A Beginner's Guide to Generalised Additive Mixed Models with R: (A Beginner's Guide to)

In this book we take the reader on an exciting voyage into the world of generalised additive mixed effects models (GAMM). Keywords are GAM, mgcv, gamm4, random effects, Poisson and negative binomial GAMM, gamma GAMM, binomial GAMM, NB-P models, GAMMs with generalised extreme value distributions, overdispersion, underdispersion, two-dimensional smoothers, zero-inflated GAMMs, spatial correlation, INLA, Markov chain Monte Carlo techniques, JAGS, and two-way nested GAMMs. The book includes three chapters on the analysis of zero-inflated data. Throughout the book frequentist approaches (gam, gamm, gamm4, lme4) are compared with Bayesian techniques (MCMC in JAGS and INLA). Datasets on squid, polar bears, coral reefs, ruddy turnstones, parasites in anchovy, Common Guillemots, harbour porpoises, forestry, brood parasitism, maximum cod length, and Common Scoters are used in case studies. The R code to construct, fit, interpret, and comparatively evaluate models is provided at every stage (either in the book or on the website for the book).

Table of Contents:
PREFACE V ACKNOWLEDGEMENTS V DATASETS USED IN THIS BOOK VI CHAPTER 1 OF ZUUR ET AL. (2012A) AND ZUUR (2012B) VI COVER ART VI CONTRIBUTORS XIII 1 INTRODUCTION 1 1.1 GAM APPLIED ON STABLE ISOTOPE RATIOS 1 1.2 GAM USING MGCV APPLIED ON THE SQUID DATA 5 1.3 LINEAR SPLINE REGRESSION 7 1.4 LINEAR SPLINE REGRESSION IN JAGS 13 1.5 B-SPLINES IN JAGS 17 1.6 LOW RANK THIN-PLATE REGRESSION SPLINES IN JAGS 19 1.6.1 Using lme to estimate the low rank thin-plate regression spline 22 1.6.2 Using JAGS to estimate the low rank thin-plate regression spline 24 1.7 O'SULLIVAN SPLINES IN JAGS 28 1.8 EFFECTIVE DEGREES OF FREEDOM OF A SMOOTHER 30 2 ADDITIVE MIXED EFFECTS MODELS APPLIED ON POLAR BEAR MOVEMENT DATA 35 2.1 INTRODUCTION 35 2.2 THE VARIABLES 36 2.3. HOUSEKEEPING 37 2.4 DATA EXPLORATION 37 2.4.1 Checking for outliers in the movement data 38 2.4.2 Relationships between movement and the covariates 38 2.4.3 Collinearity 44 2.5 MODEL FORMULATION 45 2.5.1 Distribution 45 2.5.2 Predictor function 46 2.5.3 Link function 48 2.6 FREQUENTIST APPROACH 48 2.6.1 Fitting the additive mixed effects model using mgcv 48 2.6.2 Model validation of the additive mixed effects model 52 2.6.3 Understanding $lme output from the gamm function 55 2.7 MCMC AND GAUSSIAN ADDITIVE MIXED EFFECTS MODELS 58 2.7.1 Data for JAGS 58 2.7.2 JAGS modelling code 60 2.7.3 Initial values 62 2.7.4 Parameters to save 62 2.7.5 Executing JAGS and obtaining results 62 2.7.6 Mixing of chains 63 2.7.7 Model validation 63 2.7.8 Model interpretation 64 2.8 MCMC AND GAMMA GAMM 67 2.8.1 Data for JAGS 67 2.8.2 JAGS modelling code 68 2.8.3 Initial values 69 2.8.4 Parameters to save 70 2.8.5 Executing JAGS and obtaining results 70 2.8.6 Mixing of Chains 70 2.8.7 Model validation 70 2.8.8 Model interpretation 71 2.9 DISCUSSION 71 2.10 WHAT TO PRESENT IN A PAPER 72 3 ADDITIVE MIXED EFFECTS MODELS APPLIED ON CORAL REEF DATA 73 3.1 INTRODUCTION 73 3.1.1 Coral reefs 73 3.1.2 Aim of this chapter 73 3.2 THE VARIABLES 74 3.3. HOUSEKEEPING 74 3.4 DATA EXPLORATION 75 3.4.1 Checking for outliers 75 3.4.2 Relationships 76 3.4.3 Collinearity 78 3.5 MODEL FORMULATION 79 3.6 FREQUENTIST APPROACH 80 3.6.1 Linear mixed effects model using lme 80 3.6.2 Additive mixed effects model using gamm 82 3.6.3 Model validation of the additive mixed effects model 86 3.6.4 Model interpretation 86 3.7 MCMC AND GAUSSIAN ADDITIVE MIXED EFFECTS MODELS 88 3.7.1 Data for