Applied Statistical Modelling for Ecologists

A Practical Guide to Bayesian and Likelihood Inference Using R, JAGS, NIMBLE, Stan and TMB

1st Edition - July 18, 2024
Authors: Marc Kéry, Kenneth F. Kellner
Language: English
Paperback ISBN:
9 7 8 - 0 - 4 4 3 - 1 3 7 1 5 - 0
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 1 3 7 1 6 - 7

Applied Statistical Modelling for Ecologists provides a gentle introduction to the essential models of applied statistics: linear models, generalized linear models, mixed and hiera… Read more

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Applied Statistical Modelling for Ecologists provides a gentle introduction to the essential models of applied statistics: linear models, generalized linear models, mixed and hierarchical models. All models are fit with both a likelihood and a Bayesian approach, using several powerful software packages widely used in research publications: JAGS, NIMBLE, Stan, and TMB. In addition, the foundational method of maximum likelihood is explained in a manner that ecologists can really understand.

This book is the successor of the widely used Introduction to WinBUGS for Ecologists (Kéry, Academic Press, 2010). Like its parent, it is extremely effective for both classroom use and self-study, allowing students and researchers alike to quickly learn, understand, and carry out a very wide range of statistical modelling tasks.

The examples in Applied Statistical Modelling for Ecologists come from ecology and the environmental sciences, but the underlying statistical models are very widely used by scientists across many disciplines. This book will be useful for anybody who needs to learn and quickly become proficient in statistical modelling, with either a likelihood or a Bayesian focus, and in the model-fitting engines covered, including the three latest packages NIMBLE, Stan, and TMB.

