Chemometrics in Spectroscopy (Second Edition) [2 ed.] 9780128053096

Table of contents :
Front Cover
Chemometrics in Spectroscopy
Copyright
Dedication
Contents
Preface to the First Edition
Preface to the Second Edition
The Book Companion
Chapter 1: A New Beginning
Multivariate Normal Distribution
Matrix Operations
References
Further Reading
Section 1: Elementary Matrix Algebra
Chapter 2: Elementary Matrix Algebra: Part 1
Matrix Operations
Matrix Addition
Subtraction
Matrix Multiplication
Matrix Division
Inverse of a Matrix
Transpose of a Matrix
Elementary Operations for Linear Equations
The Solution
Summary
References
Chapter 3: Elementary Matrix Algebra: Part 2
Elementary Matrix Operations
Calculating the Inverse of a Matrix
Summary
References
Section 2: Matrix Algebra and Multiple Linear Regression
Chapter 4: Matrix Algebra and Multiple Linear Regression: Part 1
Quasialgebraic Operations
Multiple Linear Regression
The Least Squares Method
References
Chapter 5: Matrix Algebra and Multiple Linear Regression: Part 2
The Power of Matrix Mathematics
References
Chapter 6: Matrix Algebra and Multiple Linear Regression: Part 3-The Concept of Determinants
References
Chapter 7: Matrix Algebra and Multiple Linear Regression: Part 4-Concluding Remarks
A Word of Caution
Reference
Section 3: Experimental Designs
Chapter 8: Experimental Designs, Part 1: Introduction
References
Chapter 9: Experimental Designs, Part 2: One-Way ANOVA*
References
Chapter 10: Experimental Designs, Part 3: Two-Factor Designs*
Chapter 11: Experimental Designs, Part 4: Varying Parameters to Expand the Design*
Introduction to Factorial Designs
References
Chapter 12: Experimental Designs, Part 5: One-at-a-Time Designs*
References
Chapter 13: Experimental Designs, Part 6: Sequential Designs*
References
Chapter 14: Experimental Designs, Part 7: β, the Power of a Test*
Reference
Chapter 15: Experimental Designs, Part 8: β, the Power of a Test (Continued)*
Reference
Chapter 16: Experimental Designs, Part 9: Sequential Designs (Concluded)*
Section 4: Analytic Geometry
Chapter 17: Analytic Geometry: Part 1-The Basics in Two and Three Dimensions
The Distance Formula
Direction Notation
The Cosine Function
Direction in 3D Space
Defining Slope in Two Dimensions
Recommended Reading
Chapter 18: Analytic Geometry: Part 2-Geometric Representation of Vectors and Algebraic Operations
Vector Multiplication (Scalar x Vector)
Vector Division (Vector Scalar)
Vector Addition (Vector + Vector)
Vector Subtraction (Vector - Vector)
Chapter 19: Analytic Geometry: Part 3-Reducing Dimensionality
Reducing Dimensionality
3D to 2D by Projection
2D Into 1D by Rotation
Chapter 20: Analytic Geometry: Part 4-The Geometry of Vectors and Matrices
Row Vectors in Column Space
Column Vectors in Row Space
Principal Components for Regression Vectors
Recommended Reading
Section 5: Regression Techniques
Chapter 21: Calculating the Solution for Regression Techniques: Part 1-Multivariate Regression Made Simple
References
Chapter 22: Calculating the Solution for Regression Techniques: Part 2-Principal Component(s) Regression Made Simp
References
Chapter 23: Calculating the Solution for Regression Techniques: Part 3-Partial Least Squares Regression Made Simple
References
Chapter 24: Calculating the Solution for Regression Techniques: Part 4-Singular Value Decomposition
References
Chapter 25: Interlude: Looking Behind and Ahead*
Reference
Chapter 26: A Simple Question*
References
Chapter 27: Challenges: Unsolved Problems in Chemometrics*
So What Are These Problems?
