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| The Big Picture | |
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| Modeling Basics | |
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| What Is a Model? | |
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| Two Model Forms: Model Equation and Probability Distribution | |
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| Types of Model Effects | |
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| Writing Models in Matrix Form | |
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| Summary: Essential Elements for a Complete Statement of the Model | |
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| Design Matters | |
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| Introductory Ideas for Translating Design and Objectives into Models | |
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| Describing "Data Architecture" to Facilitate Model Specification | |
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| From Plot Plan to Linear Predictor | |
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| Distribution Matters | |
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| More Complex Example: Multiple Factors with Different Units of Replication | |
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| Setting the Stage | |
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| Goals for Inference with Models: Overview | |
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| Basic Tools of Inference | |
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| Issue I: Data Scale vs. Model Scale | |
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| Issue II: Inference Space | |
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| Issue III: Conditional and Marginal Models | |
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| Summary | |
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| Estimation and Inference Essentials | |
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| Estimation | |
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| Introduction | |
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| Essential Background | |
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| Fixed Effects Only | |
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| Gaussian Mixed Models | |
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| Generalized Linear Mixed Models | |
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| Summary | |
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| Inference | |
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| Model Effects | |
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| Introduction | |
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| Essential Background | |
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| Approaches to Testing | |
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| Inference Using Model-Based Statistics | |
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| Inference Using Empirical Standard Error | |
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| Summary of Main Ideas and General Guidelines for Implementation | |
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| Inference | |
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| Covariance Components | |
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| Introduction | |
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| Formal Testing of Covariance Components | |
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| Fit Statistics to Compare Covariance Models | |
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| Interval Estimation | |
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| Summary | |
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| Working with GLMMs | |
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| Treatment and Explanatory Variable Structure | |
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| Types of Treatment Structures | |
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| Types of Estimable Functions | |
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| Multiple Factor Models: Overview | |
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| Multifactor Models with All Factors Qualitative | |
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| Multifactor: Some Factors Qualitative, Some Factors Quantitative | |
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| Multifactor: All Factors Quantitative | |
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| Summary | |
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| Multilevel Models | |
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| Types of Design Structure: Single- and Multilevel Models Defined | |
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| Types of Multilevel Models and How They Arise | |
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| Role of Blocking in Multilevel Models | |
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| Working with Multilevel Designs | |
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| Marginal and Conditional Multilevel Models | |
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| Summary | |
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| Best Linear Unbiased Prediction | |
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| Review of Estimable and Predictable Functions | |
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| BLUP in Random-Effects-Only Models | |
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| Gaussian Data with Fixed and Random Effects | |
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| Advanced Applications with Complex Z Matrices | |
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| Summary | |
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| Rates and Proportions | |
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| Types of Rate and Proportion Data | |
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| Discrete Proportions: Binary and Binomial Data | |
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| Alternative Link Functions for Binomial Data | |
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| Continuous Proportions | |
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| Summary | |
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| Counts | |
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| Introduction | |
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| Overdispersion in Count Data | |
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| More on Alternative Distributions | |
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| Conditional and Marginal | |
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| Too Many Zeroes | |
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| Summary | |
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| Time-to-Event Data | |
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| Introduction: Probability Concepts for Time-to-Event Data | |
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| Gamma GLMMs | |
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| GLMMs and Survival Analysis | |
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| Summary | |
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| Multinomial Data | |
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| Overview | |
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| Multinomial Data with Ordered Categories | |
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| Nominal Categories: Generalized Logit Models | |
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| Model Comparison | |
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| Summary | |
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| Correlated Errors | |
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| Repeated Measures | |
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| Overview | |
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| Gaussian Data: Correlation and Covariance Models for LMMs | |
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| Covariance Model Selection | |
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| Non-Gaussian Case | |
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| Issues for Non-Gaussian Repeated Measures | |
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| Summary | |
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| Correlated Errors | |
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| Spatial Variability | |
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| Overview | |
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| Gaussian Case with Covariance Model | |
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| Spatial Covariance Modeling by Smoothing Spline | |
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| Non-Gaussian Case | |
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| Summary | |
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| Power, Sample Size, and Planning | |
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| Basics of GLMM-Based Power and Precision Analysis | |
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| Gaussian Example | |
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| Power for Binomial GLMMs | |
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| GLMM-Based Power Analysis for Count Data | |
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| Power and Planning for Repeated Measures | |
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| Summary | |
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| Appendices | |
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| References | |
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| Index | |