Basic Chemometric Techniques in Atomic Spectroscopy

[BOOK DESCRIPTION]

The first edition of this book was a first book for atomic spectroscopists to present the basic principles of experimental designs, optimization and multivariate regression. Multivariate regression is a valuable statistical method for handling complex problems (such as spectral and chemical interferences) which arise during atomic spectrometry. However, the technique is underused as most spectroscopists do not have time to study the often complex literature on the subject. This practical introduction uses conceptual explanations and worked examples to give readers a clear understanding of the technique. Mathematics is kept to a minimum but, when required, is kept at a basic level. Practical considerations, interpretations and troubleshooting are emphasized and literature surveys are included to guide the reader to further work. The same dataset is used for all chapters dealing with calibration to demonstrate the differences between the different methodologies. Readers will learn how to handle spectral and chemical interferences in atomic spectrometry in a new, more efficient and cost-effective way.

[TABLE OF CONTENTS]

 List of Contributors                       xvii
    Chapter 1 An Overview of Atomic                1   (51)
    Spectrometric Techniques
          Alfredo Sanz-Medel
          Rosario Pereiro
          Jose Manuel Costa-Fernandez
      1.1 Introduction: Basis of Analytical        1   (2)
      Atomic Spectrometric Techniques
      1.2 Atomic Optical Spectrometry              3   (16)
        1.2.1 Classification of Techniques:        4   (5)
        Absorption, Emission and Fluorescence
        1.2.2 A Comparative View of Basic          9   (7)
        Instrumentation
        1.2.3 Comparative Analytical               16  (3)
        Performance Characteristics and
        Interferences
      1.3 Atomic Mass Spectrometry                 19  (13)
        1.3.1 Fundamentals and Basic               21  (3)
        Instrumentation of Inductively Coupled
        Plasma-Mass Spectrometry
        1.3.2 Analytical Performance               24  (4)
        Characteristics and Interferences in
        ICP-MS
        1.3.3 Isotope Ratio Measurements and       28  (4)
        Their Applications
      1.4 Flow Systems with Atomic Spectrometry    32  (9)
      Detection
        1.4.1 Flow Injection Analysis and          32  (3)
        Atomic Spectrometry
        1.4.2 Chromatographic Separations          35  (3)
        Coupled On-line to Atomic Spectrometry
        1.4.3 Detection of Fast Transient          38  (3)
        Signals
      1.5 Direct Analysis of Solids by             41  (5)
      Spectrometric Techniques
        1.5.1 Direct Elemental Analysis by         42  (3)
        Optical Spectrometry
        1.5.2 Direct Elemental Analysis by Mass    45  (1)
        Spectrometry
      1.6 Quality Control and Troubleshooting      46  (6)
        References                                 48  (4)
    Chapter 2 Classical Linear Regression by       52  (71)
    the Least Squares Method
          Jose Manuel Andrade-Garda
          Alatzne Carlosena-Zubieta
          Rosa Maria Soto-Ferreiro
          Javier Teran-Baamonde
          Michael Thompson
      2.1 Introduction                             52  (5)
        2.1.1 Defining Calibration                 54  (3)
      2.2 The Least Squares Criterion              57  (4)
        2.2.1 Basic Assumptions of the Least       58  (3)
        Squares Method
      2.3 The Least Squares Fit                    61  (5)
        2.3.1 Planning Standardization             63  (2)
        2.3.2 Setting the Working Range            65  (1)
      2.4 Validation of the Least Squares Fit      66  (12)
        2.4.1 The Correlation Coefficient          66  (4)
        2.4.2 Residuals and Outlying Data          70  (4)
        2.4.3 Tests for Equal Variances            74  (1)
        2.4.4 Tests for Linearity                  75  (3)
      2.5 Estimating Unknown Concentrations        78  (6)
      2.6 The Standard Additions Method (SAM)      84  (5)
        2.6.1 Description of the Method:           84  (2)
        Advantages and Disadvantages
        2.6.2 Interpolation or Extrapolation       86  (3)
      2.7 Practical Application                    89  (14)
