Contemporary Statistical Models for the Plant and Soil Sciences

Name: Contemporary Statistical Models for the Plant and Soil Sciences
Price: 53.03 USD
Availability: InStock
ISBN: 9781584881117

ISBN-10: 1584881119

ISBN-13: 9781584881117

Edition: 2001

Authors: Oliver Schabenberger, Francis J. Pierce

List price: $190.00

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Description:

Despite its many origins in agronomic problems, statistics today is often unrecognizable in this context. Numerous recent methodological approaches and advances originated in other subject-matter areas and agronomists frequently find it difficult to see their immediate relation to questions that their disciplines raise. On the other hand, statisticians often fail to recognize the riches of challenging data analytical problems contemporary plant and soil science provides.The first book to integrate modern statistics with crop, plant and soil science, Contemporary Statistical Models for the Plant and Soil Sciences bridges this gap. The breadth and depth of topics covered is unusual. Each of…

Book details

List price: $190.00
Copyright year: 2001
Publisher: CRC Press LLC
Publication date: 11/13/2001
Binding: Hardcover
Pages: 760
Size: 7.00" wide x 9.75" long x 1.75" tall
Weight: 3.432
Language: English



Preface


About the Authors


The CD-ROM



Statistical Models



Mathematical and Statistical Models



Functional Aspects of Models



The Inferential Steps--Estimation and Testing



t-Tests in Terms of Statistical Models



Embedding Hypotheses



Hypothesis and Significance Testing--Interpretation of the p-Value



Classes of Statistical Models



The Basic Component Equation



Linear and Nonlinear Models



Regression and Analysis of Variance Models



Univariate and Multivariate Models



Fixed, Random, and Mixed Effects Models



Generalized Linear Models



Errors in Variable Models



Data Structures



Introduction



Classification by Response Type



Classification by Study Type



Clustered Data



Clustering through Hierarchical Random Processes



Clustering through Repeated Measurements



Autocorrelated Data



The Autocorrelation Function



Consequences of Ignoring Autocorrelation



Autocorrelation in Designed Experiments



From Independent to Spatial Data--a Progression of Clustering



Linear Algebra Tools



Introduction



Matrices and Vectors



Basic Matrix Operations



Matrix Inversion--Regular and Generalized Inverse



Mean, Variance, and Covariance of Random Vectors



The Trace and Expectation of Quadratic Forms



The Multivariate Gaussian Distribution



Matrix and Vector Differentiation



Using Matrix Algebra to Specify Models



Linear Models



Nonlinear Models



Variance-Covariance Matrices and Clustering



The Classical Linear Model: Least Squares and Alternatives



Introduction



Least Squares Estimation and Partitioning of Variation



The Principle



Partitioning Variability through Sums of Squares



Sequential and Partial Sums of Squares and the Sum of Squares Reduction Test



Factorial Classification



The Means and Effects Model



Effect Types in Factorial Designs



Sum of Squares Partitioning through Contrasts



Effects and Contrasts in The SAS System



Diagnosing Regression Models



Residual Analysis



Recursive and Linearly Recovered Errors



Case Deletion Diagnostics



Collinearity Diagnostics



Ridge Regression to Combat Collinearity



Diagnosing Classification Models



What Matters?



Diagnosing and Combating Heteroscedasticity



Median Polishing of Two-Way Layouts



Robust Estimation



L[subscript 1]-Estimation



M-Estimation



Robust Regression for Prediction Efficiency Data



M-Estimation in Classification Models



Nonparametric Regression



Local Averaging and Local Regression



Choosing the Smoothing Parameter


Appendix A on CD-ROM



Mathematical Details



Least Squares



Hypothesis Testing in the Classical Linear Model



Diagnostics in Regression Models



Ridge Regression



L[subscript 1]-Estimation



M-Estimation



Nonparametric Regression



Nonlinear Models



Introduction



Models as Laws or Tools



Linear Polynomials Approximate Nonlinear Models



Fitting a Nonlinear Model to Data



Estimating the Parameters



Tracking Convergence



Starting Values



Goodness-of-Fit



Hypothesis Tests and Confidence Intervals



Testing the Linear Hypothesis



Confidence and Prediction Intervals



Transformations



Transformation to Linearity



Transformation to Stabilize the Variance



Parameterization of Nonlinear Models



Intrinsic and Parameter-Effects Curvature



Reparameterization through Defining Relationships



Applications



Basic Nonlinear Analysis with The SAS System--Mitscherlich's Yield Equation



The Sampling Distribution of Nonlinear Estimators--the Mitscherlich Equation Revisited



Linear-Plateau Models and Their Relatives--a Study of Corn Yields from Tennessee



Critical NO[subscript 3] Concentrations as a Function of Sampling Depth--Comparing Join-Points in Plateau Models



Factorial Treatment Structure with Nonlinear Response



Modeling Hormetic Dose Response through Switching Functions



Modeling a Yield-Density Relationship



Weighted Nonlinear Least Squares Analysis with Heteroscedastic Errors


Appendix A on CD-ROM



Forms of Nonlinear Models



Concave and Convex Models, Yield-Density Models



Models with Sigmoidal Shape, Growth Models



Mathematical Details



Taylor Series Involving Vectors



Nonlinear Least Squares and the Gauss-Newton Algorithm



Nonlinear Generalized Least Squares



The Newton-Raphson Algorithm



Convergence Criteria



Hypothesis Testing, Confidence and Prediction Intervals



Generalized Linear Models



Introduction



Components of a Generalized Linear Model



Random Component



Systematic Component and Link Function



Generalized Linear Models in The SAS System



Grouped and Ungrouped Data



Parameter Estimation and Inference



Solving the Likelihood Problem



Testing Hypotheses about Parameters and Their Functions



Deviance and Pearson's X[superscript 2] Statistic



Testing Hypotheses through Deviance Partitioning



Generalized R[superscript 2] Measures of Goodness-of-Fit



Modeling an Ordinal Response



Cumulative Link Models



Software Implementation and Example



Overdispersion



Applications



Dose-Response and LD[subscript 50] Estimation in a Logistic Regression Model



Binomial Proportions in a Randomized Block Design--the Hessian Fly Experiment



Gamma Regression and Yield Density Models



Effects of Judges' Experience on Bean Canning Quality Ratings



Ordinal Ratings in a Designed Experiment with Factorial Treatment Structure and Repeated Measures



