Beginner's guide to zero-inflated models with R:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
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Newburgh, United Kingdom
Highland Statistics Ltd.
2016
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 414 Seiten Illustrationen, Diagramme |
| ISBN: | 9780957174184 |
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| 245 | 1 | 0 | |a Beginner's guide to zero-inflated models with R |c Alain F. Zuur, Elena N. Ieno |
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| adam_text | Alain F Zuur
Elena N Ieno
Beginner’s Guide to
Zero-Inflated Models with R
Published by Highland Statistics Ltd
Highland Statistics Ltd
Newburgh
United Kingdom
highstat @ highstat com
ISBN: 978-0-9571741-8-4
First published in I
ULB Darmstadt
19351106
vii
Contents
Preface v
Acknowledgements v
Datasets used in this book vi
Cover art vi
CONTENTS VII
1 INTRODUCTION 1
1 1 HOW DO THE 2012 AND 2016 BOOKS DIFFER? 1
1 2 What do you need to know to use this book? 1
1 3 Outline of the book 2
1 4 What is not in this book? 3
1 5 How TO READ THIS BOOK 4
1 6 Accessing the data and the R code 4
17A FEW FINAL COMMENTS 4
2 ESSENTIAL DISTRIBUTIONS FOR ZERO-INFLATED MODELS 5
2 1 Distributions 5
2 2 Poisson distribution 5
2 3 Negative binomial distribution 7
2 4 Bernoulli distribution 9
2 5 Binomial distribution 9
2 6 Gamma distribution 11
2 7 Lognormal distribution 13
2 8 Summary of distributions 14
3 INTRODUCING ZERO-INFLATED POISSON MODELS 17
3 1 Poisson GLM 18
311 Simulating Poisson distributed data 18
312 Applying the Poisson GLM 19
313 Model validation 20
314 Dispersion 21
315 Visualising the model fit 23
316 Using two covariates in a Poisson GLM 25
3 2 Bernoulli GLM 26
321 Crocodile attack data 26
322 The model 27
323 Applying the Bernoulli GLM in R 27
324 Model validation 28
325 Visualising the model fit of the Bernoulli GLM 28
3 3 Conceptual explanations of ZIP models 29
331 Nature flips a coin 30
332 Nature creates the counts 31
333 Fitting the ZIP model in R 33
334 Model validation for the ZIP model 34
viii
335 Validation for the ZIP model 35
336 Poisson GLM applied on zero-inflated data 37
3 4 True and false zeros 40
341 The origin of zeros 40
342 The density function of a ZIP 42
3 5 Covariates in both parts of the ZIP model 43
351 The same covariate in both parts of the ZIP model 43
352 Using two different covariates in the ZIP model 48
4 ZERO-INFLATED MODELS APPLIED TO ORANGE-CROWNED
WARBLERS 53
4 1 Orange-crowned warblers 53
4 2 Data exploration 54
4 3 Poisson GLM 56
431 Model formulation 56
432 Fitting the Poisson GLM 57
433 Simulating data from the model 57
434 Fitted values 59
435 What is next? 60
4 4 ZIP MODEL 60
441 Fitting the ZIP model 60
442 Simulating data from the ZIP model 61
4 5 Model selection for the ZIP model using AIC 64
451 What is the AIC? 64
452 How do you calculate the AIC? 64
453 AICs for 16 models 67
454 The optimal ZIP model 67
4 6 Discussion 69
5 ZERO-INFLATED MODELS APPLIED TO SHARK ABUNDANCE
DATA 71
5 1 Sharks 71
5 2 Poisson GLM applied to tiger sharks 72
521 Specifying the model 72
522 Fitting the Poisson GLM in R 74
523 Poisson GLM results for the tiger sharks 74
524 Assessing overdispersion 75
525 Model selection 75
526 Model validation 76
527 Model interpretation 76
5 3 NB GLM APPLIED TO TOTAL NUMBER OF ALL SHARK SPECIES 77
531 Poisson GLM results 77
532 Negative binomial GLM results 78
533 ZIP model results 80
5 4 Zero-inflated Poisson model and silvertip sharks 81
541 Poisson and quasi-Poisson GLM 81
542 NB GLM applied to silvertip shark data 82
IX
543 ZIP model 83
5 5 Possible extensions 86
6 HURDLE MODELS FOR RIPARIAN SPIDER COUNTS 87
6 1 Riparian spiders 87
611 Introducing the data 87
612 Data exploration 88
6 2 Poisson GLM results 94
6 3 Explanation of hurdle models 96
