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JMP for Mixed Models

Release Date: 2021/06/01
ISBN: 9781952363856
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Discover the power of mixed models with JMP and JMP Pro.

Mixed models are now the mainstream method of choice for analyzing experimental data. Why? They are arguably the most straightforward and powerful way to handle correlated observations in designed experiments. Reaching well beyond standard linear models, mixed models enable you to make accurate and precise inferences about your experiments and to gain deeper understanding of sources of signal and noise in the system under study. Well-formed fixed and random effects generalize well and help you make the best data-driven decisions.

JMP for Mixed Models brings together two of the strongest traditions in SAS software: mixed models and JMP. JMP’s groundbreaking philosophy of tight integration of statistics with dynamic graphics is an ideal milieu within which to learn and apply mixed models, also known as hierarchical linear or multilevel models. If you are a scientist or engineer, the methods described herein can revolutionize how you analyze experimental data without the need to write code.

Inside you’ll find a rich collection of examples and a step-by-step approach to mixed model mastery. Topics include:

  • Learning how to appropriately recognize, set up, and interpret fixed and random effects
  • Extending analysis of variance (ANOVA) and linear regression to numerous mixed model designs
  • Understanding how degrees of freedom work using Skeleton ANOVA
  • Analyzing randomized block, split-plot, longitudinal, and repeated measures designs
  • Introducing more advanced methods such as spatial covariance and generalized linear mixed models
  • Simulating mixed models to assess power and other important sampling characteristics
  • Providing a solid framework for understanding statistical modeling in general
  • Improving perspective on modern dilemmas around Bayesian methods, p-values, and causal inference

Table of Contents

  1. About This Book
  2. About the Authors
  3. Acknowledgements
  4. 1 Introduction
    1. 1.1 What is a Mixed Model?
    2. 1.2 Cell Viability Example
    3. 1.3 Mixed Model Assumptions
    4. 1.4 Nominal and Continuous Variables
    5. 1.5 Experimental Units and Blocking, Cell Growth Example
    6. 1.6 Confounding
    7. 1.7 JMP and JMP Pro
    8. 1.8 Exercises
  5. 2 ANOVA with a Single Blocking Effect
    1. 2.1 Motivating Examples
    2. 2.2 Blocking Designs and Skeleton ANOVA
    3. 2.3 Metal Bond Breaking Example
    4. 2.4 Balanced Incomplete Blocks Example
    5. 2.5 Exercises
  6. 3 Models with Factorial Treatment Designs
    1. 3.1 Motivating Examples
    2. 3.2 Conceptual Background
    3. 3.3 RCBD with Factorial Treatments, Tensile Strength Example
    4. 3.4 Split-Plot Design, Greenhouse Example
    5. 3.5 What About Interactions Between Fixed and Random Effects?
    6. 3.6 Nested Design, Semiconductor Example
    7. 3.7 Exercises
  7. 4 Multiple Random Effects
    1. 4.1 Motivating Examples
    2. 4.2 Conceptual Background
    3. 4.3 Latin Square - Blocking in Two Orthogonal Directions
    4. 4.4 Mouse Condition: Negative Block Variance Example
    5. 4.5 Exercises
  8. 5 Regression, Random Coefficients, and Multilevel Models
    1. 5.1 Motivating Examples
    2. 5.2 Conceptual Background
    3. 5.3 Stability Trial
    4. 5.4 Student Achievement Example
    5. 5.5 Exercises
  9. 6 Repeated Measures and Longitudinal Data
    1. 6.1 Motivating Example
    2. 6.2 Conceptual Background
    3. 6.3 Repeated Measures Skeleton ANOVA and Statistical Model
    4. 6.4 Respiratory Ability
    5. 6.5 When Might We Choose Other Models?
    6. 6.6 Exercises
  10. 7 Spatial Models
    1. 7.1 Motivating Examples
    2. 7.2 Conceptual Background
    3. 7.3 Hazardous Waste Example
    4. 7.4 Alliance Wheat Trial
    5. 7.5 Further Statistical Details
    6. 7.6 Exercises
  11. 8 Simulation and Power Analysis
    1. 8.1 Motivating Examples
    2. 8.2 Simulation for Precision and Power
    3. 8.3 Type I Error Control Using the Semiconductor Design
    4. 8.4 Power Using the Semiconductor Design
    5. 8.5 Confidence Interval Coverage Using the Winter Wheat Example
    6. 8.6 Simulating Mixed Model Data Directly with JSL
    7. 8.7 Exercises
  12. 9 Generalized Linear Mixed Models
    1. 9.1 Motivating Examples
    2. 9.2 Conceptual Background
    3. 9.3 Binomial Response: Shrub Coverage
    4. 9.4 Binary Response: Salamander Mating
    5. 9.5 Count Response: Manufacturing Imperfections
    6. 9.6 Exercises
  13. 10 Mixed Models Amidst Modern Debates
    1. 10.1 Statistical Pragmatism
    2. 10.2 Fixed versus Random Effects
    3. 10.3 Frequentist versus Bayesian, p-values
    4. 10.4 Causality versus Association
    5. 10.5 Explanation versus Prediction
    6. 10.6 Randomized Experiments versus Observational Studies
    7. 10.7 Exercises
  14. A List of Examples Used in This Book
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