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E-grāmata: Environmental and Ecological Statistics with R

(The University of Toledo, Ohio, USA)
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Emphasizing the inductive nature of statistical thinking, Environmental and Ecological Statistics with R, Second Edition, connects applied statistics to the environmental and ecological fields. Using examples from published works in the ecological and environmental literature, the book explains the approach to solving a statistical problem, covering model specification, parameter estimation, and model evaluation. It includes many examples to illustrate the statistical methods and presents R code for their implementation. The emphasis is on model interpretation and assessment, and using several core examples throughout the book, the author illustrates the iterative nature of statistical inference.

The book starts with a description of commonly used statistical assumptions and exploratory data analysis tools for the verification of these assumptions. It then focuses on the process of building suitable statistical models, including linear and nonlinear models, classification and regression trees, generalized linear models, and multilevel models. It also discusses the use of simulation for model checking, and provides tools for a critical assessment of the developed models. The second edition also includes a complete critique of a threshold model.

Environmental and Ecological Statistics with R, Second Edition focuses on statistical modeling and data analysis for environmental and ecological problems. By guiding readers through the process of scientific problem solving and statistical model development, it eases the transition from scientific hypothesis to statistical model.

Recenzijas

"Environmental and Ecological Statistics with R, Second Edition offers a comprehensive and highly engaging look at modern statistical modeling. It covers a wide range of topics, including linear and non-linear regression models, classification and regression tree structures, and generalized linear models. I particularly enjoyed the third section of the book covering interesting areas of advanced statistical modeling, where the reader can find many didactical examples that are highly relevant to environmental management such as the problem of Cryptosporidium in drinking water, the uncertainty in water quality measurements using the ELISA method as an example, or the threshold indicator taxa analysis. The author has the unique ability of being able to clearly explain difficult statistical concepts whilst still making the book accessible for researchers of all levels, from undergraduate students to researchers already conducting serious empirical research. The emerging philosophical consensus that both the frequentist and Bayesian way of thinking are important in statistical practice is nicely articulated throughout the book. R codes are also provided, enabling researchers to apply statistical techniques to their own ecological or environmental management problems. Overall, this book is exceptionally well written and should prove an invaluable tool either as a classroom text or as an addition to the research bookshelf. I am very confident that Environmental and Ecological Statistics with R, Second Edition will end up being a classic!" George Arhonditsis, Professor and Chair of the Department of Physical & Environmental Sciences, University of Toronto

"Shortly after it was published, the first edition of Environmental and Ecological Statistics with R by Song S. Qian became a go-to book for environmental scientists interested in the application of Bayesian methods in R to address a broad range of environmental issues. The book serves to introduce Bayesian statistical analysis in an accessible way to ecologists and environmental scientists, with numerous applications in R. An important aspect of this book is that it is written primarily for scientists, not statisticians; thus the author emphasizes the broader context of scientific inference, within which statistical analysis plays a critical role. The second edition includes several important additions and improvements including: an expanded introduction to R code, greater emphasis on hypothesis testing and p-values, and an iterative approach to scientific inference through the continued refinement of a model for a data set as the books chapters explore more advanced statistical methods. The R code included in the book outlines key computational procedures and provides a workable foundation upon which researchers can conduct scientific inference and statistical analysis with their own data." Kenneth H. Reckhow, Professor Emeritus, Duke University

"Statistics is a science to interpret, model, and explain variation. It provides us with a strategy to evaluate potential models rather than a rule to specify a specific statistical model as most people expected. However, most of the time, the importance of model evaluation is largely underestimated in the training of studentsMost students, like mine, are taught about statistics in a classical way. They are impressed but somehow intimidated by some technical terms like significance and power effect, thus becoming afraid of applying statistics to real data and questions. This book gives us a new way to teach statistics to biological and ecological students at research level This book not only teaches us about statistical methodology but also philosophy and strategy in applied statisticsWith the modification of chapters 1 to 10, with the addition of a new chapter, this edition features a stronger emphasis on model evaluation compared to that of the previous edition." Prof. Bo-Ping Han, Department of Ecology, Jinan University

