A beginner's guide to GLM and GLMM with R: a frequentist and bayesian perspective for ecologists / Elena N. Ieno, Joseph M. Hilbe, Alain F. Zuur

Incluye bibliografía: páginas 247-250 e índice: páginas 251-253

Preface.. Acknowledgements.. Datasets and R Code Used in This Book.. Chapter 1 of Zuur et al.: páginas 012a and Zuur: páginas 012b.. Cover Art.. Contributors.. 1 Introduction to Generalized Linear Models.. 1.1 Linear Regression Applied On Fisheries Data.. 1.2 Poisson GLM.. 1.2.1 Poisson distribution for count data.. 1.2.2 Predictor function.. 1.2.3 Linking the mean and the predictor function.. 1.2.4 Maximum likelihood to estimate the parameters.. 1.2.5 Application of Poisson GLM on the fisheries data.. 1.2.6 Overdispersion.. 1.2.7 Adding covariates.. 1.2.8 Using the offset.. 1.3 Negative Binomial GLM.. 1.3.1 Negative binomial distribution for count data.. 1.3.2 Example of Negative binomial regression.. 1.3.3 Heterogeneous Negative binomial regression.. 1.3.4 A note on modelling under-dispersion.. 1.4 Binomial GLM For Binary Data.. 1.4.1 Parasites in honeybee larvae 1.4.2 Visualizing the data.. 1.4.3 Defining the three steps of a binomial GLM.. 1.4.4 Results for the bee data.. 1.4.5 Likelihood function for a binomial GLM.. 1.4.6 Other link functions.. 1.5 Binomial GLM for Proportional Data.. 1.5.1 Binomial distribution.. 1.5.2 Predictor function.. 1.5.3 Link function.. 1.5.4 Fitting the model in R.. 1.6 Other Distributions.. 2 Generalized Linear Modelling Applied to Red Squirrel Data.. 2.1 Red Squirrels.. 2.2 Importing the Data.. 2.3 Data Exploration.. 2.3.1 Outliers.. 2.3.2 Collinearity.. 2.3.3 Relationships.. 2.4 Fitting The Poisson GLM in R.. 2.4.1 Specifying the model.. 2.4.2 Execute the Poisson GLM in R.. 2.4.3 Model validation.. 2.5 Fitting the Negative Binomial GLM in R.. 2.5.1 Using the glm.nb function.. 2.5.2 Heterogeneous negative binomial GLM.. 2.6 Bayesian Approach - Running the Poisson GLM.. 2.6.1 Obtaining and installing JAGS.. 2.6.2 Specifying the data for JAGS 2.6.3 Specifying the model for JAGS.. 2.6.4 Specifying the initial values.. 2.6.5 Parameters to store.. 2.6.6 Running JAGS via R

2.6.7 Generalizing the JAGS modelling code.. 2.7 Assessing Mixing Of Chains.. 2.7.1 Assess mixing of chains if R2jags is used.. 2.8 Model Validation.. 2.8.1 Checking for overdispersion.. 2.8.2 Obtaining Pearson residuals.. 2.9 Applying a Negative Binomial GLM in Jags.. 2.10 Mixing of Chains.. 2.11 Model Validation.. 2.12 Model Interpretation.. 2.13 Discussion.. 2.14 What to Present in A Paper.. 3 GLM Applied to Presence-Absence Polychaeta Data.. 3.1 Marine Benthic Data.. 3.2 Importing the Data and Housekeeping.. 3.3 Data Exploration.. 3.4 Binary GLM; A Frequentist Approach.. 3.4.1 Specifying the distribution and link function.. 3.4.2 Specifying the predictor function.. 3.4.3 Running the glm function.. 3.4.4 Results of the glm function.. 3.4.5 Model selection.. 3.4.6 Results of the optimal model.. 3.4.7 Model validation.. 3.4.8 Visualizing the model.. 3.5 Fitting A Bernoulli GLM in JAGS.. 3.5.1 Specifying the data for JAGS.. 3.5.2 JAGS modelling code.. 3.5.3 Initial values and parameters to save.. 3.5.4 Running JAGS from R.. 3.5.5 JAGS results presented within R.. 3.6 Model Selection Using AIC, DIC AND BIC in JAGS.. 3.7 Model Interpretation.. 3.8 Discussion.. 3.9 What to Present in A Paper.. 4 Introduction to Mixed Effects Models.. 4.1 Spiders . 4.2 Linear Regression Applied on the Spider Data.. 4.3 Linear Mixed Effects Models 4.3.1 Model formulation and interpretation.. 4.3.2 Fitting a linear mixed effects model using lmer.. 4.3.3 Analysis using lmer.. 4.4 Fitting a Linear Mixed Effects Model in Jags.. 4.5 Using a Variable As a Fixed or Random Term?.. 4.6 Random Intercept and Slope Model.. 4.7 Generalized Linear Mixed Effects Models.. 5 Glmm Applied on Honeybee Pollination Data.. 5.1 Honeybees and Dandelion Pollen.. 5.2 Data Description And Importing The Data.. 5.3 Data Exploration.. 5.4 Building Up a Model.. 5.5 Poisson GLMM Using Glmer.. 5.6 poisson GLMM Using JAGS.. 5.6.1 Data for JAGS.. 5.6.2 JAGS modelling code