631 Nature flips a coin 96
632 Nature creates count data 97
633 Crossing a hurdle 100
634 Density function of the ZAP model 101
6 4 ZAP MODEL FOR THE SPIDER DATA 102
641 Model formulation 102
642 Running the hurdle model in R 102
6 5 Doing it manually in two steps 109
6 6 Simulating from the model 110
7 MODELS FOR ZERO-INFLATED CONTINUOUS DATA APPLIED TO
CHINESE TALLOW TREES 113
7 1 Chinese tallow trees 113
711 Introduction to the data 113
712 Data exploration 114
7 2 Multiple linear regression applied to the CTT data 116
7 3 Gamma GLM 117
731 Simulating gamma distributed data 117
732 Applying the gamma GLM 118
733 Visualising the model fit 119
7 4 Explanation of hurdle models 120
741 Nature flips a coin 120
742 Nature creates continuous data 121
743 ZAG model 122
744 Density function of the hurdle GLM 126
7 5 The hurdle model applied to the CTT data 126
751 Hurdle model formulation for the CTT data 126
752 Applying the gamma GLM to the CTT data 127
753 Bernoulli GLM applied to the CTT data 128
754 Gluing together the two components 129
7 6 Discussion 131
7 7 What to put in a paper 132
8 LINEAR MIXED EFFECTS MODELS 133
8 1 Liliesand beavers 133
811 Data exploration 133
812 Model formulation 135
813 Fitting the model using Imer 138
X
814 Model validation 139
815 Sketching the fitted values 140
8 2 Chacma baboons 143
821 Dependency structure 143
822 Data exploration 146
823 Model formulation 147
824 Fitting the model using lmer 147
825 Model validation 148
826 Sketching the fitted values 149
8 3 Discussion 150
831 Lilies and beaver dataset 150
832 Baboon dataset 151
9 ZERO-ALTERED MODELS WITH TWO-WAY NESTED AND
CROSSED RANDOM EFFECTS 153
9 1 Climate change and grassland species 153
9 2 Data exploration 155
9 3 Poisson GLMM 156
931 Model formulation 156
932 Fitting the Poisson GLMM using Ime4 157
933 Model validation 158
934 How to continue: Zero inflation or GAMM? 162
935 Model fit of the Poisson GLMM 163
9 4 Zero-altered models with random effects 164
941 Bernoulli GLMM for absence and presence data 165
942 Once T montanum is present 167
943 Combining both models 171
9 5 Discussion 176
10 INTRODUCTION TO BAYESIAN STATISTICS 177
10 1 General probability rules 177
10 2 Bivariate linear regression applied to osprey data 180
10 2 1 Ospreys 1B0
10 2 2 Ordinary least squares 181
10 2 3 The frequentist interpretation 182
10 2 4 Changing the notation 185
10 2 5 Likelihood estimation as an alternative to OLS 187
10 3 Why go Bayesian? 188
10 4 A cartoon explanation of MCMC 190
10 5 Concept of MCMC 192
10 5 1 Starting values 193
10 5 2 Parameters to save 193
10 5 3 Burn-in 193
10 5 4 The Metropolis-Hastings algorithm 193
XI
10 6 Do-it-yourself MCMC in R 195
10 6 1 Standardisation of continuous covariates 195
10 6 2 Steps 1 and 2 of the MCMC algorithm in R 196
10 6 3 Step 3 of the MCMC algorithm in R 197
10 6 4 Mixing 200
10 6 5 Posterior mean values and posterior distributions 204
10 7 MCMC APPLIED TO OSPREY DATA IN JAGS 204
10 7 1 Installing JAGS and R2jags 204
10 7 2 Flowchart for running a model in JAGS 204
10 7 3 Preparing the data for JAGS 206
10 7 4 JAGS code 206
10 7 5 Initial values and parameters to save 209
10 7 6 Running JAGS 210
10 7 7 Accessing numerical output from JAGS 211
10 7 8 Assess mixing 212
10 7 9 Posterior information 213
10 8 What to remember from this chapter 214
10 9 Recommended literature 214
10 10 What s next? 214
10 11 Exercises with video solution files 214
10 11 1 Exercise 1: Irish pH data 214
10 11 2 Exercise 2: Crayfish data 215
11 BAYESIAN ANALYSIS FOR POISSON, NB, ZIP AND BERNOULLI
MODELS 217
11 1 Fitting a Poisson GLM in a Bayesian context 217
11 1 1 Poisson GLM for tiger shark data 217
11 1 2 Preparing the data for JAGS 218
11 1 3 JAGS code for a Poisson GLM 219
11 1 4 Initial values and parameters to save 221
