Analyzing Environmental Data

Walter W. Piegorsch, University of South Carolina, Columbia, South Carolina, USAWalter 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.A. John Bailer, Department of Mathematics & Statistics, Miami University, USA.

"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)

• Preface xiii1 Linear regression 11.1 Simple linear regression 21.2 Multiple linear regression 101.3 Qualitative predictors: ANOVA and ANCOVA models 161.3.1 ANOVA models 161.3.2 ANCOVA models 201.4 Random-effects models 241.5 Polynomial regression 26Exercises 312 Nonlinear regression 412.1 Estimation and testing 422.2 Piecewise regression models 442.3 Exponential regression models 552.4 Growth curves 652.4.1 Gompertz model 662.4.2 Logistic growth curves 692.4.3 Weibull growth curves 792.5 Rational polynomials 832.5.1 Michaelis–Menten model 832.5.2 Morgan–Mercer–Flodin model 872.6 Multiple nonlinear regression 89Exercises 913 Generalized linear models 1033.1 Generalizing the classical linear model 1043.1.1 Non-normal data and the exponential class 1043.1.2 Linking the mean response to the predictor variables 1063.2 Theory of generalized linear models 1073.2.1 Estimation via maximum likelihood 1083.2.2 Deviance function 1093.2.3 Residuals 1123.2.4 Inference and model assessment 1133.2.5 Estimation via maximum quasi-likelihood 1163.2.6 Generalized estimating equations 1173.3 Specific forms of generalized linear models 1213.3.1 Continuous/homogeneous-variance data GLiMs 1213.3.2 Binary data GLiMs (including logistic regression) 1243.3.3 Overdispersion: extra-binomial variability 1353.3.4 Count data GLiMs 1413.3.5 Overdispersion: extra-Poisson variability 1493.3.6 Continuous/constant-CV data GLiMs 152Exercises 1584 Quantitative risk assessment with stimulus-response data 1714.1 Potency estimation for stimulus-response data 1724.1.1 Median effective dose 1724.1.2 Other levels of effective dose 1764.1.3 Other potency measures 1784.2 Risk estimation 1804.2.1 Additional risk and extra risk 1804.2.2 Risk at low doses 1874.3 Benchmark analysis 1904.3.1 Benchmark dose estimation 1904.3.2 Confidence limits on benchmark dose 1924.4 Uncertainty analysis 1934.4.1 Uncertainty factors 1944.4.2 Monte Carlo methods 1964.5 Sensitivity analysis 2004.5.1 Identifying sensitivity to input variables 2004.5.2 Correlation ratios 2044.5.3 Identifying sensitivity to model assumptions 2064.6 Additional topics 206Exercises 2075 Temporal data and autoregressive modeling 2155.1 Time series 2155.2 Harmonic regression 2165.2.1 Simple harmonic regression 2175.2.2 Multiple harmonic regression 2215.2.3 Identifying harmonics: Fourier analysis 2215.3 Autocorrelation 2335.3.1 Testing for autocorrelation 2335.3.2 The autocorrelation function 2355.4 Autocorrelated regression models 2395.4.1 AR models 2395.4.2 Extensions: MA, ARMA, and ARIMA 2415.5 Simple trend and intervention analysis 2425.5.1 Simple linear trend 2435.5.2 Trend with seasonality 2435.5.3 Simple intervention at a known time 2485.5.4 Change in trend at a known time 2495.5.5 Jump and change in trend at a known time 2495.6 Growth curves revisited 2545.6.1 Longitudinal growth data 2545.6.2 Mixed models for growth curves 255Exercises 2646 Spatially correlated data 2756.1 Spatial correlation 2756.2 Spatial point patterns and complete spatial randomness 2766.2.1 Chi-square tests 2776.2.2 Distance methods 2816.2.3 Ripley’s K function 2836.3 Spatial measurement 2876.3.1 Spatial autocorrelation 2886.3.2 Moran’s I coefficient 2906.3.3 Geary’s c coefficient 2926.3.4 The semivariogram 2936.3.5 Semivariogram models 2966.3.6 The empirical semivariogram 2976.4 Spatial prediction 3026.4.1 Simple kriging 3046.4.2 Ordinary kriging 3066.4.3 Universal kriging 3076.4.4 Unknown g 3096.4.5 Two-dimensional spatial prediction 3126.4.6 Kriging under a normal likelihood 314Exercises 3237 Combining environmental information 3337.1 Combining P-values 3347.2 Effect size estimation 3377.3 Meta-analysis 3437.3.1 Inverse-variance weighting 3437.3.2 Fixed-effects and random-effects models 3467.3.3 Publication bias 3497.4 Historical control information 3517.4.1 Guidelines for using historical data 3527.4.2 Target-vs.-control hypothesis testing 353Exercises 3588 Fundamentals of environmental sampling 3678.1 Sampling populations – simple random sampling 3688.2 Designs to extend simple random sampling 3768.2.1 Systematic sampling 3768.2.2 Stratified random sampling 3778.2.3 Cluster sampling 3838.2.4 Two-stage cluster sampling 3868.3 Specialized techniques for environmental sampling 3888.3.1 Capture–recapture sampling 3888.3.2 Quadrat sampling 3918.3.3 Line-intercept sampling 3928.3.4 Ranked set sampling 3948.3.5 Composite sampling 398Exercises 401A Review of probability and statistical inference 411A. 1 Probability functions 411A. 2 Families of distributions 414A.2. 1 Binomial distribution 415A.. 2 Beta-binomial distribution 415A.2. 3 Hypergeometric distribution 416A.2. 4 Poisson distribution 417A.2. 5 Negative binomial distribution 417A.2. 6 Discrete uniform distribution 418A.2. 7 Continuous uniform distribution 418A.2. 8 Exponential, gamma, and chi-square distributions 418A.2. 9 Weibull and extreme-value distributions 419A.2. 10 Normal distribution 419A.2. 11 Distributions derived from the normal 421A.2. 12 Bivariate normal distribution 424A. 3 Random sampling 425A.3. 1 Random samples and independence 425A.3. 2 The likelihood function 425A. 4 Parameter estimation 426A.4. 1 Least squares and weighted least squares 426A.4. 2 The method of moments 427A.4. 3 Maximum likelihood 427A.4 Bias 428A. 5 Statistical inference 428A.5. 1 Confidence intervals 429A.5. 2 Bootstrap-based confidence intervals 430A.5. 3 Hypothesis tests 432A.5. 4 Multiple comparisons and the Bonferroni inequality 434A. 6 The delta method 435A.6. 1 Inferences on a function of an unknown parameter 435A.6. 2 Inferences on a function of multiple parameters 437B Tables 441References 447Author index 473Subject index 480