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Mixed effects models and extensions in ecology with R

Part of the Statistics for Biology and Health Book Series

DOI: 10.1007/978-0-387-87458-6

ISBN: 978-0-387-87457-9

Publisher: Springer New York - Springer Journals

Feb 27, 2009

1 - 10 of 23 Chapters

LitStream

Chapter 1Introduction

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 1 –10

[Does your data have repeated measurements; is it nested (hierarchical)? Is it sampled at multiple locations or sampled repeatedly over time? Or is your response variable heterogeneous? Welcome to our world, the world of mixed effects modelling. The bad news is that it is a complicated world....
LitStream

Chapter 2Limitations of Linear Regression Applied on Ecological Data

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 11 –33

[This chapter revises the basic concepts of linear regression, shows how to apply linear regression in R, discusses model validation, and outlines the limitations of linear regression when applied to ecological data. Later chapters present methods to overcome some of these limitations; but as...
LitStream

Chapter 3Things are not Always Linear; Additive Modelling

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 35 –69

[In the previous chapter, we looked at linear regression, and although the word linear implies modelling only linear relationships, this is not necessarily the case. A model of the form Yi = α + β1 × Xi + β2 × Xi2 + ɛi is a linear regression model, but the relationship between Yi and Xi is...
LitStream

Chapter 4Dealing with Heterogeneity

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 71 –100

[This chapter, and the following three chapters, discuss solutions to the problems introduced in Chapters 2 and 3: heterogeneity, nested data, temporal correlation, and spatial correlation. We use both the linear regression model and the additive model as starting points. Figure 4.1 shows an...
LitStream

Chapter 5Mixed Effects Modelling for Nested Data

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 101 –142

[In this chapter, we continue with Gaussian linear and additive mixed modelling methods and discuss their application on nested data. Nested data is also referred to as hierarchical data or multilevel data in other scientific fields (Snijders and Boskers, 1999; Raudenbush and Bryk, 2002).]
LitStream

Chapter 6Violation of Independence – Part I

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 143 –160

[This chapter explains how correlation structures can be added to the linear regression and additive model. The mixed effects models from Chapters 4 and 5 can also be extended with a temporal correlation structure. The title of this chapter contains ‘Part I’, suggesting that there is also a Part...
LitStream

Chapter 7Violation of Independence – Part II

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 161 –191

[In the previous chapter, we discussed violation of independence for measurements taken repeatedly over time and how temporal correlation structures can be added to linear regression and additive models. We used a regular spaced data set. In this chapter, we consider data measured at multiple...
LitStream

Chapter 8Meet the Exponential Family

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 193 –208

[In Chapters 2 and 3 and in Appendix A, linear regression and additive modelling were discussed and various extensions allowing for different variances, nested data, temporal correlation, and spatial correlation were then discussed in Chapters 4, 5, 6, and 7. In Chapters 8, 9, and 10, we discuss...
LitStream

Chapter 9GLM and GAM for Count Data

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 209 –243

[A generalised linear model (GLM) or a generalised additive model (GAM) consists of three steps: (i) the distribution of the response variable, (ii) the specification of the systematic component in terms of explanatory variables, and (iii) the link between the mean of the response variable and...
LitStream

Chapter 10GLM and GAM for Absence–Presence and Proportional Data

Zuur, Alain F.; Ieno, Elena N.; Walker, Neil J.; Saveliev, Anatoly A.; Smith, Graham M.

Pages: 245 –259

[In the previous chapter, count data with no upper limit were analysed using Poisson generalised linear modelling (GLM) and negative binomial GLM. In Section 10.2 of this chapter, we discuss GLMs for 0−1 data, also called absence–presence or binary data, and in Section 10.3 GLM for proportional...

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