Verfügbarkeit: Zero inflated models and generalized linear mixed models with R

Zero inflated models and generalized linear mixed models with R:

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Bibliographische Detailangaben
Hauptverfasser:	Zuur, Alain F. (VerfasserIn), Saveliev, Anatoly A. (VerfasserIn), Ieno, Elena N. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Newburgh Highland Statistics 2012
Schlagworte:	Statistische Analyse R > Programm Statistik Gemischtes Modell
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XVIII, 324 S. Ill., graph. Darst.
ISBN:	9780957174108 9780957174115

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Datensatz im Suchindex

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adam_text	IX Contents PREFACE ........................................................................................................................................................ V CONTENTS .................................................................................................................................................... IX CONTRIBUTORS ........................................................................................................................................... XV 1 INTRODUCTION TO BAYESIAN STATISTICS, MCMC TECHNIQUES, AND WINBUGS ........................................1 1.1 Probabilities and Bayes Theorem .............................................................................................................1 1.2 Likelihood functions ................................................................................................................................3 1.3 Conjugate prior distributions ..................................................................................................................6 1.4 MCMC .....................................................................................................................................................9 1.4.1 Markov Chain ..................................................................................................................................9 1.4.2 Transition rules* ...........................................................................................................................10 1.5 Using WinBUGS .....................................................................................................................................16 1.6 Summary ...............................................................................................................................................21 2 ZERO INFLATED GLMM APPLIED TO BARN OWL DATA ...............................................................................25 2.1 Introduction .........................................................................................................................................25 2.1.1 Vocal begging behaviour of nestling barn owls ............................................................................25 2.1.2 Previous analyses of the owl data .................................................................................................26 2.1.3 Prerequisite knowledge for this chapter .......................................................................................28 2.2 Importing and coding the data ...............................................................................................................28 2.3 Data exploration ...................................................................................................................................29 2.4 Overdispersion in the Poisson GLMM .....................................................................................................34 2.4.1 Assessing overdispersion using Pearson residuals ........................................................................34 2.4.2 Assessing overdispersion using an observation level random effect term ....................................35 2.4.3 Simulation study demonstrating observation level random effect ...............................................35 2.4.4 A GLMM with observation level random effect ............................................................................40 2.5 WHY ZERO INFLATED MODELS? ....................................................................................................................41 2.6 Implementing a Poisson GLM in WinBUGS ..............................................................................................43 2.6.1 Converting vectors to matrices .....................................................................................................43 2.6.2 Data for WinBUGS. ........................................................................................................................45 2.6.3 Modelling code for WinBUGS ........................................................................................................45 2.6.4 Initialising the chains ....................................................................................................................46 2.6.5 Parameters, thinning rate and length of the chains .....................................................................47 2.6.6 Starting WinBUGS from within R ..................................................................................................47 2.6.7 Assessing convergence of the chains ............................................................................................48 2.6.8 Summarising the posterior distributions .......................................................................................49 2.6.9 Pearson residuals ..........................................................................................................................51 2.6.10 WinBUGS versus GLM results ......................................................................................................53 2.7 Implementing a Poisson GLMM in WinBUGS ..........................................................................................54 2.8 Implementing a zero inflated Poisson GLM in WinBUGS using artificial data .........................................56 2.9 Application of ZIP GLMM in WinBUGS using the owl data .....................................................................62 2.10 USING DICTO FIND THE OPTIMAL ZIP GLMM FOR THE OWL DATA ...................................................................64 2.11 zip gamm for 1-way nested data ........................................................................................................66 2.12 Whatto present in a paper? .................................................................................................................66 Contents 3 A ROADMAP FOR ANALYSIS OF OVERDISPERSED SANDEEL COUNTS IN SEAL SCAT ....................................67 3.1 sandeel otoliths and seal scat ............................................................................................................... 