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Author McCullagh, P
Title Generalized Linear Models
Imprint Boca Raton : CRC Press LLC, 1989
©1989
book jacket
Edition 2nd ed
Descript 1 online resource (532 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Chapman and Hall/CRC Monographs on Statistics and Applied Probability ; v.37
Chapman and Hall/CRC Monographs on Statistics and Applied Probability
Note 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 notes -- 1.5 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 models -- 2.5.1 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 terms -- 3.4.6 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 methods -- 3.8.3 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 -- 4.4.1 Log likelihood for binomial data -- 4.4.2 Parameter estimation -- 4.4.3 Deviance function -- 4.4.4 Bias and precision of estimates -- 4.4.5 Sparseness -- 4.4.6 Extrapolation -- 4.5 Over-dispersion -- 4.5.1 Genesis -- 4.5.2 Parameter estimation -- 4.6 Example -- 4.6.1 Habitat preferences of lizards -- 4.7 Bibliographic notes -- 4.8 Further results and exercises 4 -- 5: Models for polytomous data -- 5.1 Introduction -- 5.2 Measurement scales -- 5.2.1 General points -- 5.2.2 Models for ordinal scales -- 5.2.3 Models for interval scale -- 5.2.4 Models for nominal scales -- 5.2.5 Nested or hierarchical response scales
5.3 The multinomial distribution -- 5.3.1 Genesis -- 5.3.2 Moments and cumulants -- 5.3.3 Generalized inverse matrices -- 5.3.4 Quadratic forms -- 5.3.5 Marginal and conditional distributions -- 5.4 Likelihood functions -- 5.4.1 Log likelihood for multinomial responses -- 5.4.2 Parameter estimation -- 5.4.3 Deviance function -- 5.5 Over-dispersion -- 5.6 Examples -- 5.6.1 A cheese-tasting experiment -- 5.6.2 Pneumoconiosis among coalminers -- 5.7 Bibliographic notes -- 5.8 Further results and exercises 5 -- 6: Log-linear models -- 6.1 Introduction -- 6.2 Likelihood functions -- 6.2.1 Poisson distribution -- 6.2.2 The Poisson log-likelihood function -- 6.2.3 Over-dispersion -- 6.2.4 Asymptotic theory -- 6.3 Examples -- 6.3.1 A biological assay of tuberculins -- 6.3.2 A study of wave damage to cargo ships -- 6.4 Log-linear models and multinomial response models -- 6.4.1 Comparison of two or more Poisson means -- 6.4.2 Multinomial response models -- 6.4.3 Summary -- 6.5 Multiple responses -- 6.5.1 Introduction -- 6.5.2 Independence and conditional independence -- 6.5.3 Canonical correlation models -- 6.5.4 Multivariate regression models -- 6.5.5 Multivariate model formulae -- 6.5.6 Log-linear regression models -- 6.5.7 Likelihood equations -- 6.6 Example -- 6.6.1 Respiratory ailments of coalminers -- 6.6.2 Parameter interpretation -- 6.7 Bibliographic notes -- 6.8 Further results and exercises 6 -- 7: Conditional likelihoods* -- 7.1 Introduction -- 7.2 Marginal and conditional likelihoods -- 7.2.1 Marginal likelihood -- 7.2.2 Conditional likelihood -- 7.2.3 Exponential-family models -- 7.2.4 Profile likelihood -- 7.3 Hypergeometric distributions -- 7.3.1 Central hypergeometric distribution -- 7.3.2 Non-central hypergeometric distribution -- 7.3.3 Multivariate hypergeometric distribution -- 7.3.4 Multivariate non-central distribution
