93 Classical Least Squares, Part 4: Spectroscopic Theory Continued☆
• Chapter 94 Classical Least Squares, Part 5: ExperimentalResults☆
• Chapter 95 Classical Least Squares, Part 6: Spectral Results☆
• Chapter 96 Classical Least Squares, Part 7: Spectral Reconstruction of Mixtures☆
• Chapter 97 Classical Least Squares, Part 8: Comparison of CLS Values With Known Values☆
• Chapter 98 Classical Least Squares, Part 9: Spectral Results from a Second Laboratory☆
• Chapter 99 Classical Least Squares, Part 10: Numerical Results From the Second Laboratory☆
• Chapter 100 Classical Least Squares, Part 11: Comparison of Results From the Two Laboratories (Continued)
• Chapter 101 Transfer of Calibrations, Part 1: An Overview
• Chapter 102 Calibration Transfer, Part 2: The Instrumentation Aspects
• Chapter 103 Calibration Transfer, Part 3: The Mathematical Aspects
• Chapter 104 Calibration Transfer, Part 4: Measuring the Agreement Between Instruments Following Calibration Transfer
• Chapter 105 Calibration Transfer, Part 5: The Mathematics of Wavelength Standards Used for Spectroscopy
• Chapter 106 Calibration Transfer, Part 6: The Mathematics of Photometric Standards Used for Spectroscopy
• Chapter 107 Units of Measure in Spectroscopy, Part 1: … and Then the Light Dawned☆
• Chapter 108 Units of Measure in Spectroscopy, Part 2:It's the VOLUME, Folks!☆
• Chapter 109 Units of Measure in Spectroscopy, Part 3: What Does It All Mean☆
• Chapter 110 Units of Measure in Spectroscopy, Part 4: Summary of Our Findings
• Chapter 111 Units of Measure in Spectroscopy, Part 5: The “Mythbusters” and Spectral Reconstruction
• Chapter 112 Choosing the Best Regression Model
• Chapter 113 Optimizing the Regression Model: The Challenge of Intercept/Bias and Slope “Correction”
• Chapter 114 Statistics, Part 1: First FoundatioN: Probability Theory☆
• Chapter 115 Statistics, Part 2:Second FoundatioN: Analysis of Variance☆
• Chapter 116 Statistics, Part 3: Third FoundatioN: Least Squares☆
• Chapter 117 How to Select the Appropriate Degrees of Freedom for Multivariate Calibration☆
• Chapter 118 Bias and Slope Correction☆
• Chapter 119 Outliers—Part 1: What Are Outliers?
• Chapter 120 Outliers—Part 2:Pitfalls in Detecting Outliers☆
• Chapter 121 Outliers—Part 3: Dealing With Outliers☆
• Chapter 122 Calibration Transfer Chemometrics, Part 1: Review of the Subject
• Chapter 123 Calibration Transfer Chemometrics, Part 2: Review of the Subject☆
• Chapter 124 Using Reference Materials, Part 1: Standards for Aligning the x-Axis
• Chapter 125 Using ReferenceMaterials, Part 2:Aligning the y-Axis☆
• Chapter 126 More about cls, part 1: expanding the concept
• Chapter 127 More About CLS, Part 2: Spectral Results and CLS (Not Requiring Constituent Values)☆
• Chapter 128 More About CLS, Part 3: Expanding the Analysis to Include Concentration Information (PCR and PLS)☆
• Index