Section 6: Linearity in Calibration
Chapter 28: Linearity in Calibration- Act I*
Chapter 29: Linearity in Calibration-Act II Scene I
References
Chapter 30: Linearity in Calibration-Act II Scene II: Reader Responses*
Reference
Chapter 31: Linearity in Calibration-Act II Scene III*
References
Chapter 32: Linearity in Calibration-Act II Scene IV*
References
Chapter 33: Linearity in Calibration-Act II Scene V*
References
Section 7: Collaborative Laboratory Studies
Chapter 34: Collaborative Laboratory Studies: Part 1-A Blueprint
Experimental Design
Analytical Methods
Sample Collection and Handling
Method A and B Analysis
Results and Data Analysis
Comparing All Laboratories and All Methods for Precision and Accuracy
References
Chapter 35: Collaborative Laboratory Studies: Part 2-Using ANOVA
ANOVA Test Comparisons for Laboratories and Methods (ANOVA_s4 Worksheet)
ANOVA Test Comparisons (Using ANOVA_s2 Worksheet)
References
Chapter 36: Collaborative Laboratory Studies: Part 3-Testing for Systematic Error
Testing for Systematic Error in a Method: Comparison Test for a Set of Measurements Versus True Value-Spiked Recovery Metho ...
References
Chapter 37: Collaborative Laboratory Studies: Part 4-Ranking Test
Ranking Test for Laboratories and Methods (Manual Computations)
Reference
Chapter 38: Collaborative Laboratory Studies: Part 5-Efficient Comparison of Two Methods
Computations for Efficient Comparison of Two Methods (Comp_Meth Worksheet)
Measuring the Precision and Standard Deviation of the Methods (Youden/Steiner)
Sr2 ratio
SD2 ratio
Enter alpha value as α2
Summary
References
Chapter 39: Collaborative Laboratory Studies: Part 6-MathCad Worksheet Text
References
Section 8: Analysis of Noise
Chapter 40: Is Noise Brought by the Stork? Analysis of Noise-Part 1*
References
Chapter 41: Analysis of Noise-Part 2*
Appendix: Proof That the Variance of a Sum Equals the Sum of the Variances
References
Chapter 42: Analysis of Noise-Part 3*
References
Chapter 43: Analysis of Noise-Part 4*
Reference
Chapter 44: Analysis of Noise-Part 5*
Update
Continuation
References
Chapter 45: Analysis of Noise-Part 6*
Chapter 46: Analysis of Noise-Part 7
Variation of the Reflectance Due to Noise
Noise of the KM Function
Expressing the Variations in Terms of Measured Energies
Passing Into the Statistical Domain
Optimizing the KM Function
Go to the Statistical Domain
Summary
Chapter 47: Analysis of Noise-Part 8*
Effect of Noise on Computed Transmittance
Computed Transmittance Noise
Reference
Chapter 48: Analysis of Noise-Part 9*
References
Chapter 49: Analysis of Noise-Part 10*
Reference
Chapter 50: Analysis of Noise-Part 11*
Discussion
Reference
Chapter 51: Analysis of Noise-Part 12*
Chapter 52: Analysis of Noise-Part 13*
References
Chapter 53: Analysis of Noise-Part 14*
Reference
Chapter 54: Analysis of Noise-Part 15*
Preliminary Steps
Evaluation of the Function
Noise
Reference
Section 9: Derivatives
Chapter 55: Derivatives in Spectroscopy: Part 1-The Behavior of the Theoretical Derivative*
The Behavior of Theoretical Derivatives
The Behavior of Computed Derivatives
References
Chapter 56: Derivatives in Spectroscopy: Part 2-The ``True´´ Derivative*
Better Derivative Approximations
References
Chapter 57: Derivatives in Spectroscopy: Part 3-Computing the Derivative (the Savitzky-Golay Method)*
Methods of Computing the Derivative
Limitations of the Savitzky-Golay Method
Extensions to the Savitzky-Golay Method
References
Chapter 58: Derivatives in Spectroscopy: Part 4-Calibrating With Derivatives*
References
Chapter 59: Corrections and Discussion Regarding Derivatives*
Section 10: Goodness of Fit Statistics
Chapter 60: Comparison of Goodness of Fit Statistics for Linear Regression: Part 1-Introduction
Reference
Chapter 61: Comparison of Goodness of Fit Statistics for Linear Regression: Part 2-The Correlation Coefficient
References
Chapter 62: Comparison of Goodness of Fit Statistics for Linear Regression: Part 3-Computing Confidence Limits for the Co ...