67 3.2 Data exploration ................................................................................................................................... 68 3.3 GLM with a Poisson distribution ............................................................................................................ 71 3.4 GLM WITH A NEGATIVE BINOMIAL DISTRIBUTION .............................................................................................73 3.5 GAM WITH A POISSON DISTRIBUTION ........................................................................................................... 75 3.6 GAM WITH A NEGATIVE BINOMIAL DISTRIBUTION ............................................................................................76 3.6.1 Model and R code .........................................................................................................................76 3.6.2 Model validation of the negative binomial GAM ..........................................................................77 3.6.3 Model interpretation .....................................................................................................................78 3.7 Zero inflated GAM with a Poisson distribution ......................................................................................80 3.7.1 True and false zeros ......................................................................................................................81 3.7.2 The ZIP model ................................................................................................................................81 3.7.3 Result for the ZIP GAM ..................................................................................................................83 3.7.4 Result for the ZINB GAM ...............................................................................................................84 3.8 Final remarks .........................................................................................................................................87 3.9 Discussion ..............................................................................................................................................88 3.10 whatto present in a paper? .................................................................................................................89 4 GLMM AND ZERO INFLATED POISSON GLMM APPLIED TO 2-WAY NESTED MARMOT DATA ......................91 4.1 Introduction .........................................................................................................................................91 4.2 data exploration and visualisation ........................................................................................................93 4.2.1 Import the data and get a first impression ...................................................................................93 4.2.2 Zero inflation in the response variable ..........................................................................................94 4.2.3 Number of missing values .............................................................................................................95 4.2.4 Outliers ..........................................................................................................................................96 4.2.5 Collinearity ....................................................................................................................................96 4.2.6 Visualisation of relationships between number of young and the covariates ..............................98 4.3 WHAT MAKES THIS A DIFFICULT ANALYSIS? ...................................................................................................101 4.4 WHICH STATISTICAL TECHNIQUES AND SOFTWARE TO APPLY? ...........................................................................102 4.5 SHORT DESCRIPTION OF THE STATISTICAL METHODOLOGY ................................................................................103 4.5.1 Viewing it (wrongly) as a Gaussian linear mixed effects model ..................................................103 4.5.2 Viewing the data (potentially wrongly) as a Poisson GLM or GLMM .........................................106 4.5.3 Viewing the data (potentially wrong) as a zero inflated Poisson GLM .......................................107 4.5.4 Viewing the data (possibly correct) as a 2-way nested ZIP GLMM .............................................108 4.6 Dealing with 25 covariates in a 2-way nested ZIP GLMM ......................................................................109 4.7 WinBUGS and R code for Poisson GLM, GLMM, and ZIP models ..........................................................112 4.7.1 WinBUGS code for a Poisson GLM ..............................................................................................112 4.7.2 WinBUGS code for 1-way and 2-way nested Poisson GLMMs ....................................................116 4.7.3 WinBUGS code for ZIP GLM ........................................................................................................121 4.7.4 WinBUGS code for 2-way nested ZIP Polsson GLMMs ................................................................126 4.8 Validating the 2-way nested ZIP GLMM ...............................................................................................128 4.9 Interpretation of the 2-way nested ZIP GLMM model ..........................................................................133 4.10 Discussion .........................................................................................................................................134 4.11 What то present in a paper? ...............................................................................................................136 Appendix A: Correlation between observations in GLMMs* .......................................................................137 A.I Correlations in a Poisson GLMM for 1-way nested data* .............................................................137 A.2 Correlations in a Poisson GLMM for 2-way nested data* .............................................................138 A.3 Correlations in a binomial GLMM for 1-way nested data* ............................................................140 A.4 Correlations in a GLMM binomial model for 2-way nested data* .................................................142 A. 5 Correlations in a ZIP model for 1-way nested data* ......................................................................144 A.6 Correlations in a ZIP model for 2-way nested data* ......................................................................145 A.7 Non-technical summary of the appendix .......................................................................................145 A.8 Example of correlations for the 2-way nested ZIP GLMM* ...........................................................146 XI 5 TWO-STAGE GAMM APPLIED TO ZERO INFLATED COMMON MURRE DENSITY DATA ...............................149 5.1 Introduction .......................................................................................................................................149 5.2 Sampling ..............................................................................................................................................149 5.3 Covariates ...........................................................................................................................................153 5.4 Data exploration .................................................................................................................................154 5.4.1 Potential outliers in the bird data ...............................................................................................154 5.4.2 Zero inflation of the bird data .....................................................................................................154 5.4.3 Outliers in the covariates ............................................................................................................155 5.4.4 Collinearity of the covariates ......................................................................................................156 5.4.5 Visualisation of relationships between birds and covariates ......................................................159 5.4.6 Cruise and transect effects ..........................................................................................................161 5.4.7 Summary of the data exploration ...............................................................................................162 5.5 GAMM FOR ZERO INFLATED AND CORRELATED DENSITIES ...............................................................................163 5.5.1 Brainstorming .............................................................................................................................164 5.5.2 Four model selection approaches ...............................................................................................165 5.6 Results of the full model approach ......................................................................................................165 5.6.1 Results of the presence/absence GAMM ....................................................................................165 5.6.2 More detailed output for the binomial GAMM ...........................................................................167 5.6.3 Post-hoc testing ..........................................................................................................................168 5.5.4 Validation of the binomial GAMM ..............................................................................................170 5.5.5 Analysis of the presence-only data using a gamma GAMM .......................................................172 5.7 Fitting a Gamma GAMM with CAR correlation in WinBUGS ............................................................173 5.7.1 Fitting a Gamma GLM in WinBUGS .........................................................................................174 5.7.2 Fitting a ZIP GAM on the Common Murre counts in WinBUGS ...............................................176 5.7.3 Fitting a ZIP GAM with residual CAR in WinBUGS ...................................................................180 5.8 Discussion ............................................................................................................................................181 5.9 What то present in a paper? .................................................................................................................182 6 ZERO INFLATED SPATIALLY CORRELATED COASTAL SKATE DATA .............................................................183 6.1 Introduction .......................................................................................................................................183 6.2 Importing the data and data coding .....................................................................................................183 6.3 Data exploration .................................................................................................................................184 6.3.1 Outliers ........................................................................................................................................184 6.3.2 Collinearity ..................................................................................................................................185 6.3.3 Relationships ...............................................................................................................................187 6.3.4 Geographical position of the sites ...............................................................................................188 6.3.5 Zero inflation in the species data ................................................................................................189 6.3.6 What makes this a difficult analysis? ..........................................................................................190 6.4 Zero inflated GLM applied то R. agassizi data .......................................................................................191 6.4.1 What is the starting point? .........................................................................................................191 6.4.2 Poisson GLM applied to R. agassizi data .....................................................................................191 6.4.3 NB GLM applied to R. agassizi data ............................................................................................192 6.4.4 Zero inflated Poisson GLM applied to R. agassizi data ...............................................................193 6.4.5 Zero inflated negative binomial GLM applied to R. agassizi data ...............................................196 6.4.6 Model validation of the ZIP GLM applied to R. agassizi data ......................................................201 6.5 Zero inflated GLM applied to A. castelnaui data ..................................................................................203 6.6 ADDING SPATIAL CORRELATION TO A GLM MODEL .........................................................................................206 6.6.1 Who are the neighbours? ............................................................................................................206 6.6.2 Neighbouring sites ......................................................................................................................210 6.6.3 The CAR model* ..........................................................................................................................210 6.6.4 Applying CAR to simulated spatially correlated data ..................................................................212 6.7 Analysis of species 3: Sympterygia bonapart» ........................................................................................218 6.7.1 Poisson or negative binomial distribution? .................................................................................218 6.7.2 Adding spatial correlation to the zero inflated Poisson GLM ......................................................218 6.7.3 Stetting up the required matrices for car.proper ........................................................................219 6.7.4 Preparing MCMC code for a ZIP with residual CAR correlation ..................................................222 ХП Contents 6.7.5 МСМС results for ZIP with residual CAR structure ......................................................................225 6.8 Discussion ............................................................................................................................................229 6.9 whatto present in a paper? ................................................................................................................. 