Cover image
Title page
Table of Contents
Copyright
Dedication
Foreword
Acknowledgments
Chapter 1. Introduction
Abstract
Chapter outline
1.1 Statistical models and why you need them
1.2 Why linear statistical models?
1.3 Why go beyond the linear model?
1.4 Random effects and why you need them
1.5 Why do you need both Bayesian and non-Bayesian statistical inference?
1.6 More reasons for why you should really understand maximum likelihood
1.7 The data simulation/model fitting dualism
1.8 The “experimental approach” to statistics
1.9 The first principle of modeling: start simple!
1.10 Overview of the ASM book and additional resources
1.11 How to use the ASM book for self-study and in courses
1.12 Summary and outlook
Chapter 2. Introduction to statistical inference
Abstract
Chapter outline
2.1 Probability as the basis for statistical inference
2.2 Random variables and their description by probability distributions
2.3 Statistical models and their usages
2.4 The likelihood function
2.5 Classical inference by maximum likelihood and its application to a single-parameter model
2.6 Maximum likelihood estimation in a two-parameter model
2.7 Bayesian inference using posterior distributions
2.8 Bayesian computation by Markov chain Monte Carlo (MCMC)
2.9 So should you now be a Bayesian or a frequentist?
2.10 Summary and outlook
Further reading
Chapter 3. Linear regression models and their extensions to generalized linear, hierarchical, and integrated models
Abstract
Chapter outline
3.1 Introduction
3.2 Statistical distributions for the random variables in our model
3.3 Link functions to model parameters on a transformed scale
3.4 Linear modeling of covariate effects
3.5 Brief overview of linear, generalized linear, (generalized) linear mixed, hierarchical, and integrated models
3.6 Summary and outlook
Chapter 4. Introduction to general-purpose model fitting engines and the “model of the mean”
Abstract
Chapter outline
4.1 Introduction
4.2 Data generation
4.3 Analysis using canned functions in R
4.4 JAGS
4.5 NIMBLE
4.6 Stan
4.7 Maximum likelihood in R
4.8 Maximum likelihood using Template Model Builder (TMB)
4.9 Comparison of engines and concluding remarks
Chapter 5. Normal linear regression
Abstract
Chapter outline
5.1 Introduction
5.2 Data generation
5.3 Analysis with canned functions in R
5.4 Bayesian analysis with JAGS
5.5 Bayesian analysis with NIMBLE
5.6 Bayesian analysis with Stan
5.7 Do-it-yourself maximum likelihood estimates
5.8 Likelihood analysis with TMB
5.9 Comparison of the parameter estimates
5.10 Summary and outlook
Chapter 6. Comparing two groups in a normal model
Abstract
Chapter outline
6.1 Introduction
6.2 Comparing two groups with equal variances
6.3 Comparing two groups with unequal variances
6.4 Summary and a comment on the modeling of variances
Chapter 7. Models with a single categorical covariate with more than two levels
Abstract
Chapter outline
7.1 Introduction: fixed and random effects
7.2 Fixed-effects models
7.3 Random-effects models
7.4 Summary and outlook
Chapter 8. Comparisons along two classifications in a model with two factors
Abstract
Chapter outline
8.1 Introduction: main and interaction effects
8.2 Data generation
8.3 Likelihood analysis with canned functions in R
8.4 An aside: using simulation to assess bias and precision of an estimator … and to understand what a standard error is
8.5 Bayesian analysis with JAGS
8.6 Bayesian analysis with NIMBLE
8.7 Bayesian analysis with Stan
8.8 Do-it-yourself maximum likelihood estimates
8.9 Likelihood analysis with TMB
8.10 Comparison of the parameter estimates
8.11 Summary and outlook
Chapter 9. General linear model for a normal response with continuous and categorical explanatory variables
Abstract
Chapter outline
9.1 Introduction
9.2 Data generation
9.3 Likelihood analysis with canned functions in R
9.4 Bayesian analysis with JAGS
9.5 Bayesian analysis with NIMBLE
9.6 Bayesian analysis with Stan
9.7 Do-it-yourself maximum likelihood estimates
9.8 Likelihood analysis with TMB
9.9 Comparison of the parameter estimates
9.10 Summary and outlook
Chapter 10. Linear mixed-effects model
Abstract
Chapter outline
10.1 Introduction
10.2 Data generation
10.3 Analysis under a random-intercepts model
10.4 Analysis under a random-coefficients model without correlation between intercept and slope
10.5 The random-coefficients model with correlation between intercept and slope
10.6 Summary and outlook
Chapter 11. Introduction to the generalized linear model (GLM): comparing two groups in a Poisson regression
Abstract
Chapter outline
11.1 Introduction
11.2 An important but often forgotten issue with count data
11.3 How to deal with missing values in our data
11.4 Data generation
11.5 Likelihood analysis with canned functions in R
11.6 Bayesian analysis with JAGS
11.7 Bayesian analysis with NIMBLE
11.8 Bayesian analysis with Stan
11.9 Do-it-yourself maximum likelihood estimates
11.10 Likelihood analysis with TMB
11.11 Comparison of the parameter estimates
11.12 Summary and outlook
Chapter 12. Overdispersion, zero inflation, and offsets in a Poisson GLM
Abstract
Chapter outline
12.1 Introduction
12.2 Overdispersion
12.3 Zero inflation
12.4 Offsets
12.5 Summary and outlook
Chapter 13. Poisson GLM with continuous and categorical explanatory variables
Abstract
Chapter outline
13.1 Introduction
13.2 Data generation
13.3 Likelihood analysis with canned functions in R
13.4 Bayesian analysis with JAGS
13.5 Bayesian analysis with NIMBLE
13.6 Bayesian analysis with Stan
13.7 Do-it-yourself maximum likelihood estimates
13.8 Likelihood analysis with TMB
13.9 Comparison of the parameter estimates
13.10 Summary
Chapter 14. Poisson generalized linear mixed model, or Poisson GLMM
Abstract
Chapter outline
14.1 Introduction
14.2 Data generation
14.3 Likelihood analysis with canned functions in R
14.4 Bayesian analysis with JAGS
14.5 Bayesian analysis with NIMBLE
14.6 Bayesian analysis with Stan
14.7 Do-it-yourself maximum likelihood estimates
14.8 Likelihood analysis with TMB
14.9 Comparison of the parameter estimates
14.10 Summary
Chapter 15. Comparing two groups in a logistic regression model
Abstract
Chapter outline
15.1 Introduction
15.2 Data generation
15.3 Likelihood analysis with canned functions in R
15.4 Bayesian analysis with JAGS
15.5 Bayesian analysis with NIMBLE
15.6 Bayesian analysis with Stan
15.7 Do-it-yourself maximum likelihood estimates
15.8 Likelihood analysis with TMB
15.9 Comparison of the parameter estimates
15.10 Summary
Chapter 16. Binomial GLM with continuous and categorical explanatory variables
Abstract
Chapter outline
16.1 Introduction
16.2 Data generation
16.3 Likelihood analysis with canned functions in R
16.4 Bayesian analysis with JAGS
16.5 Bayesian analysis with NIMBLE
16.6 Bayesian analysis with Stan
16.7 Do-it-yourself maximum likelihood estimates
16.8 Likelihood analysis with TMB
16.9 Comparison of the estimates
16.10 Summary
Chapter 17. Binomial generalized linear mixed model
Abstract
Chapter outline
17.1 Introduction
17.2 Data generation
17.3 Likelihood analysis with canned functions in R
17.4 Bayesian analysis with JAGS
17.5 Bayesian analysis with NIMBLE
17.6 Bayesian analysis with Stan
17.7 Do-it-yourself maximum likelihood estimates
17.8 Likelihood analysis with TMB
17.9 Comparison of the parameter estimates
17.10 Summary
Chapter 18. Model building, model checking, and model selection
Abstract
Chapter outline
18.1 Introduction
18.2 Why do we build a statistical model?
18.3 Ticklish rattlesnakes
18.4 How do we build a statistical model?
18.5 Model checking and goodness-of-fit testing
18.6 Model selection
18.7 Model averaging
18.8 Regularization: penalization, shrinkage, ridge, and lasso
18.9 Summary and outlook
Chapter 19. Occupancy models
Abstract
Chapter outline
19.1 Introduction
19.2 Data generation
19.3 Likelihood analysis with canned functions in the R package unmarked
19.4 Bayesian analysis with JAGS
19.5 Bayesian analysis with NIMBLE
19.6 Bayesian analysis with Stan
19.7 Bayesian analysis with canned functions in the R package ubms
19.8 Do-it-yourself maximum likelihood estimates
19.9 Likelihood analysis with TMB
19.10 Comparison of the parameter estimates
19.11 Summary and outlook
Chapter 20. Integrated models
Abstract
Chapter outline
20.1 Introduction
20.2 Data generation: simulating three abundance data sets with different observation/aggregation models
20.3 Fitting models to the three individual data sets first
20.4 Fitting the integrated model to all three data sets simultaneously
20.5 What do we gain by analyzing the joint likelihood in our analysis?
20.6 Summary and outlook
Chapter 21. Conclusion
Abstract
Chapter outline
21.1 Looking back
21.2 Looking ahead
Bibliography
Index

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