Testing Correlation for Different Size Populations
References
Chapter 63: Comparison of Goodness of Fit Statistics for Linear Regression: Part 4-Confidence Limits for Slope and Intercept
References
Section 11: More About Linearity in Calibration
Chapter 64: Linearity in Calibration, Act III Scene I: Importance of (Non)linearity*
Why Is Nonlinearity Important?
References
Chapter 65: Linearity in Calibration, Act III Scene II: A Discussion of the Durbin-Watson Statistic, a Step in the Right
References
Chapter 66: Linearity in Calibration, Act III Scene III: Other Tests for Nonlinearity*
F-test
Normality of Residuals
Chapter 67: Linearity in Calibration, Act III Scene IV: How Test for Nonlinearity*
Conclusion
Appendix A: Derivation and Discussion of the Formula in Eq. (67-11)
References
Chapter 68: Linearity in Calibration, Act III Scene V: Quantifying Nonlinearity*
References
Chapter 69: Linearity in Calibration, Act III Scene VI: Quantifying Nonlinearity, Part II, and a News Flash*
News Flash!!
References
Section 12: Connecting Chemometrics to Statistics
Chapter 70: Connecting Chemometrics to Statistics: Part 1-The Chemometrics Side*
References
Chapter 71: Connecting Chemometrics to Statistics: Part 2-The Statistics Side*
Multivariate ANOVA
References
Section 13: Limitations in Analytical Accuracy
Chapter 72: Limitations in Analytical Accuracy: Part 1-Horwitzs Trumpet
References
Chapter 73: Limitations in Analytical Accuracy: Part 2-Theories to Describe the Limits in Analytical Accuracy
Detection Limit for Concentrations Near Zero
References
Chapter 74: Limitations in Analytical Accuracy: Part 3-Comparing Test Results for Analytical Uncertainty
Uncertainty in an Analytical Measurement
Comparison Test for a Single Set of Measurements Versus a True Analytical Result
Comparison Test for Two Sets of Measurements
Calculating the Number of Measurements Required to Establish a Mean Value (or Analytical Result) With a Prescribed Uncertai ...
The Q-Test for Outliers [1-3]
Summation of Variance From Several Data Sets
References
Chapter 75: The Statistics of Spectral Searches
Common Spectral Matching Approaches
Mahalanobis Distance Measurements
Euclidean Distance
Common Spectral Matching (Correlation or Dot Product)
References
Chapter 76: The Chemometrics of Imaging Spectroscopy
Image Projection of Spectroscopic Data
References
Chapter 77: Corrections to Analysis of Noise-Part 1*
Alternate Analysis
Chapter 78: Corrections to Analysis of Noise-Part 2*
Absorbance Noise in the ``High-Noise´´ Regime
Chapter 79: What Can NIR Predict?*
Part A-Results From a Model Created Using Real Reference Values
Part B-Results from a Model Created Using Random Reference Values
Part C-So What Does It All Mean?
References
Section 14: Derivations of Principal Components
Chapter 80: The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When Youre Through Reading T ...
Some Preliminary Discussion
Some Preliminary Results
Application of the ANOVA Principle
Appendix A: Matrices and Matrix Notation
Special Matrices
Key Matrix Operations
References
Chapter 81: The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When Youre Through Reading T ...
Chapter 82: The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When Youre Through Reading T ...
Appendix B
Reference
Chapter 83: The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When youre Through Reading T ...
Appendix C
References
Chapter 84: The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When youre Through Reading T ...
References
Chapter 85: The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When Youre Through Reading T ...