        2.7.1 Experimental Design                  89  (5)
        2.7.2 Effect on the Predictions and        94  (7)
        Confidence Intervals
        2.7.3 Comparison of the Predictions and    101 (2)
        Confidence Intervals Obtained with
        Interpolation and Extrapolation
      2.8 Polynomial Regression                    103 (4)
        2.8.1 Over-fitting                         104 (1)
        2.8.2 Shape of the Polynomial              105 (2)
      2.9 Appendix 1. Mandel's Test to Check       107 (6)
      for Linearity
        Comparing the Two Definitions              110 (3)
      2.10 Appendix 2. Comparison of Two           113 (10)
      Regression Lines
        Another Possibility                        116 (1)
        Acknowledgements                           117 (1)
        References                                 117 (6)
    Chapter 3 Implementing a Robust                123 (133)
    Methodology: Experimental Designs and
    Optimisation
          Xavier Tomas-Morer
          Lucinio Gonzalez-Sabate
          Laura Fernandez-Ruano
          Maria Paz Gomez-Carracedo
      3.1 Basics of Experimental Design            123 (2)
        3.1.1 Objectives and Strategies            123 (1)
        3.1.2 Variables and Responses: Factors,    124 (1)
        Levels, Effects and Interactions
      3.2 Analysis of Experimental Designs         125 (13)
        3.2.1 Factorial Designs                    125 (1)
        3.2.2 If Factorial Designs                 126 (2)
        3.2.3 Algorithms: BH2 and Yates            128 (2)
        3.2.4 Graphical and Statistical Analysis   130 (3)
        3.2.5 Blocking Experiments                 133 (1)
        3.2.6 Confounding: Fractional Factorial    134 (2)
        Designs
        3.2.7 Saturated Designs:                   136 (2)
        Plackett-Burman Designs. Use in
        Screening and Robustness Studies
      3.3 Taguchi's Approach to Experimental       138 (16)
      Design
        3.3.1 Strategies for Robust Designs        138 (1)
        3.3.2 Planning Experiments: Orthogonal     139 (6)
        Arrays
        3.3.3 Robust Parameter Design: Reducing    145 (2)
        Variation
        3.3.4 Worked Example                       147 (7)
      3.4 Optimisation                             154 (21)
        3.4.1 Experimental Optimisation            154 (1)
        3.4.2 The Simplex Method                   155 (9)
        3.4.3 The Modified Simplex Method          164 (3)
        3.4.4 Response Surface Designs             167 (8)
      3.5 Examples of Practical Applications       175 (81)
        References                                 232 (24)
    Chapter 4 Ordinary Multiple Linear             256 (24)
    Regression and Principal Components
    Regression
          Joan Ferre-Baldrich
          Ricard Boque-Marti
      4.1 Introduction                             256 (4)
        4.1.1 Multivariate Calibration in          256 (3)
        Quantitative Analysis
        4.1.2 Notation                             259 (1)
      4.2 Basics of Multivariate Regression        260 (3)
        4.2.1 The Multiple Linear Regression       260 (1)
        Model
        4.2.2 Estimation of the Model              261 (1)
        Coefficients
        4.2.3 Prediction                           262 (1)
        4.2.4 The Collinearity Problem in          262 (1)
        Multivariate Regression
      4.3 Multivariate Direct Models               263 (4)
        4.3.1 Classical Least Squares              263 (4)
      4.4 Multivariate Inverse Models              267 (7)
        4.4.1 Inverse Least Squares                267 (2)
        4.4.2 Principal Components Regression      269 (5)
      4.5 Practical Applications and               274 (3)
      Comparative Example
      4.6 Appendix                                 277 (3)
        References                                 277 (3)
    Chapter 5 Partial Least-Squares Regression     280 (68)
          Jose Manuel Andrade-Garda
          Alatzne Carlosena-Zubieta
          Ricard Boque-Marti
          Joan Ferre-Baldrich
      5.1 A Graphical Approach to the Basic PLS    280 (11)
      Algorithm
      5.2 Sample Sets                              291 (2)
      5.3 Data Pretreatment                        293 (6)