JAGS 89 3.7.2 JAGS modelling code 90 3.7.3 Initial values 92 3.7.4 Parameters to save 92 3.7.5 Executing JAGS and obtaining results 92 3.7.6 Mixing of Chains 93 3.7.7 Model validation 93 3.7.8 Model interpretation 93 3.8 DISCUSSION 97 3.9 WHAT TO PRESENT IN A PAPER 98 4 POISSON GAMM APPLIED ON RUDDY TURNSTONE DATA 99 4.1 GROUP SIZE EFFECT ON VIGILANCE IN RUDDY TURNSTONES 99 4.2 THE VARIABLES 100 4.3. HOUSEKEEPING 100 4.4 DATA EXPLORATION 101 4.5 POISSON GAMM 104 4.5.1 GLMM or GAMM? 105 4.5.2 GAMM formulation 105 4.5.3 Fitting GAMM using gamm4 106 4.5.4 Estimated smoothers 109 4.5.5 Model validation 110 4.6 USING FLOCK SIZE AS AN OFFSET? 110 4.7 UNBALANCED RANDOM EFFECTS; SIMULATION STUDY 111 4.8 DISCUSSION 114 5 GAMM APPLIED ON PARASITE DATA 115 5.1 INTRODUCTION 115 5.2 THE VARIABLES 116 5.3. HOUSEKEEPING 116 5.4 DATA EXPLORATION 117 5.4.1 Checking for missing values 117 5.4.2 Checking for outliers 117 5.4.3 Relationships 118 5.4.4 Collinearity 119 5.4.5 Zero inflation 119 5.5 MODEL FORMULATION 119 5.6 POISSON AND NEGATIVE BINOMIAL GLMM FOR TOTAL ABUNDANCE 121 5.6.1 Poisson GLMM using lme4 121 5.6.2 Negative binomial GAMM using JAGS 125 5.6.3 Negative binomial-P GLMs and GAMMs 136 5.7 GENERALISED POISSON GAMM FOR UNDERDISPERSED SPECIES RICHNESS 142 5.8 BINOMIAL GAMM FOR ABSENCE/PRESENCE DATA 144 6 ZERO-INFLATED SEA BIRD DATA SAMPLED AT OFFSHORE WIND FARMS 145 6.1 COMMON GUILLEMOTS 145 6.2 THE DATA 146 6.2.1 Importing the data 146 6.2.2 Recoding of variables 146 6.3 LOADING THE REQUIRED PACKAGES 148 6.4 DATA EXPLORATION 148 6.5 BUILDING TOWARDS A MODEL 153 6.5.1 Poisson GAM with a bivariate smoother 153 6.5.2 Applying the Poisson GAM with a bivariate smoother 155 6.5.3 Poisson GAM with multiple bivariate smoothers 157 6.5.4 Poisson GAMM with multiple bivariate smoothers 159 6.6 ZERO-INFLATED POISSON GAMM WITH BIVARIATE SMOOTHERS 161 6.7 ZERO-INFLATED NEGATIVE BINOMIAL GAMM WITH BIVARIATE SMOOTHERS 163 6.8 TECHNICAL DETAILS OF FITTING THE TWO-WAY NESTED ZIP GAMM 163 6.8.1 Underlying mixed effects model 163 6.8.2 MCMC code for a two-dimensional smoother for data from one survey 166 6.9 MODEL SELECTION USING DATA FROM SURVEY 1 176 6.10 A MODEL FOR ALL 13 SURVEYS 177 6.11 MCMC RESULTS FOR ALL 13 SURVEYS 179 6.12 ADDING INDICATOR FUNCTIONS 182 6.13 MODEL VALIDATION 182 6.14 DISCUSSION 185 6.15 WHAT TO PRESENT IN A PAPER 186 7 ZERO-INFLATED GAMM APPLIED ON HARBOUR PORPOISE 187 7.1 HARBOUR PORPOISE 187 7.2 IMPORTING THE DATA AND HOUSEKEEPING 188 7.3 DATA EXPLORATION 189 7.3.1 Spatial and temporal sampling positions 189 7.3.2 Outliers 192 7.3.3 Collinearity 193 7.3.4 Relationships 194 7.4 BRAINSTORMING 196 7.4.1 Adding correlation to the model 196 7.4.2 Specifying the fixed part of the models 197 7.4.3 Mathematical formulation of the models 198 7.5 ZIP GAMM USING UNIVARIATE SMOOTHERS 199 7.5.1 Implementation of ZIP GAMM with univariate smoothers 199 7.5.2 ZIP GAMM results 208 7.5.3 ZIP GLMM results 210 7.6 ZIP GAMM USING TWO-DIMENSIONAL SPATIAL SMOOTHERS 210 7.6.1 Implementation of ZIP GAMM with multivariate smoother - 210 7.6.2 ZIP GAMM results 211 7.7 DISCUSSION 214 7.8 WHAT TO PRESENT IN A PAPER 214 8 GAMMA GAMM APPLIED ON TREE GROWTH DATA 217 8.1 INTRODUCTION 217 8.2 THE VARIABLES 218 8.3. HOUSEKEEPING 218 8.4 DATA EXPLORATION 219 8.5 MODEL SPECIFICATION 221 8.6 FREQUENTIST APPROACH 222 8.7 BAYESIAN APPROACH 226 8.7.1 Schematic overview 226 8.7.2 Data for JAGS 226 8.7.3 JAGS modelling code 228 8.7.4 Initial values and parameters to save 231 8.7.5 Running JAGS 232 8.7.6 Assess mixing of chains and model fit 