7.4 Some applications involving binary data -- 7.4.1 Comparison of two binomial probabilities -- 7.4.2 Combination of information from 2x2 tables -- 7.4.3 Ille-et-Vilaine study of oesophageal cancer -- 7.5 Some applications involving polytomous data -- 7.5.1 Matched pairs: nominal response -- 7.5.2 Ordinal responses -- 7.5.3 Example -- 7.6 Bibliographic notes -- 7.7 Further results and exercises 7 -- 8: Models with constant coefficient of variation -- 8.1 Introduction -- 8.2 The gamma distribution -- 8.3 Models with gamma-distributed observations -- 8.3.1 The variance function -- 8.3.2 The deviance -- 8.3.3 The canonical link -- 8.3.4 Multiplicative models: log link -- 8.3.5 Linear models: identity link -- 8.3.6 Estimation of the dispersion parameter -- 8.4 Examples -- 8.4.1 Car insurance claims -- 8.4.2 Clotting times of blood -- 8.4.3 Modelling rainfall data using two generalized linear models -- 8.4.4 Developmental rate of Drosophila melanogaster -- 8.5 Bibliographic notes -- 8.6 Further results and exercises 8 -- 9: Quasi-likelihood functions -- 9.1 Introduction -- 9.2 Independent observations -- 9.2.1 Covariance functions -- 9.2.2 Construction of the quasi-likelihood function -- 9.2.3 Parameter estimation -- 9.2.4 Example: incidence of leaf-blotch on barley -- 9.3 Dependent observations -- 9.3.1 Quasi-likelihood estimating equations -- 9.3.2 Quasi-likelihood function -- 9.3.3 Example: estimation of probabilities from marginal frequencies -- 9.4 Optimal estimating functions -- 9.4.1 Introduction -- 9.4.2 Combination of estimating functions -- 9.4.3 Example: estimation for megalithic stone rings -- 9.5 Optimality criteria -- 9.6 Extended quasi-likelihood -- 9.7 Bibliographic notes -- 9.8 Further results and exercises 9 -- 10: Joint modelling of mean and dispersion -- 10.1 Introduction -- 10.2 Model specification
10.3 Interaction between mean and dispersion effects -- 10.4 Extended quasi-likelihood as a criterion -- 10.5 Adjustments of the estimating equations -- 10.5.1 Adjustment for kurtosis -- 10.5.2 Adjustment for degrees of freedom -- 10.5.3 Summary of estimating equations for the dispersion model -- 10.6 Joint optimum estimating equations -- 10.7 Example: the production of leaf-springs for trucks -- 10.8 Bibliographic notes -- 10.9 Further results and exercises 10 -- 11: Models with additional non-linear parameters -- 11.1 Introduction -- 11.2 Parameters in the variance function -- 11.3 Parameters in the link function -- 11.3.1 One link parameter -- 11.3.2 More than one link parameter -- 11.3.3 Transformation of data vs transformation of fitted values -- 11.4 Non-linear parameters in the covariates -- 11.5 Examples -- 11.5.1 The effects of fertilizers on coastal Bermuda grass -- 11.5.2 Assay of an insecticide with a synergist -- 11.5.3 Mixtures of drugs -- 11.6 Bibliographic notes -- 11.7 Further results and exercises 11 -- 12: Model checking -- 12.1 Introduction -- 12.2 Techniques in model checking -- 12.3 Score tests for extra parameters -- 12.4 Smoothing as an aid to informal checks -- 12.5 The raw materials of model checking -- 12.6 Checks for systematic departure from model -- 12.6.1 Informal checks using residuals -- 12.6.2 Checking the variance function -- 12.6.3 Checking the link function -- 12.6.4 Checking the scales of covariates -- 12.6.5 Checks for compound discrepancies -- 12.7 Checks for isolated departures from the model -- 12.7.1 Measure of leverage -- 12.7.2 Measure of consistency -- 12.7.3 Measure of influence -- 12.7.4 Informal assessment of extreme values -- 12.7.5 Extreme points and checks for systematic discrepancies -- 12.8 Examples -- 12.8.1 Carrot damage in an insecticide experiment -- 12.8.2 Minitab tree data
12.8.3 Insurance claims (continued)
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: McCullagh, P. Generalized Linear Models Boca Raton : CRC Press LLC,c1989 9780412317606
Subject Linear models (Statistics)
Electronic books
Alt Author Nelder, J. A
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