        5.3.1 Baseline Correction                  294 (1)
        5.3.2 Smoothing                            294 (3)
        5.3.3 Mean Centring and Autoscaling        297 (1)
        5.3.4 Derivatives                          298 (1)
      5.4 Dimensionality of the Model              299 (9)
        5.4.1 Crossvalidation                      303 (1)
        5.4.2 Other Approaches                     304 (4)
      5.5 Diagnostics                              308 (9)
        5.5.1 t vs. t Plots                        308 (1)
        5.5.2 t vs. u Plots                        309 (1)
        5.5.3 The T2, h and Q Statistics           310 (4)
        5.5.4 Studentized Concentration            314 (1)
        Residuals
        5.5.5 Predicted vs. Reference Plot         315 (2)
      5.6 Validation                               317 (2)
      5.7 Multivariate Figures of Merit            319 (10)
        5.7.1 Accuracy (Trueness and Precision)    319 (2)
        5.7.2 Limit of Detection                   321 (3)
        5.7.3 Limit of Quantification              324 (1)
        5.7.4 Sensitivity                          325 (1)
        5.7.5 Selectivity                          326 (1)
        5.7.6 Sample-specific Standard Error of    326 (3)
        Prediction
      5.8 Chemical Interpretation of the Model     329 (2)
      5.9 Examples of Practical Applications       331 (17)
        5.9.1 Flame and Electrothermal Atomic      331 (2)
        Spectrometry (FAAS and ETAAS)
        5.9.2 Inductively Coupled Plasma           333 (1)
        Optical Emission Spectrometry (ICP-OES)
        5.9.3 Inductively Coupled Plasma Mass      334 (1)
        Spectrometry (ICP-MS)
        5.9.4 Laser-Induced Breakdown              334 (3)
        Spectrometry (LIBS)
        5.9.5 Direct Analysis of Solids            337 (1)
        References                                 338 (10)
    Chapter 6 Multivariate Regression using        348 (50)
    Artificial Neural Networks and Support
    Vector Machines
          Jose Manuel Andrade-Garda
          Marcos Gestal-Pose
          Francisco Abel Cedron-Santaeufemia
          Julian Dorado-de-la-Calle
          Maria Paz Gomez-Carracedo
      6.1 Introduction                             348 (3)
      6.2 Neurons and Artificial Neural Networks   351 (4)
      6.3 Basic Elements of the Neuron             355 (4)
        6.3.1 Input Function                       355 (1)
        6.3.2 Activation and Transfer Function     355 (2)
        6.3.3 Output Function                      357 (1)
        6.3.4 Raw Data Preprocessing               357 (2)
      6.4 Training an Artificial Neural Network    359 (4)
        6.4.1 Learning Mechanisms                  360 (2)
        6.4.2 Evolution of the Weights             362 (1)
      6.5 Error Back-Propagation Artificial        363 (1)
      Neural Networks
      6.6 When to Stop Learning                    364 (2)
      6.7 Validating the Artificial Neural         366 (1)
      Network
      6.8 Limitations of the Artificial Neural     367 (1)
      Networks
      6.9 Relationships with other Regression      368 (2)
      Methods
      6.10 Worked Example                          370 (4)
      6.11 Support Vector Machines                 374 (6)
        6.11.1 Support Vector Machines for         375 (3)
        Classification
        6.11.2 Support Vector Machines for         378 (2)
        Regression
        6.11.3 Worked Example                      380 (1)
      6.12 Examples of Practical Applications      380 (18)
        6.12.1 Flame Atomic Absorption and         381 (1)
        Atomic Emission Spectrometry (FAAS and
        FAES)
        6.12.2 Electrothermal Atomic Absorption    382 (1)
        Spectrometry (ETAAS)
        6.12.3 Inductively Coupled Plasma          382 (2)
        Optical Emission Spectrometry (ICP-OES)
        6.12.4 Inductively Coupled Plasma Mass     384 (1)
        Spectrometry (ICP-MS)
        6.12.5 X-Ray Fluorescence (XRF)            385 (1)
        6.12.6 Laser-Induced Breakdown             386 (2)
        Spectrometry (LIBS)
        6.12.7 Secondary Ion Mass Spectrometry     388 (1)
        (SIMS)
        6.12.8 Applications of SVM                 388 (1)
        References                                 389 (9)
Subject Index                                      398