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BK

New York : Springer, c2009

xxii, 574 s. : il. ; 24 cm

ISBN 978-0-387-87457-9 (váz.)

Statistics for biology and health, ISSN 1431-8776

Obsahuje bibliografii na s. 553-561 a rejstřík

000236275

Contents // 1 Introduction... // 1.1 What Is in the Book?... // 1.1.1 To Include or Not to Include GLM and GAM . . . // 1.1.2 Case Studies... // 1.1.3 Flowchart of the Content... // 1.2 Software... // 1.3 How to Use This Book If You Are an Instructor... // 1.4 What We Did Not Do and Why... // 1.5 How to Cite R and Associated Packages... // 1.6 Our R Programming Style ... // 1.7 Getting Data into R... // 1.7.1 Data in a Package... // 2 Limitations of Linear Regression Applied on Ecological Data // 2.1 Data Exploration... // 2.1.1 Cleveland Dotplots... // 2.1.2 Pairplots... // 2.1.3 Boxplots ... // 2.1.4 xyplot from the Lattice Package...:... // 2.2 The Linear Regression Model ... // 2.3 Violating the Assumptions; Exception or Rule?... // 2.3.1 Introduction... // 2.3.2 Normality ... // 2.3.3 Heterogeneity... // 2.3.4 Fixed X... // 2.3.5 Independence... // 2.3.6 Example 1 ; Wedge Clam Data... // 2.3.7 Example 2; Moby’s Teeth... // 2.3.8 Example 3; Nereis... // 2.3.9 Example 4; Pelagic Bioluminescence ... // 2.4 Where to Go from Here ... // 1 // 1 // 3 // 4 // 4 // 5 // 6 // 6 // 7 // 8 // 9 // 10 // 11 // 12 // 12 // 14 // 15 // 15 // 17 // 19 // 19 // 19 // 20 // 21 // 21 // 22 // 26 // 28 // 30 // 31 // 3 Things Are Not Always Linear; Additive Modelling... 35 // 3.1 Introduction... 35 // 3.2 Additive Modelling... 36 // 3.2.1 GAM in gam and GAM in mgcv... 37 // 3.2.2 GAM in gam with LOESS ... 38 // 3.2.3 GAM in mgcv with Cubic Regression Splines... 42 // 3.3 Technical Details

of GAM in mgcv... 44 // 3.3.1 A (Little) Bit More Technical Information // on Regression Splines... 47 // 3.3.2 Smoothing Splines Alias Penalised Splines... 49 // 3.3.3 Cross-Validation... 51 // 3.3.4 Additive Models with Multiple Explanatory Variables ... 53 // 3.3.5 Two More Things... 53 // 3.4 GAM Example 1 ; Bioluminescent Data for Two Stations... 55 // 3.4.1 Interaction Between a Continuous and Nominal Variable . 59 // 3.5 GAM Example 2: Dealing with Collinearity... 63 // 3.6 Inference... 66 // 3.7 Summary and Where to Go from Here?... 67 // 4 Dealing with Heterogeneity... 71 // 4.1 Dealing with Heterogeneity... 72 // 4.1.1 Linear Regression Applied on Squid... 72 // 4.1.2 The Fixed Variance Structure... 74 // 4.1.3 The Varldent Variance Structure... 75 // 4.1.4 The varPower Variance Structure... 78 // 4.1.5 The varExp Variance Structure... 80 // 4.1.6 The varConstPower Variance Structure... 80 // 4.1.7 The varComb Variance Structure... 81 // 4.1.8 Overview of All Variance Structures... 82 // 4.1.9 Graphical Validation of the Optimal Model... 84 // 4.2 Benthic Biodiversity Experiment... 86 // 4.2.1 Linear Regression Applied on the Benthic // Biodiversity Data... 86 // 4.2.2 GLS Applied on the Benthic Biodiversity Data... 89 // 4.2.3 A Protocol... 90 // 4.2.4 Application of the Protocol on the Benthic Biodiversity // Data ... 92 // 5 Mixed Effects Modelling for Nested Data ...101 // 5.1 Introduction...101 // 5.2 2-Stage Analysis Method...103 // 5.3 The Linear Mixed Effects