232 8.7.7 JAGS results 233 8.7.8 Model validation 234 8.7.9 Heterogeneous gamma GAMM 237 8.8 DISCUSSION 238 8.9 WHAT TO PRESENT IN A PAPER 239 9 BERNOULLI GAMM APPLIED ON COWBIRD BROOD PARASITISM 241 9.1 INTRODUCTION 241 9.2 THE VARIABLES 242 9.3. HOUSEKEEPING 243 9.4 DATA EXPLORATION 243 9.5 MODEL FORMULATION 245 9.6 FREQUENTIST APPROACH 245 9.7 BAYESIAN APPROACH 247 9.7.1 Preparing the data for JAGS 248 9.7.2 JAGS modelling code 249 9.7.3 Running JAGS and mixing of chains 251 9.7.4 Estimated smoothers and fitted values obtained by JAGS 251 9.7.5 Differences between fitted values 253 9.8 DISCUSSION 254 10 GAMM APPLIED ON MAXIMUM COD LENGTH USING INLA 255 10.1 INTRODUCTION 255 10.2 THE VARIABLES 256 10.3 DATA EXPLORATION 256 10.4 GAM IN MGCV 259 10.5 ADDING SPATIAL CORRELATION TO THE GAM 261 10.6 FITTING A GAM USING INLA 263 10.6.1 What is INLA? 263 10.6.2 Installing INLA 265 10.6.3 Applying regression models in INLA 265 10.6.4 GAM in inla 268 10.7 GAM WITH SPATIAL CORRELATION IN INLA 270 10.7.1 Defining a mesh 270 10.7.2 Projector matrix 272 10.7.3 Setting up the model 272 10.7.4 Executing inla 273 10.7.5 Plotting the spatial random field 274 10.7.6 Theoretical and estimated spatial correlation 275 10.8 GAM WITH EXTREME VALUE DISTRIBUTION IN INLA 278 10.8.1 Generalised extreme value distribution 278 10.8.2 Applying gev models using the ismev package in R 279 10.8.3 Applying gev models using inla in R 282 10.9 GAM WITH EXTREME VALUE DISTRIBUTION AND SPATIAL CORRELATION IN INLA 283 10.10 DISCUSSION 284 10.11 WHAT TO PRESENT IN A PAPER 284 11 ZERO-INFLATED AND SPATIAL CORRELATED COMMON SCOTER DATA 285 11.1 INTRODUCTION 285 11.2 THE VARIABLES 286 11.3 DATA EXPLORATION 286 11.3.1 Outliers 286 11.3.2 Collinearity 287 11.3.3 Relationships between response and covariates 288 11.4 POISSON GLM 291 11.5 ZERO-INFLATED POISSON GLM USING PSCL AND INLA 295 11.6 ZERO-INFLATED POISSON GAM USING INLA 298 11.7 ZIP GLM WITH SPATIAL CORRELATION USING INLA 303 11.8 ZIP GAM WITH SPATIAL CORRELATION USING INLA 306 11.9 NB GLM WITH SPATIAL CORRELATION USING INLA 308 11.10 THE EFFECT OF A NEW EXCLUSION ZONE 311 11.11 DISCUSSION 317 11.12 WHAT TO PRESENT IN A PAPER 318 REFERENCES 319 INDEX 325 BOOKS BY HIGHLAND STATISTICS 329 UPCOMING BOOKS IN 2014 331

About the Author :
Alain F Zuur is senior statistician and director of Highland Statistics Ltd., a statistics consultancy based in the UK. He is the author of seven books on the analysis of ecological data. He has extensive experience teaching statistical methods to ecologists and environmental scientists in academic and nonacademic courses worldwide. Anatoly A Saveliev is a professor at the Institute of Ecology and Geography at Kazan Federal State University, Russian Federation, where he teaches GIS and statistics. He also provides consultancy in statistics, GIS and remote sensing, and spatial modelling, and software development in these areas. Elena N Ieno is senior marine biologist at Highland Statistics Ltd. She teaches data analysis to ecologists and has shown the ability to challenge the gap between both disciplines. She is co-author of six books on analysis of ecological data.

Review :
This book is the foremost text on generalised additive mixed models. Presented from both the frequentist and Bayesian perspective using real ecological data, the theory is clearly explained, and full working code in R is provided so that an analyst can easily employ these methods into their own research. Professor Joseph M Hilbe. Arizona State University. Jet Propulsion Laboratory, Caltech