Summary
Chapter 86: The Long, Complicated, Tedious, and Difficult Route to Principal Components (or, When Youre Through Reading T ...
Section 15: Clinical Data Reporting
Chapter 87: Statistics and Chemometrics for Clinical Data Reporting, Part 1
Introduction
Definitions
Measurement Error
Accuracy
Trueness and Bias
Precision
Sample Data Calculations
Computation of the Regression Line
Pearson Product-Moment Correlation Coefficient (r)
Coefficient of determination (R2)
Slope (m0)
y-Intercept (i)
References
Chapter 88: Statistics and Chemometrics for Clinical Data Reporting, Part 2 (Using Excel for Computations)
Introduction
Basic Definitions
Measurement Error
Accuracy
Trueness and Bias
Standard Deviation (as a Measure of Repeatability)
Precision
Computation of the Regression Line
Coefficient of Determination (R2)
Slope (m0)
y-Intercept (i)
Linear Regression Corrected Results
References
Chapter 89: Statistics and Chemometrics for Clinical Data Reporting, Part 3 (Using Excel for Data Plotting)
Introduction
Comparing a Reference Method to a Second Test Method
Correcting One Analytical Method to Report Values of a Second Method
Comparisons of Two Analytical Methods
Bland-Altman Plot
Tukey Mean-Difference Plot
References
Section 16: Classical Least Squares (CLS)
Chapter 90: Classical Least Squares, Part 1: MathematicalTheory*
The Mathematics Behind the CLS Method
References
Chapter 91: Classical Least Squares, Part 2: MathematicalTheory Continued*
References
Chapter 92: Classical Least Squares, Part 3: Spectroscopic Theory*
Equivalence of Spectra and Numbers
References
Chapter 93: Classical Least Squares, Part 4: Spectroscopic Theory Continued*
Chapter 94: Classical Least Squares, Part 5: ExperimentalResults*
Experimental
The Data
Postscript
Reference
Chapter 95: Classical Least Squares, Part 6: Spectral Results*
Chapter 96: Classical Least Squares, Part 7: Spectral Reconstruction of Mixtures*
Adding Some Calculations
Chapter 97: Classical Least Squares, Part 8: Comparison of CLS Values With Known Values*
Troubleshooting
The Search for Composition
First Alternate Unit Considered
Second Alternate Unit Considered
Third Alternate Unit Considered
Chapter 98: Classical Least Squares, Part 9: Spectral Results from a Second Laboratory*
Spectral Results
References
Chapter 99: Classical Least Squares, Part 10: Numerical Results From the Second Laboratory*
Reference
Chapter 100: Classical Least Squares, Part 11: Comparison of Results From the Two Laboratories Continued
The Light Dawns
Section 17: Transfer of Calibrations
Chapter 101: Transfer of Calibrations, Part 1*
Introduction
Experimental
Results
Discussion
Conclusions
Definition
Summary
References
Chapter 102: Calibration Transfer, Part 2: The Instrumentation Aspects
Introduction
Modeling Approaches
Instrument Types
Standardization Methods
Instrument Comparison and Evaluation Methods
Instrument Optical Quality Performance Tests
Wavenumber Accuracy Test
Wavenumber Repeatability Test
Absorbance/Response Accuracy Test
Absorbance/Response Repeatability Test
Photometric Linearity Test
Photometric Noise Test
Signal Averaging Test
Random Noise Test
Noise Test (Including Medium- or Short-Term Drift)
Noise Test (Including Long-Term Drift)
Signal Averaging Test
Instrument Line Shape Test
Measurements of Laser Line
Summary and Test Data Analysis Considerations
Summary Specifications for Instrument ``Alikeness´´ Testing
References
Chapter 103: Calibration Transfer, Part 3: The Mathematical Aspects
Introduction
The Mathematical Approaches to Calibration Transfer
What to Compare When Transferring Calibrations?