230 7 ZERO INFLATED GLMS WITH SPATIAL CORRELATION- ANALYSIS OF PARROTFISH ABUNDANCE ...............231 7.1 Introduction .......................................................................................................................................231 7.2 The data ..............................................................................................................................................232 7.2.1 Surveying .....................................................................................................................................232 7.2.2 Response variable .......................................................................................................................234 7.2.3 Covariates ...................................................................................................................................234 7.3 ANALYSIS OF THE ZERO INFLATED DATA IGNORING THE CORRELATION .................................................................238 7.3.1 Poisson and NB GLMs .................................................................................................................238 7.3.2 ZIP and ZINBGLMs ......................................................................................................................239 7.3.3 Model selection for ZINB .............................................................................................................243 7.3.4 Independence ..............................................................................................................................244 7.3.5 Independence - model misspecification .....................................................................................245 7.3.6 Adding year to the ZINB? ............................................................................................................245 7.3.7 Dive effect on the residuals .........................................................................................................246 7.3.8 Adjusting the sample variogram for land between transects .....................................................246 7.3.9 Which model to choose? .............................................................................................................249 7.4 ZERO INFLATED MODELS WITH A RANDOM INTERCEPT FOR DIVE .......................................................................250 7.5 ZERO INFLATED MODELS WITH SPATIAL CORRELATION .....................................................................................250 7.5.1 Adding a residual correlation structure to the ZINB ...................................................................250 7.5.2 ZINB with a residual CAR correlation in R ...................................................................................251 7.5.3 МСМС results ..............................................................................................................................253 7.6 Predictions ..........................................................................................................................................254 7.7 Discussion ............................................................................................................................................255 7.8 What то write in a paper ......................................................................................................................255 8 ANALYSIS OF ZERO INFLATED CLICK-BEETLE DATA ...................................................................................257 8.1 Introduction .......................................................................................................................................257 8.2 The setup of the experiment ..................................................................................................................257 8.3 Importing data and coding ..................................................................................................................258 8.4 Data exploration .................................................................................................................................259 8.4.1 Spatial position of the sites .........................................................................................................259 8.4.2 Response and explanatory variables ...........................................................................................260 8.4.3 Viewing the data as time series ..................................................................................................261 8.4.4 Spatial and temporal patterns ....................................................................................................262 8.4.5 Big trouble ...................................................................................................................................263 8.4.6 Effects and interactions for the species data ..............................................................................265 8.4.7 Zero inflation ...............................................................................................................................267 8.4.8 Direction ......................................................................................................................................267 8.4.9 Where to go f rom here; zero inflated models? ...........................................................................268 e.S.ZIPGLM ..............................................................................................................................................268 8.6 zip glm without correlation for the species data ...............................................................................269 8.7 results for the female-male data .......................................................................................................274 8.8 Discussion ............................................................................................................................................276 8.9 Whatto write in a paper? ....................................................................................................................276 