Model...105 // 5.3.1 Introduction...105 // 5.3.2 The Random Intercept Model...106 // 5.3.3 The Random Intercept and Slope Model...109 // 5.3.4 Random Effects Model ...Ill // 5.4 Induced Correlations...112 // 5.4.1 Intraclass Correlation Coefficient...114 // 5.5 The Marginal Model...114 // 5.6 Maximum Likelihood and REML Estimation ...116 // 5.6.1 Illustration of Difference Between ML and REML...119 // 5.7 Model Selection in (Additive) Mixed Effects Modelling ...120 // 5.8 RIKZ Data: Good Versus Bad Model Selection...122 // 5.8.1 The Wrong Approach ...122 // 5.8.2 The Good Approach...127 // 5.9 Model Validation...128 // 5.10 Begging Behaviour of Nestling Barn Owls...129 // 5.10.1 Step 1 of the Protocol: Linear Regression...130 // 5.10.2 Step 2 of the Protocol: Fit the Model with GLS...132 // 5.10.3 Step 3 of the Protocol: Choose a Variance Structure ...132 // 5.10.4 Step 4: Fit the Model...133 // 5.10.5 Step 5 of the Protocol: Compare New Model with // Old Model... 133 // 5.10.6 Step 6 of the Protocol: Everything Ok?...134 // 5.10.7 Steps 7 and 8 of the Protocol: The Optimal // Fixed Structure ... 135 // 5.10.8 Step 9 of the Protocol: Refit with REML and Validate // the Model... 137 // 5.10.9 Step 10 of the Protocol...139 // 5.10.10 Sorry, We are Not Done Yet...139 // 6 Violation of Independence - Part I...143 // 6.1 Temporal Correlation and Linear Regression...143 // 6.1.1 ARMA Error Structures...150 // 6.2 Linear Regression Model and Multivariate Time Series...152 // 6.3 Owl

Sibling Negotiation Data...158 // 7 Violation of Independence - Part II ...161 // 7.1 Tools to Detect Violation of Independence...161 // 7.2 Adding Spatial Correlation Structures to the Model...166 // 7.3 Revisiting the Hawaiian Birds...171 // 7.4 Nitrogen Isotope Ratios in Whales ...172 // 7.4.1 Moby...172 // 7.4.2 All Whales ...174 // 7.5 Spatial Correlation due to a Missing Covariate...177 // 7.6 Short God wits Time Series...182 // 7.6.1 Description of the Data...182 // 7.6.2 Data Exploration...183 // 7.6.3 Linear Regression...184 // 7.6.4 Protocol Time...186 // 7.6.5 Why All the Fuss?...190 // 8 Meet the Exponential Family...193 // 8.1 Introduction...193 // 8.2 The Normal Distribution...194 // 8.3 The Poisson Distribution...196 // 8.3.1 Preparation for the Offset in GLM...198 // 8.4 The Negative Binomial Distribution...199 // 8.5 The Gamma Distribution ...201 // 8.6 The Bernoulli and Binomial Distributions...202 // 8.7 The Natural Exponential Family...204 // 8.7.1 Which Distribution to Select?...205 // 8.8 Zero Truncated Distributions for Count Data...206 // 9 GLM and GAM for Count Data ...209 // 9.1 Introduction...209 // 9.2 Gaussian Linear Regression as a GLM...210 // 9.3 Introducing Poisson GLM with an Artificial Example ...211 // 9.4 Likelihood Criterion...213 // 9.5 Introducing the Poisson GLM with a Real Example...215 // 9.5.1 Introduction...215 // 9.5.2 R Code and Results...216 // 9.5.3 Deviance...217 // 9.5.4 Sketching the Fitted Values...218 // 9.6 Model Selection

