Analysis of Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences
ACSESS Books
Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences provides readers with an understanding and appreciation for the design and analysis of mixed models for non-normally distributed data. It is the only publication of its kind directed specifically toward the agricultural and natural resources sciences audience. Readers will especially benefit from the numerous worked examples based on actual experimental data and the discussion of pitfalls associated with incorrect analyses.
Foreword vii
Preface ix
Authors xi
Conversion Factors for SI and Non-SI Units xiii
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 Generalized Linear Mixed Models 2
1.3 Historical Development 3
1.4 Objectives of this Book 5
Chapter 2 Background 7
2.1 Introduction 7
2.2 Distributions used in Generalized Linear Modeling 7
2.3 Descriptions of the Distributions 10
2.4 Likelihood Based Approach to Estimation 15
2.5 Variations on Maximum Likelihood Estimation 18
2.6 Likelihood Based Approach to Hypo
2.7 Computational Issues 22
2.8 Fixed, Random, and Mixed Models 24
2.9 The Design-Analysis of Variance-Generalized Linear Mixed Model Connection 25
2.10 Conditional versus Marginal Models 30
2.11 Software 30
Chapter 3 Generalized Linear Models 35
3.1 Introduction 35
3.2 Inference in Generalized Linear Models 37
3.3 Diagnostics and Model Fit 46
3.4 Generalized Linear Modeling versus Transformations 52
Chapter 4 Linear Mixed Models 59
4.1 Introduction 59
4.2 Estimation and Inference in Linear Mixed Models 60
4.3 Conditional and Marginal Models 61
4.4 Split Plot Experiments 67
4.5 Experiments Involving Repeated Measures 77
4.6 Selection of a Covariance Model 78
4.7 A Repeated Measures Example 80
4.8 Analysis of Covariance 88
4.9 Best Linear Unbiased Prediction 99
Chapter 5 Generalized Linear Mixed Models 109
5.1 Introduction 109
5.2 Estimation and Inference in Generalized Linear Mixed Models 110
5.3 Conditional and Marginal Models 111
5.4 Three Simple Examples 125
5.5 Over-Dispersion in Generalized Linear Mixed Models 149
5.6 Over-Dispersion from an Incorrectly Specified Distribution 151
5.7 Over-Dispersion from an Incorrect Linear Predictor 160
5.8 Experiments Involving Repeated Measures 167
5.9 Inference Issues for Repeated Measures Generalized Linear Mixed Models 181
5.10 Multinomial Data 184
Chapter 6 More Complex Examples 199
6.1 Introduction 199
6.2 Repeated Measures in Time and Space 199
6.3 Analysis of a Precision Agriculture Experiment 210
Chapter 7 Designing Experiments 237
7.1 Introduction 237
7.2 Power and Precision 238
7.3 Power and Precision Analyses for Generalized Linear Mixed Models 239
7.4 Methods of Determining Power and Precision 241
7.5 Implementation of the Probability Distribution Method 243
7.6 A Factorial Experiment with Different Design Options 250
7.7 A Multi-location Experiment with a Binomial Response Variable 255
7.8 A Split Plot Revisited with a Count as the Response Variable 262
7.9 Summary and Conclusions 268
Chapter 8 Parting Thoughts and Future Directions 271
8.1 The Old Standard Statistical Practice 271
8.2 The New Standard 272
8.3 The Challenge to Adapt 274
Index 277
Preface ix
Authors xi
Conversion Factors for SI and Non-SI Units xiii
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 Generalized Linear Mixed Models 2
1.3 Historical Development 3
1.4 Objectives of this Book 5
Chapter 2 Background 7
2.1 Introduction 7
2.2 Distributions used in Generalized Linear Modeling 7
2.3 Descriptions of the Distributions 10
2.4 Likelihood Based Approach to Estimation 15
2.5 Variations on Maximum Likelihood Estimation 18
2.6 Likelihood Based Approach to Hypo
2.7 Computational Issues 22
2.8 Fixed, Random, and Mixed Models 24
2.9 The Design-Analysis of Variance-Generalized Linear Mixed Model Connection 25
2.10 Conditional versus Marginal Models 30
2.11 Software 30
Chapter 3 Generalized Linear Models 35
3.1 Introduction 35
3.2 Inference in Generalized Linear Models 37
3.3 Diagnostics and Model Fit 46
3.4 Generalized Linear Modeling versus Transformations 52
Chapter 4 Linear Mixed Models 59
4.1 Introduction 59
4.2 Estimation and Inference in Linear Mixed Models 60
4.3 Conditional and Marginal Models 61
4.4 Split Plot Experiments 67
4.5 Experiments Involving Repeated Measures 77
4.6 Selection of a Covariance Model 78
4.7 A Repeated Measures Example 80
4.8 Analysis of Covariance 88
4.9 Best Linear Unbiased Prediction 99
Chapter 5 Generalized Linear Mixed Models 109
5.1 Introduction 109
5.2 Estimation and Inference in Generalized Linear Mixed Models 110
5.3 Conditional and Marginal Models 111
5.4 Three Simple Examples 125
5.5 Over-Dispersion in Generalized Linear Mixed Models 149
5.6 Over-Dispersion from an Incorrectly Specified Distribution 151
5.7 Over-Dispersion from an Incorrect Linear Predictor 160
5.8 Experiments Involving Repeated Measures 167
5.9 Inference Issues for Repeated Measures Generalized Linear Mixed Models 181
5.10 Multinomial Data 184
Chapter 6 More Complex Examples 199
6.1 Introduction 199
6.2 Repeated Measures in Time and Space 199
6.3 Analysis of a Precision Agriculture Experiment 210
Chapter 7 Designing Experiments 237
7.1 Introduction 237
7.2 Power and Precision 238
7.3 Power and Precision Analyses for Generalized Linear Mixed Models 239
7.4 Methods of Determining Power and Precision 241
7.5 Implementation of the Probability Distribution Method 243
7.6 A Factorial Experiment with Different Design Options 250
7.7 A Multi-location Experiment with a Binomial Response Variable 255
7.8 A Split Plot Revisited with a Count as the Response Variable 262
7.9 Summary and Conclusions 268
Chapter 8 Parting Thoughts and Future Directions 271
8.1 The Old Standard Statistical Practice 271
8.2 The New Standard 272
8.3 The Challenge to Adapt 274
Index 277