9 ZERO INFLATED GAM FOR TEMPORAL CORRELATED SPERM WHALE STRANDINGS TIME SERIES ..............277 9.1 Introduction .......................................................................................................................................277 9.2 what makes this a difficult analysis? ...................................................................................................277 9.3 Importing and data coding ..................................................................................................................278 9.4 Data exploration .................................................................................................................................278 9.5 Poisson GAM with a single smoother in WinBUGS ...............................................................................280 9.5.1 Fitting a Poisson GAM using gam from mgcv .............................................................................280 9.5.2 Fitting the binomial GAM from Pierce et al. (2007)....................................................................282 XIII 9.5.3 Knots ...........................................................................................................................................283 9.5.4 Low rank thin plate splines .........................................................................................................284 9.5.5 Mathematics for low rank thin plate splines ..............................................................................286 9.5.6 Bypassing the mathematics ........................................................................................................288 9.5.7 WinBUGS code for GAM ..............................................................................................................289 9.5.8 Results .........................................................................................................................................290 9.6 Poisson GAM with two smoothers in WinBUGS ...................................................................................293 9.7ZERO inflated Poisson GAM in WinBUGS ..............................................................................................296 9.7.1 Justification for zero inflated models ..........................................................................................296 9.7.2 Underlying equations for the ZIP GAM .......................................................................................297 9.7.3 R code for a ZIP GAM ..................................................................................................................298 9.7.4 Results for the ZIP GAM ..............................................................................................................299 9.7.5 Model validation of the ZIP GAM ................................................................................................301 9.8 Zero inflated Poisson GAM with temporal correlation in WinBUGS ....................................................302 9.8.1 CAR residual correlation in the ZIP GAM .....................................................................................303 9.8.2 Auto-regressive residual correlation in the ZIP GAM ..................................................................306 9.9 Discussion ............................................................................................................................................308 9.10 Whatto write in a paper? ..................................................................................................................308 10 EPILOGUE ..............................................................................................................................................309 10.1 An excessive number of zeros does not mean zero inflation ................................................................309 10.2 do we need false zeros in order to apply mixture models? ..................................................................311 10.3 were the false zeros in our examples really false? .............................................................................311 10.4 does the algorithm know which zeros are false? ...............................................................................312 REFERENCES ..............................................................................................................................................315 INDEX ........................................................................................................................................................321
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publisher	Highland Statistics
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spelling	Zuur, Alain F. Verfasser aut Zero inflated models and generalized linear mixed models with R Alain F. Zuur ; Anatoly A. Savaliev ; Elena N. Ieno Newburgh Highland Statistics 2012 XVIII, 324 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistische Analyse (DE-588)4116599-8 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Gemischtes Modell (DE-588)4156565-4 gnd rswk-swf Statistik (DE-588)4056995-0 s R Programm (DE-588)4705956-4 s DE-604 Statistische Analyse (DE-588)4116599-8 s Gemischtes Modell (DE-588)4156565-4 s Saveliev, Anatoly A. Verfasser aut Ieno, Elena N. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024965154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Zuur, Alain F. Saveliev, Anatoly A. Ieno, Elena N. Zero inflated models and generalized linear mixed models with R Statistische Analyse (DE-588)4116599-8 gnd R Programm (DE-588)4705956-4 gnd Statistik (DE-588)4056995-0 gnd Gemischtes Modell (DE-588)4156565-4 gnd
subject_GND	(DE-588)4116599-8 (DE-588)4705956-4 (DE-588)4056995-0 (DE-588)4156565-4
title	Zero inflated models and generalized linear mixed models with R
title_auth	Zero inflated models and generalized linear mixed models with R
title_exact_search	Zero inflated models and generalized linear mixed models with R
title_full	Zero inflated models and generalized linear mixed models with R Alain F. Zuur ; Anatoly A. Savaliev ; Elena N. Ieno
title_fullStr	Zero inflated models and generalized linear mixed models with R Alain F. Zuur ; Anatoly A. Savaliev ; Elena N. Ieno
title_full_unstemmed	Zero inflated models and generalized linear mixed models with R Alain F. Zuur ; Anatoly A. Savaliev ; Elena N. Ieno
title_short	Zero inflated models and generalized linear mixed models with R
title_sort	zero inflated models and generalized linear mixed models with r
topic	Statistische Analyse (DE-588)4116599-8 gnd R Programm (DE-588)4705956-4 gnd Statistik (DE-588)4056995-0 gnd Gemischtes Modell (DE-588)4156565-4 gnd
topic_facet	Statistische Analyse R Programm Statistik Gemischtes Modell
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024965154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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