Beginner's Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA
Highland Statistics Ltd (Verlag)
9780957174191 (ISBN)
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In Chapter 2 we discuss an important topic: dependency. Ignoring this means that we have pseudoreplication. We present a series of examples and discuss how dependency can manifest itself. We briefly discuss frequentist tools that are available for the analysis of temporal and spatial data in Chapters 3 and 4, and we will conclude that their application is rather limited, especially if non-Gaussian distributions are required. We will therefore consider alternative models, but these require Bayesian techniques. In Chapter 5 we discuss linear mixed-effects models to analyse hierarchical (i.e. clustered or nested) data, and in Chapter 6 we outline how we add spatial and spatial-temporal dependency to regression models via spatial (and/or temporal) correlated random effects. In Chapter 7 we introduce Bayesian analysis, Markov chain Monte Carlo techniques (MCMC), and Integrated Nested Laplace Approximation (INLA). INLA allows us to apply models to spatial, temporal, or spatial-temporal data. In Chapters 8 through 16 we present a series of INLA examples. We start by applying linear regression and mixed-effects models in INLA (Chapters 8 and 9), followed by GLM examples in Chapter 10.
In Chapters 11 through 13 we show how to apply GLM models on spatial data. In Chapter 14 we discuss time-series techniques and how to implement them in INLA. Finally, in Chapters 15 and 16 we analyse spatial-temporal models in INLA.
Alain F Zuur is senior statistician and director of Highland Statistics Ltd., a statistics consultancy based in the UK. He is the author of ten books on the analysis of ecological data. He has extensive experience teaching statistical methods to ecologists and environmental scientists in academic and non-academic courses worldwide. Elena N Ieno is senior marine biologist at Highland Statistics Ltd. She is the author of eight books on the analysis of ecological data. She teaches data analysis to ecologists and environmental scientists worldwide and is adept at bridging the gap between the two disciplines to dispel the fear of statistics. 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.
1 OVERVIEW OF THIS BOOK1 1.1 VOLUMES I AND II1 1.1.1 Volume I1 1.1.2 Volume II1 1.2 WHAT TYPE OF SPATIAL DATA DO WE ANALYSE IN THIS BOOK?1 1.2.1 Areal and lattice data1 1.2.2 Geostatistical data2 1.2.3 Spatial point pattern data3 1.3 OUTLINE OF THIS BOOK3 1.4 PREREQUISITES4 1.5 AVAILABILITY OF R CODE AND DATA4 2 RECOGNISING STATISTICAL DEPENDENCY5 2.1 PSEUDOREPLICATION5 2.2 LINEAR REGRESSION APPLIED TO SPATIAL DATA7 2.2.1 Irish pH data7 2.2.2 Protocol from Zuur et al. (2016)8 2.2.3 Visualisation of the experimental design9 2.2.4 Data exploration9 2.2.5 Dependency12 2.2.6 Statistical model15 2.2.7 Fit the model16 2.2.8 Model validation17 2.3 GAM APPLIED TO TEMPORAL DATA21 2.3.1 Subnivium temperature data21 2.3.2 Sources of dependency22 2.3.3 The model23 2.3.4 Model validation24 2.4 GLMM APPLIED ON HIERARCHICAL AND SPATIAL DATA26 2.5 TECHNICALITIES28 2.5.1 Matrix notation28 2.5.2 How is dependency causing problems?31 2.6 DISCUSSION32 3 TIME SERIES AND GLS33 3.1 OSPREYS33 3.2 COVARIANCE AND CORRELATION COEFFICIENTS33 3.3 LINEAR REGRESSION MODEL35 