Contemporary Statistical Models for the Plant and Soil Sciences

ISBN: 9781584881117 出版年：2001 页码：762 Schabenberger, Oliver Pierce, Francis J CRC Press

Statistical Models Mathematical and Statistical Models Functional Aspects of Models The Inferential Steps o Estimation and Testing t-Tests in Terms of Statistical Models Embedding Hypotheses Hypothesis and Significance Testing o Interpretation of the p-Value Classes of Statistical Models Data Structures Introduction Classification by Response Type Classification by Study Type Clustered Data Autocorrelated Data From Independent to Spatial Data o A Progression of Clustering Linear Algebra Tools Introduction Matrices and Vectors Basic Matrix Operations Matrix Inversion o 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 The Classical Linear Model: Least Squares and Alternatives Introduction Least Squares Estimation and Partitioning of Variation Factorial Classification Diagnosing Regression Models Diagnosing Classification Models Robust Estimation Nonparametric Regression Nonlinear Models Introduction Models as Laws or Tools Linear Polynomials Approximate Nonlinear Models Fitting a Nonlinear Model to Data Hypothesis Tests and Confidence Intervals Transformations Parameterization of Nonlinear Models Applications Generalized Linear Models Introduction Components of a Generalized Linear Model Grouped and Ungrouped Data Parameter Estimation and Inference Modeling an Ordinal Response Overdispersion Applications Linear Mixed Models for Clustered Data Introduction The Laird-Ware Model Choosing the Inference Space Estimation and Inference Correlations in Mixed Models Applications Nonlinear Models for Clustered Data Introduction Nonlinear and Generalized Linear Mixed Models Towards an Approximate Objective Function Applications Statistical Models for Spatial Data Changing the Mindset Semivariogram Analysis and Estimation The Spatial Model Spatial Prediction and the Kriging Paradigm Spatial Regression and Classification Models Autoregressive Models for Lattice Data Analyzing Mapped Spatial Point Patterns Applications Bibliography