Praise for the First Edition:

"...Overall, I liked the book. I expect that I will be pulling examples from it when I teach methods courses to students in the sciences. it does contain many interesting and intriguing examples, and good examples of R code. So I can and do recommend it as a helpful resource" Jane L. Harvill, The American Statistician, November 2011

"Qian effectively blends fundamentals of scientific methods with statistical thinking, modeling, computing, and inference. the text is well formatted with liberal use of illustrative portions of R code It is clear that Qian has taken great care in developing this book and has succeeded in meeting his stated purpose. The book reflects Qians insights into teaching environmental and ecological modeling developed over many years in applied statistics and as an educator in applied sciences" Biometrics, June 2011

"This book gives a data-oriented introduction to statistical modeling of environmental and ecological phenomena. It is a beautiful scientific guideline for a computer-based model building and evaluation process. This introductory book gives a diversified overview of modern applied statistics while always following an inductive, data-based approach...Meaningful graphics and R code/output embedded in the text support the conclusions drawn and facilitate the application to own data sets. Students and researchers of environmental sciences with basic knowledge in statistics will find this book valuable as both a work of reference and an introductory guide to statistical modeling with R" Sebastian Engelke and Martin Schlather, Biometrical Journal, 2011

Preface xiii
List of Figures
xvii
List of Tables
xxiii
I Basic Concepts
1(146)
1 Introduction
3(16)
1.1 Tool for Inductive Reasoning
3(4)
1.2 The Everglades Example
7(7)
1.2.1 Statistical Issues
10(4)
1.3 Effects of Urbanization on Stream Ecosystems
14(2)
1.3.1 Statistical Issues
15(1)
1.4 PCB in Fish from Lake Michigan
16(1)
1.4.1 Statistical Issues
16(1)
1.5 Measuring Harmful Algal Bloom Toxin
17(1)
1.6 Bibliography Notes
18(1)
1.7 Exercise
18(1)
2 A Crash Course on R
19(28)
2.1 What is R?
19(1)
2.2 Getting Started with R
20(7)
2.2.1 R Commands and Scripts
21(1)
2.2.2 R Packages
22(1)
2.2.3 R Working Directory
22(1)
2.2.4 Data Types
23(2)
2.2.5 R Functions
25(2)
2.3 Getting Data into R
27(7)
2.3.1 Functions for Creating Data
29(2)
2.3.2 A Simulation Example
31(3)
2.4 Data Preparation
34(10)
2.4.1 Data Cleaning
35(1)
2.4.1.1 Missing Values
36(1)
2.4.2 Subsetting and Combining Data
36(2)
2.4.3 Data Transformation
38(1)
2.4.4 Data Aggregation and Reshaping
38(4)
2.4.5 Dates
42(2)
2.5 Exercises
44(3)
3 Statistical Assumptions
47(30)
3.1 The Normality Assumption
48(6)
3.2 The Independence Assumption
54(1)
3.3 The Constant Variance Assumption
55(1)
3.4 Exploratory Data Analysis
56(13)
3.4.1 Graphs for Displaying Distributions
57(2)
3.4.2 Graphs for Comparing Distributions
59(2)
3.4.3 Graphs for Exploring Dependency among Variables
61(8)
3.5 From Graphs to Statistical Thinking
69(3)
3.6 Bibliography Notes
72(1)
3.7 Exercises
73(4)
4 Statistical Inference
77(70)
4.1 Introduction
77(1)
