Analyzing Environmental Data

Environmental statistics is a rapidly growing field, supported by advances in digital computing power, automated data collection systems, and interactive, linkable Internet software. Concerns over public and ecological health and the continuing need to support environmental policy-making and regulation have driven a concurrent explosion in environmental data analysis. This textbook is designed to address the need for trained professionals in this area. The book is based on a course which the authors have taught for many years, and prepares students for careers in environmental analysis centered on statistics and allied quantitative methods of data evaluation. The text extends beyond the introductory level, allowing students and environmental science practitioners to develop the expertise to design and perform sophisticated environmental data analyses. In particular, it: Provides a coherent introduction to intermediate and advanced methods for modeling and analyzing environmental data. Takes a data-oriented approach to describing the various methods. Illustrates the methods with real-world examples Features extensive exercises, enabling use as a course text. Includes examples of SAS computer code for implementation of the statistical methods. Connects to a Web site featuring solutions to exercises, extra computer code, and additional material. Serves as an overview of methods for analyzing environmental data, enabling use as a reference text for environmental science professionals. Graduate students of statistics studying environmental data analysis will find this invaluable as will practicing data analysts and environmental scientists including specialists in atmospheric science, biology and biomedicine, chemistry, ecology, environmental health, geography, and geology.

Table of Contents:
Preface xiii 1 Linear regression 1 1.1 Simple linear regression 2 1.2 Multiple linear regression 10 1.3 Qualitative predictors: ANOVA and ANCOVA models 16 1.3.1 ANOVA models 16 1.3.2 ANCOVA models 20 1.4 Random-effects models 24 1.5 Polynomial regression 26 Exercises 31 2 Nonlinear regression 41 2.1 Estimation and testing 42 2.2 Piecewise regression models 44 2.3 Exponential regression models 55 2.4 Growth curves 65 2.4.1 Gompertz model 66 2.4.2 Logistic growth curves 69 2.4.3 Weibull growth curves 79 2.5 Rational polynomials 83 2.5.1 Michaelis–Menten model 83 2.5.2 Morgan–Mercer–Flodin model 87 2.6 Multiple nonlinear regression 89 Exercises 91 3 Generalized linear models 103 3.1 Generalizing the classical linear model 104 3.1.1 Non-normal data and the exponential class 104 3.1.2 Linking the mean response to the predictor variables 106 3.2 Theory of generalized linear models 107 3.2.1 Estimation via maximum likelihood 108 3.2.2 Deviance function 109 3.2.3 Residuals 112 3.2.4 Inference and model assessment 113 3.2.5 Estimation via maximum quasi-likelihood 116 3.2.6 Generalized estimating equations 117 3.3 Specific forms of generalized linear models 121 3.3.1 Continuous/homogeneous-variance data GLiMs 121 3.3.2 Binary data GLiMs (including logistic regression) 124 3.3.3 Overdispersion: extra-binomial variability 135 3.3.4 Count data GLiMs 141 3.3.5 Overdispersion: extra-Poisson variability 149 3.3.6 Continuous/constant-CV data GLiMs 152 Exercises 158 4 Quantitative risk assessment with stimulus-response data 171 4.1 Potency estimation for stimulus-response data 172 4.1.1 Median effective dose 172 4.1.2 Other levels of effective dose 176 4.1.3 Other potency measures 178 4.2 Risk estimation 180 4.2.1 Additional risk and extra risk 180 4.2.2 Risk at low doses 187 4.3 Benchmark analysis 190 4.3.1 Benchmark dose estimation 190 4.3.2 Confidence limits on benchmark dose 192 4.4 Uncertainty analysis 193 4.4.1 Uncertainty factors 194 4.4.2 Monte Carlo methods 196 4.5 Sensitivity analysis 200 4.5.1 Identifying sensitivity to input variables 200 4.5.2 Correlation ratios 204 4.5.3 Identifying sensitivity to model assumptions 206 4.6 Additional topics 206 Exercises 207 5 Temporal data and autoregressive modeling 215 5.1 Time series 215 5.2 Harmonic regression 216 5.2.1 Simple harmonic regression 217 5.2.2 Multiple harmonic regression 221 5.2.3 Identifying harmonics: Fourier analysis 221 5.3 Autocorrelation 233 5.3.1 Testing for autocorrelation 233 5.3.2 The autocorrelation function 235 5.4 Autocorrelated regression models 239 5.4.1 AR models 239 5.4.2 Extensions: MA, ARMA, and ARIMA 241 5.5 Simple trend and intervention analysis 242 5.5.1 Simple linear trend 243 5.5.2 Trend with seasonality 243 5.5.3 Simple intervention at a known time 248 5.5.4 Change in trend at a known time 249 5.5.5 Jump and change in trend at a known time 249 5.6 Growth curves revisited 254 5.6.1 Longitudinal growth data 254 5.6.2 Mixed models for growth curves 255 Exercises 264 6 Spatially correlated data 275 6.1 Spatial correlation 275 6.2 Spatial point patterns and complete spatial randomness 276 6.2.1 Chi-square tests 277 6.2.2 Distance methods 281 6.2.3 Ripley’s K function 283 6.3 Spatial measurement 287 6.3.1 Spatial autocorrelation 288 6.3.2 Moran’s I coefficient 290 6.3.3 Geary’s c coefficient 292 6.3.4 The semivariogram 293 6.3.5 Semivariogram models 296 6.3.6 The empirical semivariogram 297 6.4 Spatial prediction 302 6.4.1 Simple kriging 304 6.4.2 Ordinary kriging 306 6.4.3 Universal kriging 307 6.4.4 Unknown g 309 6.4.5 Two-dimensional spatial prediction 312 6.4.6 Kriging under a normal likelihood 314 Exercises 323 7 Combining environmental information 333 7.1 Combining P-values 334 7.2 Effect size estimation 337 7.3 Meta-analysis 343 7.3.1 Inverse-variance weighting 343 7.3.2 Fixed-effects and random-effects models 346 7.3.3 Publication bias 349 7.4 Historical control information 351 7.4.1 Guidelines for using historical data 352 7.4.2 Target-vs.-control hypothesis testing 353 Exercises 358 8 Fundamentals of environmental sampling 367 8.1 Sampling populations – simple random sampling 368 8.2 Designs to extend simple random sampling 376 8.2.1 Systematic sampling 376 8.2.2 Stratified random sampling 377 8.2.3 Cluster sampling 383 8.2.4 Two-stage cluster sampling 386 8.3 Specialized techniques for environmental sampling 388 8.3.1 Capture–recapture sampling 388 8.3.2 Quadrat sampling 391 8.3.3 Line-intercept sampling 392 8.3.4 Ranked set sampling 394 8.3.5 Composite sampling 398 Exercises 401 A Review of probability and statistical inference 411 A. 1 Probability functions 411 A. 2 Families of distributions 414 A.2. 1 Binomial distribution 415 A.. 2 Beta-binomial distribution 415 A.2. 3 Hypergeometric distribution 416 A.2. 4 Poisson distribution 417 A.2. 5 Negative binomial distribution 417 A.2. 6 Discrete uniform distribution 418 A.2. 7 Continuous uniform distribution 418 A.2. 8 Exponential, gamma, and chi-square distributions 418 A.2. 9 Weibull and extreme-value distributions 419 A.2. 10 Normal distribution 419 A.2. 11 Distributions derived from the normal 421 A.2. 12 Bivariate normal distribution 424 A. 3 Random sampling 425 A.3. 1 Random samples and independence 425 A.3. 2 The likelihood function 425 A. 4 Parameter estimation 426 A.4. 1 Least squares and weighted least squares 426 A.4. 2 The method of moments 427 A.4. 3 Maximum likelihood 427 A.4 Bias 428 A. 5 Statistical inference 428 A.5. 1 Confidence intervals 429 A.5. 2 Bootstrap-based confidence intervals 430 A.5. 3 Hypothesis tests 432 A.5. 4 Multiple comparisons and the Bonferroni inequality 434 A. 6 The delta method 435 A.6. 1 Inferences on a function of an unknown parameter 435 A.6. 2 Inferences on a function of multiple parameters 437 B Tables 441 References 447 Author index 473 Subject index 480