Virtual Instrument Standardization
Bias or Slope Adjustments of Predicted Results Cross Parent and Child Instruments
Bias (Means) One-Sample t-Test Between Parent and Child Instruments
Bias (Means) Two-Sample t-Test Between Parent and Child Instruments
Comparing the Correlation Coefficients Between Parent and Child Instruments Using the (r-to-z Transform) Significance Test
Slope Significance Limit Test Between Parent and Child Instruments
Developing Global or Robust Models Including Variation Between Instruments
Augmenting Models Over time
Sample Selection to Improve Spectral Data
Spectral Data Transformation
Special Standardization Mathematical Approaches
Local Methods
Use of Indicator Variables
Summary
References
Chapter 104: Calibration Transfer, Part 4: Measuring the Agreement Between Instruments Following Calibration Transfer
Introduction
How to Tell If Two Instrument Predictions, or Method Results, Are Statistically Alike
Standard Uncertainty and Relative Standard Uncertainty
Uncertainty Defined
Relative Standard Uncertainty
Bland-Altman ``Limits of Agreement´´
Conclusion
References
Additional Reading
Chapter 105: Calibration Transfer, Part 5: The Mathematics of Wavelength Standards Used for Spectroscopy
Introduction
Different Approaches to Alignment of the Wavelength Axis
The NIST Uncertainty Number for SRMs
Commercial Instrument Wavelength Data
The Relative Standard Uncertainty Across Commercial Instruments
The Confidence Levels and Uncertainty Across Commercial Instrument Manufacturers A Through D (Table 105-3)
Using a NIST-Like Uncertainty Measurement
References
Chapter 106: Calibration Transfer, Part 6: The Mathematics of Photometric Standards Used for Spectroscopy
Introduction
Different Approaches to Alignment of the Photometric Axis
The NIST Uncertainty Number for SRMs
Commercial Instrument Photometric Data
Measurement of Photometric Accuracy
Measurement of Photometric Precision
Estimating the Relative Uncertainty Across the Tested Commercial Instruments
References
Section 18: The Importance of Units of Measure
Chapter 107: Units of Measure in Spectroscopy, Part 1: and Then the Light Dawned*
Reference
Chapter 108: Units of Measure in Spectroscopy, Part 2: It's the Volume, Folks!*
Progress
References
Chapter 109: Units of Measure in Spectroscopy, Part 3: What Does It All Mean*
A Short Review
The Mathematics
References
Chapter 110: Units of Measure in Spectroscopy, Part 4: Summary of Our Findings
Summary of Our Findings
CLS Versus Beer's Law
Meaning of ``Concentration´´
Calibration Transfer
Partial Molal Volumes
References
Chapter 111: Units of Measure in Spectroscopy, Part 5: The ``Mythbusters´´ and Spectral Reconstruction
Calculation of Pure-Component Spectra
References
Section 19: The Best Calibration Model
Chapter 112: Choosing the Best Regression Model
Introduction
Optimizing the Experimental Design for Calibration
Validating the Regression Model
Summary
References
Chapter 113: Optimizing the Regression Model: The Challenge of Intercept/Bias and Slope ``Correction´´
Introduction
The Initial Spectra and Calibration Equation
Changing the Wavelength Registration
Changing the Photometric Registration
Changing the Linewidth/Lineshape
Discussion and Review of Results
Confidence Limits for Predicted Values From a Regression
Confidence Limits for Slope From a Regression
Confidence Limits for Intercept/Bias From a Regression
Summary of Results
References
Section 20: Statistics
Chapter 114: Statistics, Part 1: First Foundation*
Introduction
The Foundations
First Foundation: Probability Theory
Reference
Chapter 115: Statistics, Part 2: Second Foundation*
Second Foundation: The Principle of Analysis of Variance
Analysis of Variance of Synthetic Data
The Effect of Adding a Perturbation
Reference
Chapter 116: Statistics, Part 3: Third Foundation*
Third Foundation: The Principle of Least Squares
References
Chapter 117: How to Select the Appropriate Degrees of Freedom for Multivariate Calibration
Introduction
The Subject of Degrees of Freedom
General Discussion
Summary
References
Chapter 118: Bias and Slope Correction
Introduction
Analysis of the Issues
Instrument Differences Versus SEP
Instrument Differences Versus Bias
Instrument Differences Versus Slope
Summary
References
Section 21: Outliers
Chapter 119: Outliers-Part 1: What Are Outliers?*
Introduction
What Are Outliers?