4.2 Estimation of Population Mean and Confidence Interval
78(12)
4.2.1 Bootstrap Method for Estimating Standard Error
86(4)
4.3 Hypothesis Testing
90(11)
4.3.1 t-Test
91(7)
4.3.2 Two-Sided Alternatives
98(1)
4.3.3 Hypothesis Testing Using the Confidence Interval
99(2)
4.4 A General Procedure
101(1)
4.5 Nonparametric Methods for Hypothesis Testing
102(7)
4.5.1 Rank Transformation
102(1)
4.5.2 Wilcoxon Signed Rank Test
103(1)
4.5.3 Wilcoxon Rank Sum Test
104(2)
4.5.4 A Comment on Distribution-Free Methods
106(3)
4.6 Significance Level α, Power 1 - β, and p-Value
109(7)
4.7 One-Way Analysis of Variance
116(11)
4.7.1 Analysis of Variance
117(2)
4.7.2 Statistical Inference
119(2)
4.7.3 Multiple Comparisons
121(6)
4.8 Examples
127(15)
4.8.1 The Everglades Example
127(1)
4.8.2 Kemp's Ridley Turtles
128(6)
4.8.3 Assessing Water Quality Standard Compliance
134(3)
4.8.4 Interaction between Red Mangrove and Sponges
137(5)
4.9 Bibliography Notes
142(1)
4.10 Exercises
142(5)
II Statistical Modeling
147(238)
5 Linear Models
149(60)
5.1 Introduction
149(3)
5.2 From t-test to Linear Models
152(2)
5.3 Simple and Multiple Linear Regression Models
154(31)
5.3.1 The Least Squares
154(2)
5.3.2 Regression with One Predictor
156(2)
5.3.3 Multiple Regression
158(2)
5.3.4 Interaction
160(2)
5.3.5 Residuals and Model Assessment
162(8)
5.3.6 Categorical Predictors
170(4)
5.3.7 Collinearity and the Finnish Lakes Example
174(11)
5.4 General Considerations in Building a Predictive Model
185(4)
5.5 Uncertainty in Model Predictions
189(4)
5.5.1 Example: Uncertainty in Water Quality Measurements
191(2)
5.6 Two-Way ANOVA
193(7)
5.6.1 ANOVA as a Linear Model
193(2)
5.6.2 More Than One Categorical Predictor
195(3)
5.6.3 Interaction
198(2)
5.7 Bibliography Notes
200(1)
5.8 Exercises
200(9)
6 Nonlinear Models
209(62)
6.1 Nonlinear Regression
209(31)
6.1.1 Piecewise Linear Models
220(6)
6.1.2 Example: U.S. Lilac First Bloom Dates
226(3)
6.1.3 Selecting Starting Values
229(11)
6.2 Smoothing
240(5)
6.2.1 Scatter Plot Smoothing
240(3)
6.2.2 Fitting a Local Regression Model
243(2)
6.3 Smoothing and Additive Models
245(22)
6.3.1 Additive Models
245(3)
6.3.2 Fitting an Additive Model
248(2)
6.3.3 Example: The North American Wetlands Database
250(4)
6.3.4 Discussion: The Role of Nonparametric Regression Models in Science
254(5)
6.3.5 Seasonal Decomposition of Time Series
259(2)
6.3.5.1 The Neuse River Example
261(6)
6.4 Bibliographic Notes
267(2)
6.5 Exercises
269(2)
7 Classification and Regression Tree
271(26)
7.1 The Willamette River Example
272(3)
7.2 Statistical Methods
275(18)
7.2.1 Growing and Pruning a Regression Tree
277(8)
7.2.2 Growing and Pruning a Classification Tree
285(4)
7.2.3 Plotting Options
289(4)
7.3 Comments
293(4)
7.3.1 CART as a Model Building Tool
293(4)
2 Deviance and Probabilistic Assumptions
297(6)
7.3.3 CART and Ecological Threshold
298(2)
7.4 Bibliography Notes
300(1)
7.5 Exercises
300(3)
8 Generalized Linear Model
303(82)
8.1 Logistic Regression
305(4)
8.1.1 Example: Evaluating the Effectiveness of UV as a Drinking Water Disinfectant
306(1)
8.1.2 Statistical Issues
307(1)
8.1.3 Fitting the Model in R
308(1)