About the Author :
Walter W. Piegorsch, University of South Carolina, Columbia, South Carolina, USA Walter W. Piegorsch earned an M.S. and a Ph.D. Statistics at the Biometrics Unit, Cornell University. He was a Statistician with the U.S. National Institute of Environmental Health Sciences from 1984 to 1993, then moved to the University of South Carolina, Columbia, where he is now Professor and Director of Undergraduate Studies in Statistics. Walter has co-authored or co-edited two books, Statistics for Environmental Biology and Toxicology with A. John Bailer, and Case Studies in Environmental Statistics with Douglas W. Nychka and Lawrence H. Cox. He also serves or has served as a member of the Editorial Board of Environmental and Molecular Mutagenesis and Mutation Research, the Editorial Review Board of Environmental Health Perspectives, and as an Associate Editor for Environmetrics, Environmental and Ecological Statistics, Biometrics, and the Journal of the American Statistical Association. Walter is a Fellow of the American Statistical Association, an elected member of the International Statistical Institute, and has received a Distinguished Achievement Medal from the American Statistical Association Section on Statistics and the Environment. He has served as Vice-Chair of the American Statistical Association Council of Sections Governing Board, as Program Chairman of the Joint Statistical Meetings, and as Secretary of the Eastern North American Region of the International Biometric Society. He has also served and continues to serve on advisory boards and peer review groups for governmental agencies including the U.S. National Toxicology Program, the U.S. Environmental Protection Agency, and the U.S. National Science Foundation.

Review :
"This book covers an impressive range of topics . . . The book can be used as a basis for courses of different levels." (Stat Papers, 2010) "Some of the unique aspects of Piegorsch and Bailer’s treatment are benchmark dose estimation for toxicants, statistical issues in risk assessment, the assessment of trend and step changes in temporal data, and the discussion of sampling." (Journal of the American Statistical Association, June 2008) "I enjoyed reading this book and I recommend it to those readers interested in the field of environmental statistics." (Journal of Applied Statistics, January 2009) "This highly recommended book will provide the background for the proper application of statistical methods. These will make an invaluable contribution to the realistic assessment of the damage to the environment to be expected as a result of global warming. The subject and author indexes are both excellent." (Journal of Chemical Technology and Biotechnology, August 2006) "This highly recommended book will provide the background for the proper application of statistical methods. These will make an invaluable contribution to the realistic assessment of the damage to the environment to be expected as a result of global warming. The subject and author indexes are both excellent." (Journal of Chemical Technology and Biotechnology, Aug 2008) "...This is a substantial and thorough book...a handy reference book for any statistician's bookshelf..." (International Statistical Institute, January 2006)