Mixed effects models and extensions in ecology with R:
"In this book the authors provide an expanded introduction to using regression and its extensions in analysing ecological data. The first part of the book is a largely non-mathematical introduction to linear mixed effects modelling, GLM and GAM, zero inflated models, GEE, GLMM and GAMM. The sec...
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Schriftenreihe: | Statistics for biology and health
|
| Schlagworte: | |
| Online-Zugang: | Cover Kapitel 2 Vorwort 1 Inhaltsverzeichnis |
| Zusammenfassung: | "In this book the authors provide an expanded introduction to using regression and its extensions in analysing ecological data. The first part of the book is a largely non-mathematical introduction to linear mixed effects modelling, GLM and GAM, zero inflated models, GEE, GLMM and GAMM. The second part provides ten case studies that range from koalas to deep sea research. These chapters provide an invaluable insight into analysing complex ecological datasets, including comparisons of different approaches to the same problem. By matching ecological questions and data structure to a case study, these chapters provide an excellent starting point to analysing the reader's own data." --NHBS Environment Bookstore. |
| Beschreibung: | XXII, 574 S. graph. Darst. |
| ISBN: | 9780387874579 9781441927644 |
Internformat
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| 245 | 1 | 0 | |a Mixed effects models and extensions in ecology with R |c Alain F. Zuur ... |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XXII, 574 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Statistics for biology and health | |
| 520 | 1 | |a "In this book the authors provide an expanded introduction to using regression and its extensions in analysing ecological data. The first part of the book is a largely non-mathematical introduction to linear mixed effects modelling, GLM and GAM, zero inflated models, GEE, GLMM and GAMM. The second part provides ten case studies that range from koalas to deep sea research. These chapters provide an invaluable insight into analysing complex ecological datasets, including comparisons of different approaches to the same problem. By matching ecological questions and data structure to a case study, these chapters provide an excellent starting point to analysing the reader's own data." --NHBS Environment Bookstore. | |
| 650 | 4 | |a Ökologie | |
| 650 | 4 | |a Ecology |x Statistical methods | |
| 650 | 4 | |a R (Computer program language) | |
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Datensatz im Suchindex
| _version_ | 1817681157336072192 |
|---|---|
| adam_text |
Contents
1
Introduction
. 1
1.1
What Is in the Book?
. 1
1.1.1
To Include or Not to Include GLM and GAM
. 3
1.1.2
Case Studies
. 4
1.1.3
Flowchart of the Content
. 4
1.2
Software
. 5
1.3
How to Use This Book If You Are an Instructor
. 6
1.4
What We Did Not Do and Why
. 6
1.5
How to Cite
R
and Associated Packages
. 7
1.6
Our
R
Programming Style
. 8
1.7
Getting Data into
R
. 9
1.7.1
Data in a Package
. 10
2
Limitations of Linear Regression Applied on Ecological Data
.
II
2.1
Data Exploration
. 12
2.1.1
Cleveland Dotplots
. 12
2.1.2
Pairplots
. 14
2.1.3
Boxplots
. 15
2.1.4
xyplot from the Lattice Package
. 15
2.2
The Linear Regression Model
. 17
2.3
Violating the Assumptions; Exception or Rule?
. 19
2.3.1
Introduction
. 19
2.3.2
Normality
. 19
2.3.3
Heterogeneity
. 20
2.3.4
Fixed X
. 21
2.3.5
Independence
. 21
2.3.6
Example
1 ;
Wedge Clam Data
. 22
2.3.7
Example
2;
Moby's Teeth
. 26
2.3.8
Example
3;
Nereis
. 28
2.3.9
Example
4;
Pelagic
Bioluminescence
. 30
2.4
Where to Go from Here
. 31
cji Contents
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
Linear Regression Applied on Squid
. 72
The Fixed Variance Structure
. 74
The Varldent Variance Structure
. 75
The varPower Variance Structure
. 78
The varExp Variance Structure
. 80
The varConstPower Variance Structure
. 80
The varComb Variance Structure
. 81
Overview of All Variance Structures
. 82
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
4.
.1
4.
.2
4.
.3
4.
.4
4.
1.5
4.
1.6
4.
.7
4.
.8
4.
.9
Contents
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
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
Multi variate
Time Series
.152
6.3
Owl Sibling Negotiation Data
.158
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 Godwits 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
.
1
86
7.6.5
Why All the Fuss?
. 190
Contents
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
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 Dropl 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
Contents xv
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
1
1
.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
1
1.4
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
xv¡
Contents
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,
С.
Barbraud,
E.N.
leno,
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. Raffaelli,
A.A.
Saveliev,
N.J.
Walker, E.N. Ieno,
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
Contents xvii
16 Negative
Binomial
GAM and GAMM
to Analyse Amphibian
Roadkills
.383
A.F. Zuur,
Α.