11 1 5 Running JAGS 221
11 1 6 Results from JAGS for the Poisson GLM 222
11 1 7 Assess overdispersion 223
11 1 8 Model validation 226
11 2 Negative binomial GLM in JAGS 228
11 3 Zero-inflated models in JAGS for silvertip sharks 231
11 3 1 Data for JAGS 232
11 3 2 JAGS code for a ZIP model 232
11 3 3 Initial values and parameters to save 233
11 3 4 Running JAGS 233
11 3 5 Mixing of chains 235
11 3 6 Calculating Pearson residuals retrospectively 236
11 4 Bayesian Bernoulli GLM 237
11 4 1 Data for JAGS 238
11 4 2 JAGS code for the Bernoulli GLM 238
11 4 3 Initial values and parameters to save 239
11 4 4 Running JAGS 239
xn
11 4 5 Mixing of chains 240
11 4 6 Numerical results 240
11 4 7Sketching the results 242
11 5 References 247
12 BAYESIAN ANALYSIS FOR LINEAR MIXED EFFECTS MODELS -
BEAVER AND LILIES 249
12 1 Lilies and beaver data 249
12 2 Data for JAGS 249
12 3 JAGS code 251
12 4 INITIAL VALUES AND PARAMETERS TO SAVE 252
12 5 Running JAGS 252
12 6 Assess mixing 253
12 7 Numerical results 254
12 8 Model validation 254
12 9 Visualising the results 257
12 10 Missing values 260
13 THE ZERO TRICK TO FIT ANY DISTRIBUTION IN A BAYESIAN
ANALYSIS 265
13 1 Underlying mathematics 265
13 2 Zero trick for a Poisson GLM 267
13 2 1 Preparing the data for JAGS 267
13 2 2 JAGS code 268
13 2 3 Initial values and parameters to save 269
13 2 4 Running JAGS 269
13 2 5 Numerical output 269
13 3 Zero trick for the ZIP model 270
13 4 Zero trick for a ZAP model 271
13 5 Applying a Bayesian gamma GLM to the CTT data 272
13 6 The hurdle model applied to the CTT data 275
13 6 1 Data for JAGS 275
13 6 2 JAGS code for the hurdle model 276
13 6 3 Initial values and parameters to save 277
13 6 4 Running JAGS 277
13 6 5 Mixing of chains 278
13 6 6 Numerical results 278
13 6 7 Model validation 280
13 6 8 Sketching the fitted values 282
13 7 Lognormal regression applied to the CTT data 284
13 8 Discussion 286
14 BAYESIAN MODEL SELECTION TECHNIQUES 287
14 1 Critical notes on model selection 288
14 1 1 Dropping covariates based on p-values? 288
14 1 2 Using theAIC 289
14 1 3 Information theoretic approach 289
14 1 4 Other approaches 289
xiii
14 2 Bayesian analysis of orange-crowned warblers 290
14 2 1 Fitting the Poisson GLM 290
14 2 2 Fitting a zero inflated Poisson model 293
14 3 Comparing the Poisson and ZIP models 295
14 4 Bayesian model selection: AIC and Die 297
14 4 1 Using the AIC 297
14 4 2 Using the D1C 299
14 5 Bayesian model selection: LASSO 302
14 5 1 Simulation study for LASSO 303
14 5 2 Bayesian LASSO 305
14 5 3 LASSO and ZIP model? 307
14 6 Bayesian model selection with indicator functions 307
14 6 1 Kuo and Mallick 308
14 6 2 Gibbs variable selection 314
14 7 Bayesian model selection: Model probabilities 318
14 7 1 Non-mathematical introduction 318
14 72A little bit of mathematics 319
14 8 Discussion 322
15 BAYESIAN MODEL SELECTION APPLIED TO ZERO-INFLATED
BUTTERFLY DATA 325
15 1 Butterflies 325
15 2 Data exploration 326
15 3 POISSON GLMM 329
15 3 1 Data for JAGS 330
15 3 2 JAGS code 331
15 3 3 Initial values and parameters to save 332
15 3 4 Running JAGS 332
15 3 5 Mixing 332
15 3 6 Dispersion 333
15 3 7 Model validation 333
15 4 ZIP, ZAP OR THE NB GLM? 335
15 4 1 Model probabilities 336
15 4 2 Out of sample prediction 339
15 5 ZAP MODEL WITH RANDOM EFFECTS 341
15 5 1 Data for JAGS 342
15 5 2 JAGS code 342
15 5 3 Initial values and parameters to save 344
15 5 4 Running JAGS 344
15 5 5 Mixing 344
15 5 6 Numerical output 344
15 6 ZAP MIXED MODELS AND BAYESIAN MODEL SELECTION 345
15 6 1 Data for JAGS 346
15 6 2 JAGS modelling code 347
15 6 3 Initial values and parameters to save 349
15 6 4 Running JAGS 350
15 6 5 Mixing 350
xiv
15 6 6 Numerical information 350
15 7 Visualising the optimal ZAP model 351
16 ZERO-INFLATED SEAGRASS COVERAGE DATA 353
16 1 SEAGRASS 353