5.6.3 Likelihood.. 5.6.4 Priors.. 5.6.5 Initial values.. 5.6.6 Parameters to save.. 5.6.7 Executing JAGS and obtaining results.. 5.7 Negative Binomial GLMM Using GlmmADMB.. 5.8 Negative Binomial GLMM Using JAGS.. 5.8.1 Data for JAGS.. 5.8.2 JAGS modelling code.. 5.8.3 Initial values.. 5.8.4 Parameters to save.. 5.8.5 Executing JAGS and obtaining results.. 5.8.6 Mixing of chains.. 5.8.7 Model validation.. 5.8.8 Model interpretation.. 5.9 GLMM With Auto-Regressive Correlation.. 5.9.1 Simulate temporal correlated counts.. 5.9.2 JAGS to estimate the Poisson GLM with AR correlation.. 5.9.3 Multiple Poisson time series.. 5.9.4 Poisson GLMM with AR correlation.. 5.10 What to Present in a Paper.. 6 GLMM for Strictly Positive Data: Biomass of Rainforest Trees.. 6.1 Rainforest Tree Species.. 6.2 Importing the Data and Housekeeping.. 6.3 Data Exploration.. 6.3.1 Outliers.. 6.3.2 Collinearity.. 6.3.3 Relationships.. 6.4 Multiple Linear Regression: A Frequentist Approach.. 6.5 Gamma GLM Using A Frequentist Approach.. 6.5.1. Formulating the gamma GLM.. 6.5.2 Scale and shape.. 6.5.3 Visualizing the gamma distribution.. 6.5.4 Different link functions.. 6.5.5 Running the Gamma GLM using the GLM function.. 6.5.6 Scale confusion.. 6.5.7 Identity link and inverse link function.. 6.6 Fitting A GAMMA GLM using JAGS.. 6.6.1 Specifying the data for JAGS.. 6.6.2 JAGS modelling code.. 6.6.3 Priors.. 6.6.4 Likelihood function.. 6.6.5 Initial values and parameters to save.. 6.6.6 Running JAGS from R.. 6.6.7 JAGS results presented within R.. 6.6.8 Model interpretation.. 6.6.9 Model validation.. 6.7 ADDING More Covariates to the GAMMA GLM in JAGS.. 6.8 gamma GLMM.. 6.8.1 R code for a gamma GLMM in JAGS.. 6.8.2 Results from JAGS for the gamma GLMM.. 6.9 Truncated Gaussian Linear Regression.. 6.9.1 Zero trick to fit any statistical distribution in JAGS.. 6.9.2 Multiple linear regression in JAGS with the zero trick.. 6.9.3 Tobit model in JAGS

6.9.4 Tobit model with random effects in JAGS.. 6.10 Discussion.. 6.11 What to Present in a Paper.. 7 Binomial, Beta-Binomial, and Beta GLMM Applied to Cheetah Data.. 7.1 Stereotypic Behaviours in Captive Cheetahs.. 7.2 Importing the Data.. 7.3 Data Exploration.. 7.3.1 Outliers.. 7.3.2 Collinearity.. 7.4 Binomial GLMM Using A Frequentist Approach.. 7.4.1 Standardizing covariates.. 7.4.2 Binomial GLMM with random intercept zoo.. 7.4.3 Executing the GLMM using the GLMER function.. 7.4.4 Overdispersion.. 7.4.5 Binomial GLMM with observation level random intercept.. 7.4.6 Visualization of results.. 7.5 Binomial GLMM With Random Intercept Zoo in JAGS.. 7.5.1 Data for JAGS.. 7.5.2 JAGS modelling code for a binomial GLMM.. 7.5.3 Results for the binomial GLMM 7.5.4 Overdispersion.. 7.6 Beta-Binomial GLMM in JAGS.. 7.6.1 The Beta distribution.. 7.6.2 From beta to beta-binomial distribution.. 7.6.3 JAGS code for beta-binomial GLMM.. 7.6.4 Beta-binomial GLMM results.. 7.6.5 Model validation of the beta-binomial GLMM.. 7.7 Using A Beta GLMM For Proportions.. 7.8 Comparing Estimated Parameters From All Models.. 7.9 Model Selection From a Frequentist Point of View 7.10 Model Selection From a Bayesian Point of View.. 7.10.1 Using the DIC, AIC and BIC.. 7.10.2 Inclusion probabilities.. 7.11 What To Present In A Paper.. References.. Index.. Books By Highland Statistics.. Upcoming Books In 2013 And 2014

his book presents Generalized Linear Models (GLM) and Generalized Linear Mixed Models (GLMM) based on both frequency-based and Bayesian concepts. Using ecological data from real-world studies, the text introduces the reader to the basics of GLM and mixed effects models, with demonstrations of binomial, gamma, Poisson, negative binomial regression, and beta and beta-binomial GLMs and GLMMs. The book uses the functions glm, lmer, glmer, glmmADMB, and also JAGS from within R. JAGS results are compared with frequentist results. R code to construct, fit, interpret, and comparatively evaluate models is provided at every stage. Otherwise challenging procedures are presented in a clear and comprehensible manner with each step of the modelling process explained in detail, and all code is provided so that it can be reproduced by the reader. eng