8.2 Model Interpretation
309(7)
8.2.1 Logit Transformation
310(1)
8.2.2 Intercept
310(1)
8.2.3 Slope
311(1)
8.2.4 Additional Predictors
312(2)
8.2.5 Interaction
314(1)
8.2.6 Comments on the Crypto Example
315(1)
8.3 Diagnostics
316(16)
8.3.1 Binned Residuals Plot
316(1)
8.3.2 Overdispersion
316(3)
8.3.3 Seed Predation by Rodents: A Second Example of Logistic Regression
319(13)
8.4 Poisson Regression Model
332(21)
8.4.1 Arsenic Data from Southwestern Taiwan
332(1)
8.4.2 Poisson Regression
333(7)
8.4.3 Exposure and Offset
340(1)
8.4.4 Overdispersion
341(3)
8.4.5 Interactions
344(7)
8.4.6 Negative Binomial
351(2)
8.5 Multinomial Regression
353(8)
8.5.1 Fitting a Multinomial Regression Model in R
354(4)
8.5.2 Model Evaluation
358(3)
8.6 The Poisson-Multinomial Connection
361(6)
8.7 Generalized Additive Models
367(13)
8.7.1 Example: Whales in the Western Antarctic Peninsula
369(2)
8.7.1.1 The Data
371(1)
8.7.1.2 Variable Selection Using CART
371(3)
8.7.1.3 Fitting GAM
374(4)
8.7.1.4 Summary
378(2)
8.8 Bibliography Notes
380(1)
8.9 Exercises
381(4)
III Advanced Statistical Modeling
385(130)
9 Simulation for Model Checking and Statistical Inference
387(30)
9.1 Simulation
388(2)
9.2 Summarizing Regression Models Using Simulation
390(18)
9.2.1 An Introductory Example
390(2)
9.2.2 Summarizing a Linear Regression Model
392(4)
9.2.2.1 Re-transformation Bias
396(1)
9.2.3 Simulation for Model Evaluation
397(8)
9.2.4 Predictive Uncertainty
405(3)
9.3 Simulation Based on Re-sampling
408(6)
9.3.1 Bootstrap Aggregation
410(1)
9.3.2 Example: Confidence Interval of the CART-Based Threshold
411(3)
9.4 Bibliography Notes
414(1)
9.5 Exercises
414(3)
10 Multilevel Regression
417(76)
10.1 From Stein's Paradox to Multilevel Models
417(4)
10.2 Multilevel Structure and Exchangeability
421(4)
10.3 Multilevel ANOVA
425(11)
10.3.1 Intertidal Seaweed Grazers
426(5)
10.3.2 Background N2O Emission from Agriculture Fields
431(3)
10.3.3 When to Use the Multilevel Model?
434(2)
10.4 Multilevel Linear Regression
436(29)
10.4.1 Nonnested Groups
447(6)
10.4.2 Multiple Regression Problems
453(11)
10.4.3 The ELISA Example---An Unintended Multilevel Modeling Problem
464(1)
10.5 Nonlinear Multilevel Models
465(4)
10.6 Generalized Multilevel Models
469(17)
10.6.1 Exploited Plant Monitoring---Galax
470(1)
10.6.1.1 A Multilevel Poisson Model
471(3)
10.6.1.2 A Multilevel Logistic Regression Model
474(4)
10.6.2 Cryptosporidium in U.S. Drinking Water---A Poisson Regression Example
478(4)
10.6.3 Model Checking Using Simulation
482(4)
10.7 Concluding Remarks
486(3)
10.8 Bibliography Notes
489(1)
10.9 Exercises
489(4)
11 Evaluating Models Based on Statistical Significance Testing
493(22)
11.1 Introduction
493(2)
11.2 Evaluating TITAN
495(19)
11.2.1 A Brief Description of TITAN
496(2)
11.2.2 Hypothesis Testing in TITAN
498(1)
11.2.3 Type I Error Probability
499(4)
11.2.4 Statistical Power
503(8)
11.2.5 Bootstrapping
511(1)
11.2.6 Community Threshold
512(1)
11.2.7 Conclusions
513(1)
11.3 Exercises
514(1)
Bibliography 515(14)
Index 529
Song S. Qian, PhD, is an assistant professor in the Department of Environmental Sciences at the University of Toledo, Ohio, USA