Log-Linear Modeling of Rater Agreement



Modeling the Sample Variance of Scab Infection



A Poisson/Gamma Mixing Model for Overdispersed Poppy Counts


Appendix A on CD-ROM



Mathematical Details and Special Topics



Exponential Family of Distributions



Maximum Likelihood Estimation



Iteratively Reweighted Least Squares



Hypothesis Testing



Fieller's Theorem and the Variance of a Ratio



Overdispersion Mechanisms for Counts



Linear Mixed Models for Clustered Data



Introduction



The Laird-Ware Model



Rationale



The Two-Stage Concept



Fixed or Random Effects



Choosing the Inference Space



Estimation and Inference



Maximum and Restricted Maximum Likelihood



Estimated Generalized Least Squares



Hypothesis Testing



Correlations in Mixed Models



Induced Correlations and the Direct Approach



Within-Cluster Correlation Models



Split-Plots, Repeated Measures, and the Huynh-Feldt Conditions



Applications



Two-Stage Modeling of Apple Growth over Time



On-Farm Experimentation with Randomly Selected Farms



Nested Errors through Subsampling



Recovery of Inter-Block Information in Incomplete Block Designs



A Split-Strip-Plot Experiment for Soybean Yield



Repeated Measures in a Completely Randomized Design



A Longitudinal Study of Water Usage in Horticultural Trees



Cumulative Growth of Muskmelons in Subsampling Design


Appendix A on CD-ROM



Mathematical Details and Special Topics



Henderson's Mixed Model Equations



Solutions to the Mixed Model Equations



Likelihood Based Estimation



Estimated Generalized Least Squares Estimation



Hypothesis Testing



The First-Order Autoregressive Model



Nonlinear Models for Clustered Data



Introduction



Nonlinear and Generalized Linear Mixed Models



Toward an Approximate Objective Function



Three Linearizations



Linearization in Generalized Linear Mixed Models



Integral Approximation Methods



Applications



A Nonlinear Mixed Model for Cumulative Tree Bole Volume



Poppy Counts Revisited--a Generalized Linear Mixed Model for Overdispersed Count Data



Repeated Measures with an Ordinal Response


Appendix A on CD-ROM



Mathematical Details and Special Topics



PA and SS Linearizations



Generalized Estimating Equations



Linearization in Generalized Linear Mixed Models



Gaussian Quadrature



Statistical Models for Spatial Data



Changing the Mindset



Samples of Size One



Random Functions and Random Fields



Types of Spatial Data



Stationarity and Isotropy--the Built-in Replication Mechanism of Random Fields



Semivariogram Analysis and Estimation



Elements of the Semivariogram



Parametric Isotropic Semivariogram Models



The Degree of Spatial Continuity (Structure)



Semivariogram Estimation and Fitting



The Spatial Model



Spatial Prediction and the Kriging Paradigm



Motivation of the Prediction Problem



The Concept of Optimal Prediction



Ordinary and Universal Kriging



Some Notes on Kriging



Extensions to Multiple Attributes



Spatial Regression and Classification Models



Random Field Linear Models



Some Philosophical Considerations



Parameter Estimation



Autoregressive Models for Lattice Data



The Neighborhood Structure



First-Order Simultaneous and Conditional Models



Parameter Estimation



Choosing the Neighborhood Structure



Analyzing Mapped Spatial Point Patterns



Introduction



Random, Aggregated, and Regular Patterns--the Notion of Complete Spatial Randomness



Testing the CSR Hypothesis in Mapped Point Patterns



Second-Order Properties of Point Patterns



Applications



Exploratory Tools for Spatial Data--Diagnosing Spatial Autocorrelation with Moran's I



Modeling the Semivariogram of Soil Carbon



Spatial Prediction--Kriging of Lead Concentrations



Spatial Random Field Models--Comparing C/N Ratios among Tillage Treatments



Spatial Random Field Models--Spatial Regression of Soil Carbon on Soil N



Spatial Generalized Linear Models--Spatial Trends in the Hessian Fly Experiment



Simultaneous Spatial Autoregression--Modeling Wiebe's Wheat Yield Data



Point Patterns--First- and Second-Order Properties of a Mapped Pattern


Appendix A on CD-ROM



Mathematical Details and Special Topics


Geostatistical Data



Estimating the Empirical Semivariogram



Parametric Fitting of the Semivariogram



Nonparametric Fitting of the Semivariogram



Solutions to Kriging Equations



Is Kriging Perfect Interpolation?



Block and Indicator Kriging


Spatial Random Field Models



Composite Likelihood in Spatial Generalized Linear Models


Lattice Data



Maximum Likelihood Estimation in Lattice Models



Are Autoregressive Models Stationary?


Point Patterns



Estimating First- and Second-Order Properties of Point Patterns



Point Process Models



Spectral Analysis of Spatial Point Patterns


Supplementary Application



Point Patterns--Spectral Analysis of Seedling Counts


Bibliography


Author Index


Subject Index