3.4 FOCUSSING ON THE RESIDUAL COVARIANCE MATRIX35 3.5 DEPENDENCY AND THE COVARIANCE MATRIX36 3.6 GLS: DEALING WITH TEMPORAL DEPENDENCY39 3.6.1 Adelie penguins39 3.6.2 Do we have dependency?40 3.6.3 Formulation of the linear regression model40 3.6.4 Application of the linear regression model41 3.6.5 R code for acf and variogram45 3.6.6 Formulation of the GLS model46 3.6.7 Implementation using the gls function50 3.7 MULTIPLE TIME SERIES51 3.8 DISCUSSION53 4 SPATIAL DATA AND GLS55 4.1 VARIOGRAM MODELS FOR SPATIAL DEPENDENCY55 4.2 APPLICATION ON THE IRISH PH DATA57 4.3 MATERN CORRELATION FUNCTION59 5 LINEAR MIXED EFFECTS MODELS AND DEPENDENCY61 5.1 WHITE STORKS61 5.2 CONSIDERING THE DATA (WRONGLY) AS ONE-WAY NESTED62 5.3 FITTING THE ONE-WAY NESTED MODEL USING LMER65 5.4 MODEL VALIDATION67 5.5 SKETCHING THE FITTED VALUES68 5.6 CONSIDERING THE DATA (CORRECTLY) AS TWO-WAY NESTED69 5.7 APPLICATIONS TO SPATIAL AND TEMPORAL DATA72 5.8 DIFFERENCE WITH THE AR1 PROCESS APPROACH72 6 MODELLING SPACE EXPLICITLY73 6.1 MODEL FORMULATION73 6.2 COVARIANCE MATRIX OF THE SPATIAL RANDOM EFFECT75 6.3 SPATIAL-TEMPORAL CORRELATION*79 7 INTRODUCTION TO BAYESIAN STATISTICS83 7.1 WHY GO BAYESIAN?83 7.2 GENERAL PROBABILITY RULES84 7.3 THE MEAN OF A DISTRIBUTION*85 7.4 BAYES' THEOREM AGAIN87 7.5 CONJUGATE PRIORS88 7.6 MARKOV CHAIN MONTE CARLO SIMULATION93 7.6.1 Underlying idea93 7.6.2 Installing JAGS and R2jags94 7.6.3 Flowchart for running a model in JAGS94 7.6.4 Preparing the data for JAGS95 7.6.5 JAGS code96 7.6.6 Initial values and parameters to save98 7.6.7 Running JAGS99 7.6.8 Accessing numerical output from JAGS100 7.6.9 Assess mixing100 7.6.10 Posterior information101 7.7 INTEGRATED NESTED LAPLACE APPROXIMATION*103 7.7.1 Joint posterior distribution103 7.7.2 Marginal distributions105 7.7.3 Back to high school107 7.7.4 INLA109 7.8 EXAMPLE USING R-INLA110 7.9 DISCUSSION114 8 MULTIPLE LINEAR REGRESSION IN R-INLA115 8.1 INTRODUCTION115 8.2 DATA EXPLORATION116 8.3 MODEL FORMULATION117 8.4 LINEAR REGRESSION RESULTS117 8.4.1 Executing the model in R-INLA117 8.4.2 Output for the betas117 8.4.3 Output for the hyper-parameters119 8.4.4 Fitted model123 8.5 MODEL VALIDATION123 8.6 MODEL SELECTION126 8.6.1 Should we do it?126 8.6.2 Using the DIC126 8.6.3 Out of sample prediction131 8.6.4 Posterior predictive check133 8.7 VISUALISING THE MODEL135 9 MIXED EFFECTS MODELLING IN R-INLA TO ANALYSE OTOLITH DATA139 9.1 OTOLITHS IN PLAICE139 9.2 MODEL FORMULATION140 9.3 DEPENDENCY140 9.4 DATA EXPLORATION141 9.5 RUNNING THE MODEL IN R-INLA143 9.6 MODEL VALIDATION146 9.7 MODEL SELECTION149 9.8 MODEL INTERPRETATION149 9.8.1 Option 1 for prediction: Adding extra data150 9.8.2 Option 2 for prediction: Using the inla.make.lincombs153 9.8.3 Adding extra data or inla.make.lincombs?155 9.9 MULTIPLE RANDOM EFFECTS155 9.10 CHANGING PRIORS OF FIXED PARAMETERS156 9.11 CHANGING PRIORS OF HYPERPARAMETERS158 9.12 SHOULD WE CHANGE PRIORS?164 10 POISSON, NEGATIVE BINOMIAL, BINOMIAL AND GAMMA GLMS IN R-INLA165 10.1 POISSON AND NEGATIVE BINOMIAL GLMS IN R-INLA165 10.1.1 Introduction165 10.1.2 Poisson GLM in R-INLA166 10.1.3 Negative binomial GLM in R-INLA172 10.1.4 Model selection for the NB GLM175 10.1.5 Visualisation of the NB GLM177 10.2 BERNOULLI AND BINOMIAL GLM180 10.2.1 Bernoulli GLM181 10.2.2 Model selection with the marginal likelihood184 10.2.3 Binomial