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Generalized Linear Models
The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boca Raton :
Routledge,
2018.
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| Edición: | 2nd ed. |
| Colección: | Chapman and Hall/CRC Monographs on Statistics and Applied Probability.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title Page; Copyright Page; Dedication; Table of Contents; Preface to the first edition; Preface; 1: Introduction; 1.1 Background; 1.1.1 The problem of looking at data; 1.1.2 Theory as pattern; 1.1.3 Model fitting; 1.1.4 What is a good model?; 1.2 The origins of generalized linear models; 1.2.1 Terminology; 1.2.2 Classical linear models; 1.2.3 R.A. Fisher and the design of experiments; 1.2.4 Dilution assay; 1.2.5 Probit analysis; 1.2.6 Logit models for proportions; 1.2.7 Log-linear models for counts; 1.2.8 Inverse polynomials; 1.2.9 Survival data; 1.3 Scope of the rest of the book
- 1.4 Bibliographic notes1.5 Further results and exercises 1; 2: An outline of generalized linear models; 2.1 Processes in model fitting; 2.1.1 Model selection; 2.1.2 Estimation; 2.1.3 Prediction; 2.2 The components of a generalized linear model; 2.2.1 The generalization; 2.2.2 Likelihood functions; 2.2.3 Link functions; 2.2.4 Sufficient statistics and canonical links; 2.3 Measuring the goodness of fit; 2.3.1 The discrepancy of a fit; 2.3.2 The analysis of deviance; 2.4 Residuals; 2.4.1 Pearson residual; 2.4.2 Anscombe residual; 2.4.3 Deviance residual
- 2.5 An algorithm for fitting generalized linear models2.5.1 Justification of the fitting procedure; 2.6 Bibliographic notes; 2.7 Further results and exercises 2; 3: Models for continuous data with constant variance; 3.1 Introduction; 3.2 Error structure; 3.3 Systematic component (linear predictor); 3.3.1 Continuous covariates; 3.3.2 Qualitative covariates; 3.3.3 Dummy variates; 3.3.4 Mixed terms; 3.4 Model formulae for linear predictors; 3.4.1 Individual terms; 3.4.2 The dot operator; 3.4.3 The + operator; 3.4.4 The crossing (*) and nesting (/) operators
- 3.4.5 Operators for the removal of terms3.4.6 Exponential operator; 3.5 Aliasing; 3.5.1 Intrinsic aliasing with factors; 3.5.2 Aliasing in a two-way cross-classification; 3.5.3 Extrinsic aliasing; 3.5.4 Functional relations among covariates; 3.6 Estimation; 3.6.1 The maximum-likelihood equations; 3.6.2 Geometrical interpretation; 3.6.3 Information; 3.6.4 A model with two covariates; 3.6.5 The information surface; 3.6.6 Stability; 3.7 Tables as data; 3.7.1 Empty cells; 3.7.2 Fused cells; 3.8 Algorithms for least squares; 3.8.1 Methods based on the information matrix
- 3.8.2 Direct decomposition methods3.8.3 Extension to generalized linear models; 3.9 Selection of covariates; 3.10 Bibliographic notes; 3.11 Further results and exercises 3; 4: Binary data; 4.1 Introduction; 4.1.1 Binary responses; 4.1.2 Covariate classes; 4.1.3 Contingency tables; 4.2 Binomial distribution; 4.2.1 Genesis; 4.2.2 Moments and cumulants; 4.2.3 Normal limit; 4.2.4 Poisson limit; 4.2.5 Transformations; 4.3 Models for binary responses; 4.3.1 Link functions; 4.3.2 Parameter interpretation; 4.3.3 Retrospective sampling; 4.4 Likelihood functions for binary data