Mixed and Phylogenetic Models: A Conceptual Introduction to Correlated Data (The Book + R Code)
Mixed and Phylogenetic Models: A Conceptual Introduction to Correlated Data
About the Book
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This book introduces the concepts behind statistical methods used to analyze data with correlated error structures. While correlated data arise in many ways, the focus is on ecological and evolutionary data, and two types of correlations: correlations generated by the hierarchical nature of the sampling (e.g., plots sampled within sites) and correlations generated by the phylogenetic relationships among species.
The book is integrated with R code that illustrates every point. Although it is possible to read the book without the code, or work through the code without the book, they are designed to go hand-in-hand. The R code comes with the complete downloadable package of the book on leanpub.com; if you have problems downloading it, please contact me.
I've designed the book to be read in entirety, or at least for each chapter to be read in entirety. Therefore, it is not organized like a reference manual. However, because I don't expect everybody to read the whole thing, I've tried to repeat some material between chapters, so that each chapter is more self-contained. Still, there might be places where you will want to consult another chapter, and I've included pointers to sections in other chapters where appropriate.
The material covered in the book is:
*Chapter 1, Multiple Methods for Analyzing Hierarchical Data*
The first chapter introduces and analyzes a hierarchical dataset of ruffed grouse sampled at stations (plots) within roadway routes (sites). The relationship between the chances of observing a grouse at a station and wind speed during the observation is analyzed using nine methods including linear models (LMs), generalized linear models (GLMs), linear mixed models (LLMs), and generalized linear mixed models (GLMMs). The many methods of analyzing the same dataset begs the question of which is best.
*Chapter 2, Good Statistical Properties*
Which method is best depends on the question and the data, and it is not always the obvious one. Chapter 2 presents the statistical tools for deciding which method is best to analyze a correlated dataset. The chapter discusses properties of statistical estimators, such as bias and precision, and the characteristics of good hypothesis tests, specifically proper type I error control and high statistical power. This is a very fast overview of mathematical statistics and then application to the grouse dataset presented in Chapter 1.
*Chapter 3, Phylogenetic Comparative Methods*
There is a close relationship between hierarchical data and phylogenetic data, and the same approaches can be used for their analyses. Chapter 3 employs the tools presented in Chapter 2 to evaluate common methods applied in phylogenetic analyses used to compare among species or other phylogenetic units. I also show the not-so-nice consequences of ignoring the possible correlation generated by phylogenetic relationships among species.
*Chapter 4, Phylogenetic Community Ecology*
Community data have both hierarchical structure (e.g., samples taken from plots nested within sites) and phylogenetic structure (e.g., related species occurring more often in the same sites). Combining methods for analyzing hierarchical data and phylogenetic data produces Phylogenetic GLMMs (PGLMMs) that are useful in a broad class of ecological community studies. This chapter uses PGLMMs to investigate different types of questions about community structure, and assesses the properties of the models. This material is only covered very technically in the primary literature, and the R packages that can perform the analyses are just being developed. Therefore, the Chapter 4 could function as a manual for the phylogenetic community models discussed.
Although the book is titled an introduction, it is an introduction to the concepts behind the methods discussed, not so much the methods themselves. It assumes that the user knows R and the basic application of mixed and/or phylogenetic models.
Chapter 1: Multiple Methods for Analyzing Hierarchical Data
- 1.1 Introduction
- 1.2 Take-homes
- 1.3 Dataset
- 1.4 Analyses of aggregated (site-level) data
- 1.5 Analyses of hierarchical (plot-level) data
- 1.6 Reiteration of results
- 1.7 Summary
- 1.8 Exercises
- 1.9 References
Chapter 2: Good Statistical Properties
- 2.1 Introduction
- 2.2 Take-homes
- 2.3 Estimators
- 2.4 Properties of estimators
- 2.5 Hypothesis testing
- 2.6 P-values for binary data
- 2.7 Example data: grouse
- 2.8 Summary
- 2.9 Exercises
- 2.10 References
Chapter 3: Phylogenetic Comparative Methods
- 3.1 Introduction
- 3.2 Take-homes
- 3.3 Phylogenetic correlation
- 3.4 Estimating phylogenetic signal
- 3.5. Statistical tests for phylogenetic signal
- 3.6 Estimating regression coefficients
- 3.7 How good must the phylogeny be?
- 3.8 Phylogenetic regression for binary data
- 3.9 Summary
- 3.10 Exercises
- 3.11 References
Chapter 4: Phylogenetic Community Ecology
- 4.1 Introduction
- 4.2 Take-homes
- 4.3 Phylogenetic patterns in community composition
- 4.4 Phylogenetic repulsion
- 4.5 Can traits explain phylogenetic patterns?
- 4.6 Trait-by-environment interactions
- 4.7 Bipartite phylogenetic patterns
- 4.8 Binary (presence/absence) data
- 4.9 Flexibility and caveats for phylogenetic GLMMs
- 4.10 Summary
- 4.11 Exercises
- 4.12 References
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