GLM185 10.3 GAMMA GLM187 11 MATERN CORRELATION AND SPDE191 11.1 CONTINUOUS GAUSSIAN FIELD191 11.2 MODELS THAT WE HAVE IN MIND191 11.3 MATERN CORRELATION192 11.4 SPDE APPROACH197 12 LINEAR REGRESSION MODEL WITH SPATIAL DEPENDENCY FOR THE IRISH PH DATA205 12.1 INTRODUCTION205 12.2 MODEL FORMULATION205 12.3 LINEAR REGRESSION RESULTS206 12.4 MODEL VALIDATION207 12.5 ADDING SPATIAL CORRELATION TO THE MODEL208 12.6 DEFINING THE MESH FOR THE IRISH PH DATA212 12.7 DEFINE THE WEIGHT FACTORS AIK216 12.8 DEFINE THE SPDE218 12.9 DEFINE THE SPATIAL FIELD218 12.10 DEFINE THE STACK218 12.11 DEFINE THE FORMULA FOR THE SPATIAL MODEL221 12.12 EXECUTE THE SPATIAL MODEL IN R221 12.13 RESULTS222 12.14 MODEL SELECTION227 12.15 MODEL VALIDATION228 12.16 MODEL INTERPRETATION228 12.17 DETAILED INFORMATION ABOUT THE STACK*232 12.17.1 Stack for the fitted model again232 12.17.2 Stack for the new covariate values234 12.17.3 Combine the two stacks236 12.17.4 Run the model236 13 SPATIAL POISSON MODELS APPLIED TO PLANT DIVERSITY239 13.1 INTRODUCTION239 13.2 DATA EXPLORATION239 13.2.1 Sampling locations239 13.2.2 Outliers241 13.2.3 Collinearity242 13.2.4 Relationships243 13.2.5 Numbers of zeros244 13.2.6 Conclusions data exploration244 13.3 MODEL FORMULATION244 13.4 GLM RESULTS245 13.5 ADDING SPATIAL CORRELATION TO THE MODEL248 13.5.1 Model formulation248 13.5.2 Mesh248 13.5.3 Projector matrix253 13.5.4 SPDE254 13.5.5 Spatial field254 13.5.6 Stack254 13.5.7 Formula255 13.5.8 Run R-INLA255 13.5.9 Inspect results256 13.6 SIMULATING FROM THE MODEL262 13.7 WHAT TO WRITE IN A PAPER265 14 TIME-SERIES ANALYSIS IN R-INLA267 14.1 SIMULATION STUDY267 14.2 TRENDS IN MIGRATION DATES OF SOCKEYE SALMON269 14.2.1 Applying a random walk trend model269 14.2.2 Posterior distribution of the sigmas272 14.2.3 Covariates and trends273 14.2.4 Making the trend smoother274 14.3 TRENDS IN POLAR BEAR MOVEMENTS280 14.4 TRENDS IN WHALE STRANDINGS283 14.5 MULTIVARIATE TIME SERIES FOR HAWAIIAN BIRDS285 14.5.1 Importing and preparing the data285 14.5.2 Data exploration286 14.5.3 Model formulation287 14.5.4 Executing the models288 14.5.5 Mixing Poisson and negative binomial distributions295 14.6 AR1 TRENDS297 14.6.1 AR1 trend for regularly spaced time-series data297 14.6.2 AR1 trend for irregularly spaced time-series data299 15 SPATIAL-TEMPORAL MODELS FOR ORANGE-CROWNED WARBLERS COUNT DATA307 15.1 INTRODUCTION307 15.2 POISSON GLM308 15.3 MODEL WITH SPATIAL CORRELATION312 15.4 SPATIAL-TEMPORAL CORRELATION: AR1318 15.4.1 Why do it?318 15.4.2 Explanation of the model318 15.4.4 Simulating a spatial-temporal AR random field320 15.4.5 Implementation of AR1 model in R-INLA323 15.4.6 More detailed information on the code326 15.5 SPATIAL-TEMPORAL CORRELATION: EXCHANGEABLE328 15.6 SPATIAL-TEMPORAL CORRELATION: REPLICATED329 15.7 SIMULATION STUDY330 15.8 DISCUSSION333 16 SPATIAL-TEMPORAL BERNOULLI MODELS FOR CORAL DISEASE DATA335 16.1 INTRODUCTION335 16.2 BERNOULLI MODEL IN R-INLA336 16.3 SPATIAL CORRELATED BERNOULLI MODEL338 16.4 SPATIAL-TEMPORAL CORRELATED BERNOULLI MODEL342 REFERENCES347 INDEX353 OTHER BOOKS357
| Erscheinungsdatum | 01.03.2017 |
|---|---|
| Verlagsort | Newburgh |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-13 | 9780957174191 / 9780957174191 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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