References
Chapter 120: Outliers-Part 2: Pitfalls in Detecting Outliers*
Detecting Outliers
Potential Pitfalls
References
Chapter 121: Outliers-Part 3: Dealing With Outliers*
Dealing With Outliers
Delete the Discordant Observation
Transform the Data
Accommodate the Discordant Observation(s)
Summary
References
Section 22: Spectral Transfer: Making Instruments Agree
Chapter 122: Calibration Transfer Chemometrics, Part 1: Review of the Subject
Introduction
Comparison of Transfer Methods
Instrument Alignment and Correction
The Master Instrument Concept
Filter Instrument Calibration Transfer
Direct Standardization and Piecewise Direct Standardization
Orthogonal Signal Correction
Procrustes Analysis
Finite Impulse Response
Maximum Likelihood Principal Component Analysis
Using Wavelength Standards for FT-NIR Alignment
Summary
References
Further Reading
Chapter 123: Calibration Transfer Chemometrics, Part 2: Review of the Subject
Introduction
Successive Projections Algorithm
Compressed Wavelet Domain is Called WTDS
Canonical Correlation Analysis
Positive Matrix Factorization
Spectral Regression
Wavelet Packet Transform Standardization
Stacked Partial Least-Squares Regression
Multiplicative Scatter (or Signal) Correction
Standard Normal Variate
Detrend
Classification Methods
Synthetic Calibration Spectra
Dispersive to FT Transfer
Dispersive to Handheld Transfer
Temperature Compensation
Two-Dimensional Method Transfer
Compensating for Extraneous Phenomena (or Unmodeled Variation)
Creating Transferable Calibrations in Mid-Infrared
Summary
References
Section 23: Applying Standard Reference Materials
Chapter 124: Using Reference Materials, Part 1: Standards for Aligning the x-Axis
Introduction
Ultraviolet Wavelength Measurement Standards
Holmium Oxide Liquid Wavelength Standard Traceable to SRM 2034
Holmium Oxide Glass Wavelength Standard Traceable to SRM 2034
Visible (Vis) Wavelength Measurement Standards
NIST SRM 2036 Reflectance Wavelength SRM
Near Infrared (NIR) Wavelength Measurement Standards
Polystyrene Reference Standard
SRM 1920a Former Reference Standard
Infrared Wavenumber Measurement Standards
NIST Wavenumber Standard Reference Material for Infrared
Raman Wavenumber Measurement Standards
Wavenumber Standard Reference Material for Raman
Summary
References
Further Reading
Chapter 125: Using Reference Materials, Part 2: Aligning the y-Axis
Introduction to Photometric Accuracy
Example of Reporting Photometric Accuracy
Photometric Correction for Absorbance-Based Spectrophotometers
Ultraviolet Photometric Standards
Visible (Vis) Photometric Standards
Near Infrared Reflectance Photometric Standards
Infrared Reflectance Photometric Standards
Raman Intensity Correction Standards
References
Section 24: More About CLS
Chapter 126: More About CLS, Part 1: Expanding the Concept*
Expanding Beyond the Small Dataset
Faux Linearity
References
Chapter 127: More About CLS, Part 2: Spectral Results and CLS (Not Requiring Constituent Values)*
Spectral Results Not Needing Constituent Values
CLS Results
Expanding Beyond CLS: Introducing PCA
Reference
Chapter 128: More About CLS, Part 3: Expanding the Analysis to Include Concentration Information (PCR and PLS)*
Expanding the Analysis to Include Concentration Information (PCR and PLS)
Effect of PCR Analysis
Effect on PLS Analysis
Results for Individual Analytes
Conclusions Reached
Reference
Index
Back Cover