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Multivariate calibration, by Harald Martens and Tormod Naes
H Monitor
119
about integrating graphic and alphanumeric information - have been a simple standard for Macintosh users ever since the Macintosh became available. The conference took place in September 1933. Most of the contributions to this volume were submitted in May 1989. Because of the extremely fast development of this area, this useful booklet is apt to become outdated very soon and will then just be a historical document. ERNO PRETSCH Department of Organic Chemistry, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerland D
Multivariate Calibration, by Harald Martens and Tormod Naes Wiley, Chichester, 1989, XVIII + 420 pages, price E75.&3, ISBN O471-9y)97!&3 This book provides in-depth coverage of one of the major topics in chemometrics where no such coverage had been previously available: the field of multivariate calibration. The primary applications discussed in this book involve calibration of multicomponent spectroscopic assays with a heavy emphasis on near infrared spectroscopy. The authors are widely recognized as leading experts in this field. Large portions of the book are tutorial in nature and designed to help educate scientists on how to use multivariate calibration to
aolve practical problems. In this respect, the book is appropriate for a specialized graduate course. 3eparate sections are provided at the end of many subsections of each chapter to give theoretical details and summaries of the most recent research in multivariate calibration; thus, the book will also be of interest to researchers in chemometrics. Students can skip these sections during the fist reading without significant loss of comprehension and return to them as necessary. The book consists of eight chap ters: Introduction to Multivariate Calibration, Computational and Statistical Problems and Tools, Methods for Calibration, Assessment, Validation and Choice of Calibration Method, Outlier Detection, Data Selection and Experimental Design, Pretreatment and Linearization, and Multivariate Calibration Illustrated: Quantifying Litmus in Dirty Samples. Chapter 1 provides an introduction to multivariate calibration by way of the colorful analogies for which Harald Martens is well known. Interesting examples and problems are provided to illustrate the limitations of univariate calibration and the advantages of multivariate calibration. Chapter 2 provides a review of fundamental concepts in matrix algebra and statistics. Some parts of these reviews may be difficult for novices to understand; therefore, standard textbooks that provide a good introduction to linear algebra and multivariate statistics would be a useful companion for this book while reading Chapter 2. Chapter 2 also contains summaries of some mathematical and statisti-
aal problems specific to multivariate spectroscopic calibration that statisticians frequently fail to recognize. These special needs and circumstances are nicely summarized here. Chapter 3 is by far the largest in the book (164 pages) and covers all of the major techniques chemists have used for multivariate calibration, The authors start by describing univariate calibration using the inverse or ‘forward’ approach versus the classical or ‘reverse’ approach where the ‘forward’ approach involves a regression of the Y variables on the X variables, where the Y variables are the properties or concentrations of the components to be estimated and the X variables are the spectra scopic measurements. The classical or ‘reverse’ calibration is described as a regression of the X variables on the Y variables whereby the ‘measurement process is modeled, estimated and then inverted for prediction”. Here the authors point out subtle and interesting distinctions between the two techniques and conclude that the ‘reverse’ technique is best for interpolating values within an assay working range while the ‘forward’ technique is best for extrapolating the values outside the assay working range. Very clear descriptions of the ‘data compression’ methods, PCR and PLS, are provided. Chapter 3 also covers classical multivariate calibration based on Beeis Law from both the forward’ and ‘reverse’ approach. Interesting techniques for augmenting the classical multivariate calibration model to account for the presence of unknown interferences are presented. A number of miscellaneous techniques are introduced at the end of Chapter 3 including Fourier regres-
120
sion, Hrus&ka regression, the generalized standard addition method (GSAM), projection pursuit regression, curve resolution with non-negativity constraints, target transformation factor analysis, rank a&hi&on, stepwise multiple regression, ridge regression, non-linear regression, and nonparametric regression. Chapter 4 covers important techniques for validating calibration models. The authors begin by describing difI’erent sources of prediction error including the effect of model errors, for example, underfitting, overfitting, and local approximations of non-linear X-Y relationships, random noise, and lack of a representative calibration set or validation set. The authors defied the usual figures of merit for prediction error and bias and discuss their use for internal validation of models, cross validation, and external validation. The chapter ends by offering good practical advice on how to interpret plots of residuals, pick models having the optimum complexity, and improve prediction errors by the addition of more or better calibration data. Chapter 5 describes several techniques for detecting outliers which the authors define as “data elements that are irrelevant, grossly erroneous, or abnormal in some other way compared to the majority of the data”. They make an important distinction between outliers that are mistakes and outliers that provide valuable information for calibration. Several statistical techniques for detecting outliers are described in detail including the leverage of observations in the X variables @lahalanobis distance), large residuals in the X variables,