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,
I.G. Priede, E.N. Ieno, 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. Ieno, 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
xviii
Contents
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. Ieno, 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,
CA. McAlpine, A.F. Zuur, G.M.
Smith, and E.N. Ieno
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
2
1
.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. Ieno,
and G.M. Smith
22.1
Introduction
.493
22.2
Data Exploration
.495
22.3
GLM Results Assuming Independence
.497
Contents xix
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
.53 !
A.
1
The Data
.53
1
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 |
| any_adam_object | 1 |
| author_GND | (DE-588)1068021438 |
| building | Verbundindex |
| bvnumber | BV035546050 |
| callnumber-first | Q - Science |
| callnumber-label | QH541 |
| callnumber-raw | QH541.15.S72 |
| callnumber-search | QH541.15.S72 |
| callnumber-sort | QH 3541.15 S72 |
| callnumber-subject | QH - Natural History and Biology |
| classification_rvk | ST 250 WC 7700 |
| classification_tum | UMW 002f DAT 307f MAT 620f |
| ctrlnum | (OCoLC)288985460 (DE-599)DNB990930386 |
| dewey-full | 577.0727 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 577 - Ecology |
| dewey-raw | 577.0727 |
| dewey-search | 577.0727 |
| dewey-sort | 3577.0727 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Informatik Mathematik Umwelt |
| format | Book |
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| id | DE-604.BV035546050 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T09:03:54Z |
| institution | BVB |
| isbn | 9780387874579 9781441927644 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017602029 |
| oclc_num | 288985460 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-19 DE-BY-UBM DE-M49 DE-BY-TUM DE-11 DE-Grf2 DE-188 DE-91G DE-BY-TUM DE-83 DE-29 DE-355 DE-BY-UBR DE-29T DE-Eb1 |
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| physical | XXII, 574 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Statistics for biology and health |
| spelling | Mixed effects models and extensions in ecology with R Alain F. Zuur ... New York, NY Springer 2009 XXII, 574 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics for biology and health "In this book the authors provide an expanded introduction to using regression and its extensions in analysing ecological data. The first part of the book is a largely non-mathematical introduction to linear mixed effects modelling, GLM and GAM, zero inflated models, GEE, GLMM and GAMM. The second part provides ten case studies that range from koalas to deep sea research. These chapters provide an invaluable insight into analysing complex ecological datasets, including comparisons of different approaches to the same problem. By matching ecological questions and data structure to a case study, these chapters provide an excellent starting point to analysing the reader's own data." --NHBS Environment Bookstore. Ökologie Ecology Statistical methods R (Computer program language) Ökologie (DE-588)4043207-5 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Ökologie (DE-588)4043207-5 s Datenanalyse (DE-588)4123037-1 s Statistisches Modell (DE-588)4121722-6 s R Programm (DE-588)4705956-4 s b DE-604 Zuur, Alain F. Sonstige (DE-588)1068021438 oth Erscheint auch als Online-Ausgabe 978-0-387-87458-6 DE-576;springer image/jpeg http://swbplus.bsz-bw.de/bsz305834320cov.htm 20090603063105 Cover DE-576;springer application/pdf http://swbplus.bsz-bw.de/bsz305834320kap.htm 20090623101922 Kapitel 2 DE-576;springer application/pdf http://swbplus.bsz-bw.de/bsz305834320vor.htm 20090623100140 Vorwort 1 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017602029&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mixed effects models and extensions in ecology with R Ökologie Ecology Statistical methods R (Computer program language) Ökologie (DE-588)4043207-5 gnd R Programm (DE-588)4705956-4 gnd Datenanalyse (DE-588)4123037-1 gnd Statistisches Modell (DE-588)4121722-6 gnd |
| subject_GND | (DE-588)4043207-5 (DE-588)4705956-4 (DE-588)4123037-1 (DE-588)4121722-6 |
| title | Mixed effects models and extensions in ecology with R |
| title_auth | Mixed effects models and extensions in ecology with R |
| title_exact_search | Mixed effects models and extensions in ecology with R |
| title_full | Mixed effects models and extensions in ecology with R Alain F. Zuur ... |
| title_fullStr | Mixed effects models and extensions in ecology with R Alain F. Zuur ... |
| title_full_unstemmed | Mixed effects models and extensions in ecology with R Alain F. Zuur ... |
| title_short | Mixed effects models and extensions in ecology with R |
| title_sort | mixed effects models and extensions in ecology with r |
| topic | Ökologie Ecology Statistical methods R (Computer program language) Ökologie (DE-588)4043207-5 gnd R Programm (DE-588)4705956-4 gnd Datenanalyse (DE-588)4123037-1 gnd Statistisches Modell (DE-588)4121722-6 gnd |
| topic_facet | Ökologie Ecology Statistical methods R (Computer program language) R Programm Datenanalyse Statistisches Modell |
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