Generalized Linear Mixed Models with Applications in Agriculture and Biology.
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Place / Publishing House: | Cham : : Springer International Publishing AG,, 2023. {copy}2023. |
Year of Publication: | 2023 |
Edition: | 1st ed. |
Language: | English |
Online Access: | |
Physical Description: | 1 online resource (436 pages) |
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Table of Contents:
- Intro
- Foreword
- Acknowledgments
- Contents
- Chapter 1: Elements of Generalized Linear Mixed Models
- 1.1 Introduction to Linear Models
- 1.2 Regression Models
- 1.2.1 Simple Linear Regression
- 1.2.2 Multiple Linear Regression
- 1.3 Analysis of Variance Models
- 1.3.1 One-Way Analysis of Variance
- 1.3.2 Two-Way Nested Analysis of Variance
- 1.3.3 Two-Way Analysis of Variance with Interaction
- 1.4 Analysis of Covariance (ANCOVA)
- 1.5 Mixed Models
- 1.5.1 Introduction
- 1.5.2 Mixed Models
- 1.5.3 Distribution of the Response Variable Conditional on Random Effects (y|b)
- 1.5.4 Types of Factors and Their Related Effects on LMMs
- 1.5.4.1 Fixed Factors
- 1.5.4.2 Random Factors
- 1.5.4.3 Fixed Versus Random Factors
- 1.5.5 Nested Versus Crossed Factors and Their Corresponding Effects
- 1.5.6 Estimation Methods
- 1.5.6.1 Maximum Likelihood
- 1.5.6.2 Restricted Maximum Likelihood Estimation
- 1.5.7 One-Way Random Effects Model
- 1.5.8 Analysis of Variance Model of a Randomized Block Design
- 1.6 Exercises
- Appendix
- Chapter 2: Generalized Linear Models
- 2.1 Introduction
- 2.2 Components of a GLM
- 2.2.1 The Random Component
- 2.2.2 The Systematic Component
- 2.2.3 Predictorś Link Function η
- 2.3 Assumptions of a GLM
- 2.4 Estimation and Inference of a GLM
- 2.5 Specification of a GLM
- 2.5.1 Continuous Normal Response Variable
- 2.5.2 Binary Logistic Regression
- 2.5.2.1 Model Diagnosis
- 2.5.3 Poisson Regression
- 2.5.4 Gamma Regression
- 2.5.4.1 Model Selection
- 2.5.5 Beta Regression
- 2.6 Exercises
- Appendix
- Chapter 3: Objectives of Inference for Stochastic Models
- 3.1 Three Aspects to Consider for an Inference
- 3.1.1 Data Scale in the Modeling Process Versus Original Data
- 3.1.2 Inference Space
- 3.1.3 Inference Based on Marginal and Conditional Models.
- 3.2 Illustrative Examples of the Data Scale and the Model Scale
- 3.3 Fixed and Random Effects in the Inference Space
- 3.3.1 A Broad Inference Space or a Population Inference
- 3.3.2 Mixed Models with a Normal Response
- 3.4 Marginal and Conditional Models
- 3.4.1 Marginal Versus Conditional Models
- 3.4.2 Normal Distribution
- 3.4.3 Non-normal Distribution
- 3.5 Exercises
- Chapter 4: Generalized Linear Mixed Models for Non-normal Responses
- 4.1 Introduction
- 4.2 A Brief Description of Linear Mixed Models (LMMs)
- 4.3 Generalized Linear Mixed Models
- 4.4 The Inverse Link Function
- 4.5 The Variance Function
- 4.6 Specification of a GLMM
- 4.7 Estimation of the Dispersion Parameter
- 4.8 Estimation and Inference in Generalized Linear Mixed Models
- 4.8.1 Estimation
- 4.8.2 Inference
- 4.9 Fitting the Model
- 4.10 Exercises
- Chapter 5: Generalized Linear Mixed Models for Counts
- 5.1 Introduction
- 5.2 The Poisson Model
- 5.2.1 CRD with a Poisson Response
- 5.2.2 Example 2: CRDs with Poisson Response
- 5.2.3 Example 3: Control of Weeds in Cereal Crops in an RCBD
- 5.2.4 Overdispersion in Poisson Data
- 5.2.4.1 Using the Scale Parameter
- 5.2.4.2 Linear Predictor Review
- 5.2.4.3 Using a Different Distribution
- 5.2.5 Factorial Designs
- 5.2.5.1 Example: A 2 x 4 Factorial with a Poisson Response
- 5.2.6 Latin Square (LS) Design
- 5.2.6.1 Latin Square Design with a Poisson Response
- 5.2.6.2 Randomized Complete Block Design in a Split Plot
- 5.3 Exercises
- Appendix 1
- Chapter 6: Generalized Linear Mixed Models for Proportions and Percentages
- 6.1 Response Variables as Ratios and Percentages
- 6.2 Analysis of Discrete Proportions: Binary and Binomial Responses
- 6.2.1 Completely Randomized Design (CRD): Methylation Experiment.