16 2 Brainstorming 354
16 2 1 Which covariates? 354
16 2 2 Adding dependency 354
16 2 3 Anticipated problems 355
16 2 4 Subsetting the data to shorten computing time 356
16 3 Data exploration 356
16 4 The zero-inflated beta model 359
16 4 1 The beta distribution 359
16 4 2 The beta model 360
16 4 3 Zero-inflated beta model 362
16 5 SEAGRASS DATA AND THE ZERO-ALTERED BETA MODEL 364
16 5 1 Frequentist approach 364
16 5 2 Bayesian approach 369
16 6 Visualisation of results and Bayesian post-hoc test 372
16 7 Half-Cauchy distribution 376
17 OTHER DISTRIBUTIONS 379
17 1 Zero-inflated binomial data 379
17 2 Generalised Poisson model 380
17 3 Zero-inflated negative binomial models 386
18 MULTIVARIATE GLMM 387
18 1 Pseudo-replication 387
18 2 Multivariate GLMM for plant pollen 388
18 2 1 Pollen data 388
18 2 2 Univariate Poisson GLMM 389
18 2 3 Specification of a multivariate GLMM 390
18 2 4 Multivariate GLMM in JAGS 391
18 2 5 Multivariate GLMM results for the pollen data 395
18 2 6 Differences between univariate and multivariate GLMMs 397
18 2 7 Discussion 397
REFERENCES 399
INDEX 407
|
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| spelling | Zuur, Alain F. Verfasser (DE-588)1068021438 aut Beginner's guide to zero-inflated models with R Alain F. Zuur, Elena N. Ieno Newburgh, United Kingdom Highland Statistics Ltd. 2016 xvi, 414 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Ecology / Statistical methods Multilevel models (Statistics) R (Computer program language) Regression analysis Linear models (Statistics) Generalized estimating equations Mathematics / Data processing Datenverarbeitung Mathematik Ökologie Ökologie (DE-588)4043207-5 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf R Programm (DE-588)4705956-4 s Ökologie (DE-588)4043207-5 s DE-604 Ieno, Elena N. Verfasser (DE-588)1068021616 aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029262516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zuur, Alain F. Ieno, Elena N. Beginner's guide to zero-inflated models with R Ecology / Statistical methods Multilevel models (Statistics) R (Computer program language) Regression analysis Linear models (Statistics) Generalized estimating equations Mathematics / Data processing Datenverarbeitung Mathematik Ökologie Ökologie (DE-588)4043207-5 gnd R Programm (DE-588)4705956-4 gnd |
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| title | Beginner's guide to zero-inflated models with R |
| title_auth | Beginner's guide to zero-inflated models with R |
| title_exact_search | Beginner's guide to zero-inflated models with R |
| title_full | Beginner's guide to zero-inflated models with R Alain F. Zuur, Elena N. Ieno |
| title_fullStr | Beginner's guide to zero-inflated models with R Alain F. Zuur, Elena N. Ieno |
| title_full_unstemmed | Beginner's guide to zero-inflated models with R Alain F. Zuur, Elena N. Ieno |
| title_short | Beginner's guide to zero-inflated models with R |
| title_sort | beginner s guide to zero inflated models with r |
| topic | Ecology / Statistical methods Multilevel models (Statistics) R (Computer program language) Regression analysis Linear models (Statistics) Generalized estimating equations Mathematics / Data processing Datenverarbeitung Mathematik Ökologie Ökologie (DE-588)4043207-5 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Ecology / Statistical methods Multilevel models (Statistics) R (Computer program language) Regression analysis Linear models (Statistics) Generalized estimating equations Mathematics / Data processing Datenverarbeitung Mathematik Ökologie R Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029262516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zuuralainf beginnersguidetozeroinflatedmodelswithr AT ienoelenan beginnersguidetozeroinflatedmodelswithr |