Chemometricsand IntelligentLaboratorySystemsn
large residuals in the predictA Y variables, leverage corrected Y variables, and plots showing the influence with objects with both large leverage and large leverage corrected residuals. Chapter 6 discusses techniques for applying the principles of experimental design to the selection of data for multivariate calibration, the object being to span all sources of variability in the calibration set. The difference between random calibration and controlled calibration is defined. The limiting effects of errors in both the X and Y variables on the precision of results are discussed. Factorial and simplex lattice designs are also discussed and recent applications from the literature and cluster analysis for the selection of calibration objects are presented. Chapter 7 discusses sources of non-linear response in multivariate calibration and ways for handling its presence. Chapter 7 begins by describing the use of data weighting to reduce the effect of variables with poor signal-tonoise ratios and several interesting schemes for calculating the weights. Some different sources of non-linear response in the concentration variables, Y, with respect to the response variables, X, are defined and techniques for treating the non-linearity are described. The authors show how multivariate techniques like PCR and PLS can compensate for non-linear response by inclusion of extra factors in an especially clear example. Other linearization procedures covered include the BoxCox Upower transformation”, the transformation, Kubelka-Munk polynomial functions of instrument response variables, and the Multiplicative Scatter Correction tecbni-
que. Several miscellaneous pretreatment options are mentioned at the end of Chapter 7, including the use of derivative spectra and smoothing. The final chapter of the book gives an example of how to apply many of the procedures described in Chapters 3-7 to develop a multivariate calibration of aqueous litmus solutions using ultraviolet/ visible spectra. The calibration and test samples contained variable amounts of an unknown dye in addition to litmus, variable amounts of an insoluble substance which made the solutions turbid, and variable levels of pH. Overall, the authors have put together a text which presents a sum of their research knowledge in multivariate calibration to date. Understandably, there are a tremendous number of ideas explored in the book which are not fully developed due to the ongoing nature of the authors’ research. Unfortunately, there are several recurring flaws which detract from the quality of this book including occasional spelling errors, grammatical errors, misused words, awkward phrasing, and low quality dot matrix plots. The book is reasonably expensive ($150) and for this price the editorial staff at John Wiley & Sons Ltd. could have been more careful in the production of this book. Despite the above flaws, students and researchers alike will find this book a valuable resource for many years to come. PJ. GEMPERLINE East Carolina University, Greenville, NC27858, U.S.A. m
119
about integrating graphic and alphanumeric information - have been a simple standard for Macintosh users ever since the Macintosh became available. The conference took place in September 1933. Most of the contributions to this volume were submitted in May 1989. Because of the extremely fast development of this area, this useful booklet is apt to become outdated very soon and will then just be a historical document. ERNO PRETSCH Department of Organic Chemistry, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerland D
Multivariate Calibration, by Harald Martens and Tormod Naes Wiley, Chichester, 1989, XVIII + 420 pages, price E75.&3, ISBN O471-9y)97!&3 This book provides in-depth coverage of one of the major topics in chemometrics where no such coverage had been previously available: the field of multivariate calibration. The primary applications discussed in this book involve calibration of multicomponent spectroscopic assays with a heavy emphasis on near infrared spectroscopy. The authors are widely recognized as leading experts in this field. Large portions of the book are tutorial in nature and designed to help educate scientists on how to use multivariate calibration to
aolve practical problems. In this respect, the book is appropriate for a specialized graduate course. 3eparate sections are provided at the end of many subsections of each chapter to give theoretical details and summaries of the most recent research in multivariate calibration; thus, the book will also be of interest to researchers in chemometrics. Students can skip these sections during the fist reading without significant loss of comprehension and return to them as necessary. The book consists of eight chap ters: Introduction to Multivariate Calibration, Computational and Statistical Problems and Tools, Methods for Calibration, Assessment, Validation and Choice of Calibration Method, Outlier Detection, Data Selection and Experimental Design, Pretreatment and Linearization, and Multivariate Calibration Illustrated: Quantifying Litmus in Dirty Samples. Chapter 1 provides an introduction to multivariate calibration by way of the colorful analogies for which Harald Martens is well known. Interesting examples and problems are provided to illustrate the limitations of univariate calibration and the advantages of multivariate calibration. Chapter 2 provides a review of fundamental concepts in matrix algebra and statistics. Some parts of these reviews may be difficult for novices to understand; therefore, standard textbooks that provide a good introduction to linear algebra and multivariate statistics would be a useful companion for this book while reading Chapter 2. Chapter 2 also contains summaries of some mathematical and statisti-