- 6.3 Factorial Design in a Randomized Complete Block Design (RCBD) with Binomial Data: Toxic Effect of Different Treatments on ...
- 6.4 A Split-Plot Design in an RCBD with a Normal Response
- 6.4.1 An RCBD Split Plot with Binomial Data: Carrot Fly Larval Infestation of Carrots
- 6.4.1.1 Linear Predictor Review (ηijk)
- 6.4.1.2 Scale Parameter
- 6.4.1.3 Alternative Distribution
- 6.5 A Split-Split Plot in an RCBD:- In Vitro Germination of Seeds
- 6.6 Alternative Link Functions for Binomial Data
- 6.6.1 Probit Link: A Split-Split Plot in an RCBD with a Binomial Response
- 6.6.2 Complementary Log-Log Link Function: A Split Plot in an RCBD with a Binomial Response
- 6.7 Percentages
- 6.7.1 RCBD: Dead Aphid Rate
- 6.7.2 RCBD: Percentage of Quality Malt
- 6.7.3 A Split Plot in an RCBD: Cockroach Mortality (Blattella germanica)
- 6.7.4 A Split-Plot Design in an RCBD: Percentage Disease Inhibition
- 6.7.5 Randomized Complete Block Design with a Binomial Response with Multiple Variance Components
- 6.8 Exercises
- Appendix
- Chapter 7: Time of Occurrence of an Event of Interest
- 7.1 Introduction
- 7.2 Generalized Linear Mixed Models with a Gamma Response
- 7.2.1 CRD: Estrus Induction in Pelibuey Ewes
- 7.2.2 Randomized Complete Block Design (RCBD): Itch Relief Drugs
- 7.2.3 Factorial Design: Insect Survival Time
- 7.2.4 A Split Plot with a Factorial Structure on a Large Plot in a Completely Randomized Design (CRD)
- 7.3 Survival Analysis
- 7.3.1 Concepts and Definitions
- 7.3.2 CRD: Aedes aegypti
- 7.3.3 RCBD: Aedes aegypti
- 7.4 Exercises
- Appendix 1
- Chapter 8: Generalized Linear Mixed Models for Categorical and Ordinal Responses
- 8.1 Introduction
- 8.2 Concepts and Definitions
- 8.3 Cumulative Logit Models (Proportional Odds Models)
- 8.3.1 Complete Randomize Design (CRD) with a Multinomial Response: Ordinal.
- 8.3.2 Randomized Complete Block Design (RCBD) with a Multinomial Response: Ordinal
- 8.4 Cumulative Probit Models
- 8.5 Effect of Judges ́Experience on Canned Bean Quality Ratings
- 8.6 Generalized Logit Models: Nominal Response Variables
- 8.6.1 CRDs with a Nominal Multinomial Response
- 8.6.2 CRD: Cheese Tasting
- 8.7 Exercises
- Appendix
- Chapter 9: Generalized Linear Mixed Models for Repeated Measurements
- 9.1 Introduction
- 9.2 Example of Turf Quality
- 9.3 Effect of Insecticides on Aphid Growth
- 9.4 Manufacture of Livestock Feed
- 9.5 Characterization of Spatial and Temporal Variations in Fecal Coliform Density
- 9.6 Log-Normal Distribution
- 9.6.1 Emission of Nitrous Oxide (N2O) in Beef Cattle Manure with Different Percentages of Crude Protein in the Diet
- 9.7 Effect of a Chemical Salt on the Percentage Inhibition of the Fusarium sp.
- 9.8 Carbon Dioxide (CO2) Emission as a Function of Soil Moisture and Microbial Activity
- 9.9 Effect of Soil Compaction and Soil Moisture on Microbial Activity
- 9.10 Joint Model for Binary and Poisson Data
- 9.11 Exercises
- Appendix
- References.