in a GLM...220 // 9.6.1 Introduction...220 // 9.6.2 R Code and Output...220 // 9.6.3 Options for Finding the Optimal Model...221 // 9.6.4 The Dropi Command ...222 // 9.6.5 Two Ways of Using the Anova Command...223 // 9.6.6 Results...223 // 9.7 Overdispersion...224 // 9.7.1 Introduction...’...224 // 9.7.2 Causes and Solutions for Overdispersion ...224 // 9.7.3 Quick Fix: Dealing with Overdispersion in // a Poisson GLM...225 // 9.7.4 R Code and Numerical Output...226 // 9.7.5 Model Selection in Quasi-Poisson...227 // 9.8 Model Validation in a Poisson GLM...228 // 9.8.1 Pearson Residuals...229 // 9.8.2 Deviance Residuals...229 // 9.8.3 Which One to Use? ...230 // 9.8.4 What to Plot? ...230 // 9.9 Illustration of Model Validation in Quasi-Poisson GLM...231 // 9.10 Negative Binomial GLM ...233 // 9.10.1 Introduction...233 // 9.10.2 Results...236 // 9.11 GAM...238 // 9.11.1 Distribution of larval Sea Lice Around Scottish // Fish Farms...239 // 10 GLM and GAM for Absence-Presence and Proportional Data ...245 // 10.1 Introduction...245 // 10.2 GLM for Absence-Presence Data...246 // 10.2.1 Tuberculosis in Wild Boar...246 // 10.2.2 Parasites in Cod...252 // 10.3 GLM for Proportional Data...254 // 10.4 GAM for Absence-Presence Data...258 // 10.5 Where to Go from Here? ...259 // 11 Zero-Truncated and Zero-Inflated Models for Count Data...261 // 11.1 Introduction...261 // 11.2 Zero-Truncated Data...263 // 11.2.1 The Underlying Mathematics for Truncated Models...263 // 11.2.2 Illustration of

Poisson and NB Truncated Models...265 // 11.3 Too Many Zeros...269 // 11.3.1 Sources of Zeros...270 // 11.3.2 Sources of Zeros for the Cod Parasite Data...271 // 11.3.3 Two-Part Models Versus Mixture Models, and Hippos ... 271 // 11.4 ZIP and ZINB Models...274 // 11.4.1 Mathematics of the ZIP and ZINB...274 // 11.4.2 Example of ZIP and ZINB Models...278 // 11.5 ZAP and ZANB Models, Alias Hurdle Models...286 // 11.5.1 Mathematics of the ZAP and ZANB ...287 // 11.5.2 Example of ZAP and ZANB...288 // 11.6 Comparing Poisson, Quasi-Poisson, NB, ZIP, ZINB, ZAP and // ZANB GLMs...291 // 11.7 Flowchart and Where to Go from Here...293 // 12 Generalised Estimation Equations ...295 // 12.1 GLM: Ignoring the Dependence Structure...295 // 12.1.1 The California Bird Data...295 // 12.1.2 The Owl Data...299 // 12.1.3 The Deer Data...300 // 12.2 Specifying the GEE...302 // 12.2.1 Introduction...302 // 12.2.2 Step 1 of the GEE: Systematic Component // and Link Function...303 // 12.2.3 Step 2 of the GEE: The Variance...304 // 12.2.4 Step 3 of the GEE: The Association Structure ...304 // 12.3 Why All the Fuss?...309 // 12.3.1 A Bit of Maths...310 // 12.4 Association for Binary Data...313 // 12.5 Examples of GEE...314 // 12.5.1 A GEE for the California Birds...314 // 12.5.2 A GEE for the Owls...316 // 12.5.3 A GEE for the Deer Data...319 // 12.6 Concluding Remarks...320 // 13 GLMM and GAMM...323 // 13.1 Setting the Scene for Binomial GLMM ...324 // 13.2 GLMM and GAMM for Binomial and Poisson Data

