About This Book

What Does This Book Cover?

Mixed models, which are an extension of classic statistical linear models (including analysis-of-variance and regression), are one of the most powerful and useful collection of methods for analyzing data from designed experiments. Variations of mixed models have been one of the strongest capabilities of SAS software since its beginnings in the mid 1970s. In parallel, JMP (a SAS product launched in 1989) has evolved into an incredibly powerful and popular tool for scientists and engineers. This book brings together these two legacies, and in example-driven fashion, walks through the core concepts of mixed models and how to best apply them in practice.

Mixed models are largely about how to handle experimental observations that are correlated. After introducing foundational concepts and terminology of mixed models with examples, the book covers increasing levels of complexity, revealing the richness and wide applicability of mixed models in most any discipline that collects data in well-formed experiments.

The first four chapters focus on mixed models in the context of analysis-of-variance (ANOVA). We find that ANOVA is a good place to start as it helps organize thinking around factors with a discrete number of levels, as are nearly always found in designed experiments. We proceed further and utilize a helpful construct known as a Skeleton ANOVA to help clearly break down and understand degrees of freedom as well as how information from experimental units in the design is being allocated to effects in the model.

Chapters 5 and 6 shift focus to continuous effects as commonly found in linear regression and repeated measures contexts. They fit quite naturally into the mixed model framework and can be effectively combined with ANOVA-style effects to handle a wide variety of common experimental setups. Chapter 7 covers spatial models, which extend mixed models further to handle covariance over two or more dimensions.

Chapter 8 shows how you can use simulation to rigorously explore deeper statistical properties of mixed models such as power and sampling distributions of outputs. Chapter 9 provides an introduction to generalized linear mixed models, which are used when the response is no longer normally distributed, such as when it is a discrete number of successes or a count. Chapter 10 concludes the book with discussions on how mixed models relate to current controversies in the statistical and broader scientific and engineering communities.

Is This Book For You?

JMP for Mixed Models builds on the success of the SAS for Mixed Models book series as well as several other related books and articles. In contrast to the SAS procedures and code forming the basis of previous books, JMP and JMP Pro offer the ability to fit mixed models from a dynamically interactive, mouse-driven interface. This enables you to use mixed models without having to write code and get to important results faster and with less effort. This book is designed as an instructional guide along these lines and is the very first of its kind in this regard.

If you fit one of the following two characterizations, this book is likely for you:

•   You are a scientist or engineer running experiments in which subsets of the observations are correlated due to the design or the nature of the experimental units themselves. This includes designs such as a randomized block or split-plot as generated by JMP’s rich design-of-experiments (DOE) routines.

•   You are familiar with running mixed models, hierarchical linear models, or multilevel models in SAS, R, or other languages and want to learn an easy, point-and-click interface to fit them and obtain dynamically integrated statistics and graphics to aid in their interpretation and presentation.

If you take the time to learn mixed models in JMP, they will likely become one of the most useful tools that you have for analyzing designed experiments.

What Are the Prerequisites for This Book?

We assume you have knowledge of introductory statistical concepts such as those taught in an advanced high school or first-year college curriculum. This includes topics such as the following:

•   Statistical Testing (of the mean, of the difference between two means), standard errors (of the mean, difference between two means), and t tests

•   Distributions (normal, binomial, uniform, t, chi-square, F)

•   One-Way ANOVA

•   Factorial ANOVA

•   Regression

•   ANCOVA (regression with groups)

In JMP or JMP Pro, the Fit Model platform is the central one we will use, and some basic familiarity with it will be very helpful.

What Should You Know about the Examples?

Each topical chapter in this book begins with a description of several motivating examples that utilize the topic, and then we present the necessary conceptual background. With the background in place, we analyze the examples using both JMP and JMP Pro, including full interpretations of the output.

If you already have a decent understanding of mixed models and/or JMP, you may want to skip straight to examples that best match the problem that you want to analyze. Although the book roughly proceeds from simpler to more complex topics in a somewhat logical fashion, it is also designed to be a reference book in which you can find an example that most closely matches your current problem and skip directly to it.

Software Used to Develop the Book’s Content

We use both JMP and JMP Pro throughout, highlighting key differences as they arise.

Example Code and Data

JMP tables for all of the examples are available in the books supplemental information web page. JMP Scripting Language (JSL) programs are either included with the tables themselves or provided as stand-alone programs that you can open in JMP and run.

Output and Graphics

All of the books output and graphics are generated on an Apple MacIntosh. If you are running on Microsoft Windows, the aesthetics of the output will be somewhat different but content should be the same.

We use several typeface conventions throughout the book to help demarcate between data set names, variable names, commands, etc. Data sets, variables, and functions are monospace. Platforms, menus, options, variable roles, buttons, and function groups, basically anything you click on, are italicized. Bold font is mostly used only for section headings, but it is also used to call out table names in JMP reports.

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