aal problems specific to multivariate spectroscopic calibration that statisticians frequently fail to recognize. These special needs and circumstances are nicely summarized here. Chapter 3 is by far the largest in the book (164 pages) and covers all of the major techniques chemists have used for multivariate calibration, The authors start by describing univariate calibration using the inverse or ‘forward’ approach versus the classical or ‘reverse’ approach where the ‘forward’ approach involves a regression of the Y variables on the X variables, where the Y variables are the properties or concentrations of the components to be estimated and the X variables are the spectra scopic measurements. The classical or ‘reverse’ calibration is described as a regression of the X variables on the Y variables whereby the ‘measurement process is modeled, estimated and then inverted for prediction”. Here the authors point out subtle and interesting distinctions between the two techniques and conclude that the ‘reverse’ technique is best for interpolating values within an assay working range while the ‘forward’ technique is best for extrapolating the values outside the assay working range. Very clear descriptions of the ‘data compression’ methods, PCR and PLS, are provided. Chapter 3 also covers classical multivariate calibration based on Beeis Law from both the forward’ and ‘reverse’ approach. Interesting techniques for augmenting the classical multivariate calibration model to account for the presence of unknown interferences are presented. A number of miscellaneous techniques are introduced at the end of Chapter 3 including Fourier regres-
120
sion, Hrus&ka regression, the generalized standard addition method (GSAM), projection pursuit regression, curve resolution with non-negativity constraints, target transformation factor analysis, rank a&hi&on, stepwise multiple regression, ridge regression, non-linear regression, and nonparametric regression. Chapter 4 covers important techniques for validating calibration models. The authors begin by describing difI’erent sources of prediction error including the effect of model errors, for example, underfitting, overfitting, and local approximations of non-linear X-Y relationships, random noise, and lack of a representative calibration set or validation set. The authors defied the usual figures of merit for prediction error and bias and discuss their use for internal validation of models, cross validation, and external validation. The chapter ends by offering good practical advice on how to interpret plots of residuals, pick models having the optimum complexity, and improve prediction errors by the addition of more or better calibration data. Chapter 5 describes several techniques for detecting outliers which the authors define as “data elements that are irrelevant, grossly erroneous, or abnormal in some other way compared to the majority of the data”. They make an important distinction between outliers that are mistakes and outliers that provide valuable information for calibration. Several statistical techniques for detecting outliers are described in detail including the leverage of observations in the X variables @lahalanobis distance), large residuals in the X variables,
Chemometricsand IntelligentLaboratorySystemsn
large residuals in the predictA Y variables, leverage corrected Y variables, and plots showing the influence with objects with both large leverage and large leverage corrected residuals. Chapter 6 discusses techniques for applying the principles of experimental design to the selection of data for multivariate calibration, the object being to span all sources of variability in the calibration set. The difference between random calibration and controlled calibration is defined. The limiting effects of errors in both the X and Y variables on the precision of results are discussed. Factorial and simplex lattice designs are also discussed and recent applications from the literature and cluster analysis for the selection of calibration objects are presented. Chapter 7 discusses sources of non-linear response in multivariate calibration and ways for handling its presence. Chapter 7 begins by describing the use of data weighting to reduce the effect of variables with poor signal-tonoise ratios and several interesting schemes for calculating the weights. Some different sources of non-linear response in the concentration variables, Y, with respect to the response variables, X, are defined and techniques for treating the non-linearity are described. The authors show how multivariate techniques like PCR and PLS can compensate for non-linear response by inclusion of extra factors in an especially clear example. Other linearization procedures covered include the BoxCox Upower transformation”, the transformation, Kubelka-Munk polynomial functions of instrument response variables, and the Multiplicative Scatter Correction tecbni-
que. Several miscellaneous pretreatment options are mentioned at the end of Chapter 7, including the use of derivative spectra and smoothing. The final chapter of the book gives an example of how to apply many of the procedures described in Chapters 3-7 to develop a multivariate calibration of aqueous litmus solutions using ultraviolet/ visible spectra. The calibration and test samples contained variable amounts of an unknown dye in addition to litmus, variable amounts of an insoluble substance which made the solutions turbid, and variable levels of pH. Overall, the authors have put together a text which presents a sum of their research knowledge in multivariate calibration to date. Understandably, there are a tremendous number of ideas explored in the book which are not fully developed due to the ongoing nature of the authors’ research. Unfortunately, there are several recurring flaws which detract from the quality of this book including occasional spelling errors, grammatical errors, misused words, awkward phrasing, and low quality dot matrix plots. The book is reasonably expensive ($150) and for this price the editorial staff at John Wiley & Sons Ltd. could have been more careful in the production of this book. Despite the above flaws, students and researchers alike will find this book a valuable resource for many years to come. PJ. GEMPERLINE East Carolina University, Greenville, NC27858, U.S.A. m