...327 // 13.2.1 Deer Data ...327 // 13.2.2 The Owl Data Revisited...333 // 13.2.3 A Word of Warning...339 // 13.3 The Underlying Mathematics in GLMM ...339 // 14 Estimating Trends for Antarctic Birds in Relation // to Climate Change ...343 // A.F. Zuur, C. Barbraud, E.N. léno, H. Weimerskirch, G.M. Smith, and N.J. Walker // 14.1 Introduction...343 // 14.1.1 Explanatory Variables...344 // 14.2 Data Exploration...345 // 14.3 Trends and Auto-correlation...350 // 14.4 Using Ice Extent as an Explanatory Variable...352 // 14.5 SOI and Differences Between Arrival and Laying Dates ...354 // 14.6 Discussion ...360 // 14.7 What to Report in a Paper...361 // 15 Large-Scale Impacts of Land-Use Change in a Scottish // Farming Catchment...363 // A.F. Zuur, D. Raffaeli!, A.A. Saveliev, N.J. Walker, E.N. leno, and G.M. Smith // 15.1 Introduction...363 // 15.2 Data Exploration...365 // 15.3 Estimation of Trends for the Bird Data...367 // 15.3.1 Model Validation...368 // 15.3.2 Failed Approach 1 ...372 // 15.3.3 Failed Approach 2...373 // 15.3.4 Assume Homogeneity?...374 // 15.4 Dealing with Independence...374 // 15.5 To Transform or Not to Transform...378 // 15.6 Birds and Explanatory Variables...378 // 15.7 Conclusions...380 // 15.8 What to Write in a Paper...381 // 16 Negative Binomial GAM and GAMM to Analyse Amphibian // Roadkills...383 // A.F. Zuur, A. Mira, F. Carvalho, E.N. leno, A.A. Saveliev, G.M. Smith, // and N.J. Walker // 16.1 Introduction...383 // 16.1.1 Roadkills...383 // 16.2

Data Exploration...385 // 16.3 GAM...389 // 16.4 Understanding What the Negative Binomial is Doing...394 // 16.5 GAMM: Adding Spatial Correlation...396 // 16.6 Discussion ...397 // 16.7 What to Write in a Paper...397 // 17 Additive Mixed Modelling Applied on Deep-Sea Pelagic // Bioluminescent Organisms...399 // A.F. Zuur, LG. Friede, E.N. leno, G.M. Smith, A.A. Saveliev, and N.J. Walker // 17.1 Biological Introduction...399 // 17.2 The Data and Underlying Questions...401 // 17.3 Construction of Multi-panel Plots for Grouped Data...402 // 17.3.1 Approach 1 ...402 // 17.3.2 Approach 2...407 // 17.3.3 Approach 3...408 // 17.4 Estimating Common Patterns Using Additive Mixed Modelling ... 410 // 17.4.1 One Smoothing Curve for All Stations ...410 // 17.4.2 Four Smoothers; One for Each Month...414 // 17.4.3 Smoothing Curves for Groups Based // on Geographical Distances...417 // 17.4.4 Smoothing Curves for Groups Based on Source // Correlations...418 // 17.5 Choosing the Best Model...:...419 // 17.6 Discussion ...420 // 17.7 What to Write in a Paper...421 // 18 Additive Mixed Modelling Applied on Phytoplankton Time Series // Data...423 // A.F. Zuur, M.J Latuhihin, E.N. leno, J.G. Baretta-Bekker, G.M. Smith, and N.J. Walker // 18.1 Introduction...423 // 18.1.1 Biological Background of the Project ...424 // 18.2 Data Exploration...427 // 18.3 A Statistical Data Analysis Strategy for DIN...429 // 18.4 Results for Temperature...439 // 18.5 Results for DIATI...441 // 18.6 Comparing Phytoplankton

and Environmental Trends...443 // 18.7 Conclusions...445 // 18.8 What to Write in a Paper...446 // 19 Mixed Effects Modelling Applied on American Foulbrood Affecting // Honey Bees Larvae...447 // A.F. Zuur, L.B. Gende, E.N. leno, N.J. Fernández, M.J. Eguaras, // R. Fritz, N.J. Walker, A.A. Saveliev, and G.M. Smith // 19.1 Introduction...447 // 19.2 Data Exploration...448 // 19.3 Analysis of the Data...450 // 19.4 Discussion ...458 // 19.5 What to Write in a Paper...458 // 20 Three-Way Nested Data for Age Determination Techniques Applied // to Cetaceans...459 // E.N. leno, PL. Luque, G.J. Pierce, A.F. Zuur, M.B. Santos, N.J. Walker, // A.A. Saveliev, and G.M. Smith // 20.1 Introduction...459 // 20.2 Data Exploration...460 // 20.3 Data Analysis...462 // 20.3.1 Intraclass Correlations...466 // 20.4 Discussion ...467 // 20.5 What to Write in a Paper...468 // 21 GLMM Applied on the Spatial Distribution of Koalas in a // Fragmented Landscape...469 // J.R. Rhodes, C.A. McAlpine, A.F. Zuur, G.M. Smith, and E.N. leno // 21.1 Introduction...469 // 21.2 The Data...471 // 21.3 Data Exploration and Preliminary Analysis...473 // 21.3.1 Collinearity...473 // 21.3.2 Spatial Auto-correlation...479 // 21.4 Generalised Linear Mixed Effects Modelling...481 // 21.4.1 Model Selection...483 // 21.4.2 Model Adequacy ...487 // 21.5 Discussion ...490 // 21.6 What to Write in a Paper...492 // 22 A Comparison of GLM, GEE, and GLMM Applied to Badger // Activity Data...493 // N.J. Walker, A.F. Zuur, A. Ward,

A.A. Saveliev, E.N. leno, and G.M. Smith // 22.1 Introduction...493 // 22.2 Data Exploration...495 // 22.3 GLM Results Assuming Independence...497 // 22.4 GEE Results...499 // 22.5 GLMM Results...500 // 22.6 Discussion ...501 // 22.7 What to Write in a Paper...502 // 23 Incorporating Temporal Correlation in Seal Abundance Data with // MCMC...503 // A.A. Saveliev, M. Cronin, A.F. Zuur, E.N. leno, N.J. Walker, and G.M. Smith // 23.1 Introduction...503 // 23.2 Preliminary Results...504 // 23.3 GLM...507 // 23.3.1 Validation ...509 // 23.4 What Is Bayesian Statistics?...510 // 23.4.1 Theory Behind Bayesian Statistics...510 // 23.4.2 Markov Chain Monte Carlo Techniques ...511 // 23.5 Fitting the Poisson Model in BRugs...513 // 23.5.1 Code in R ...513 // 23.5.2 Model Code...514 // 23.5.3 Initialising the Chains...515 // 23.5.4 Summarising the Posterior Distributions...517 // 23.5.5 Inference...518 // 23.6 Poisson Model with Random Effects...520 // 23.7 Poisson Model with Random Effects and Auto-correlation ...523 // 23.8 Negative Binomial Distribution with Auto-correlated Random // Effects ...525 // 23.8.1 Comparison of Models...528 // 23.9 Conclusions...528 // A Required Pre-knowledge: A Linear Regression and Additive // Modelling Example...531 // A.l The Data...531 // A.2 Data Exploration...532 // A.2.1 Step 1: Outliers...532 // A.2.2 Step 2: Collinearity ...533 // A.2.3 Relationships ...536 // A.3 Linear Regression...536 // A.3.1 Model Selection...540 // A.3.2 Model Validation...542

// A.3.3 Model Interpretation ...543 // A.4 Additive Modelling...546 // A.5 Further Extensions...550 // A.6 Information Theory and Multi-model Inference...550 // A.7 Maximum Likelihood Estimation in Linear Regression Context ... 552 // References...553 // Index // 563