An introduction to generalized linear models:
Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers Normal, Poisson, and Binomial distributions; linear regression models; classical estimation and model fitting method...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
[2018]
|
| Ausgabe: | Fourth edition |
| Schriftenreihe: | Chapman & Hall/CRC texts in statistical science series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers Normal, Poisson, and Binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods. |
| Beschreibung: | "A Chapman & Hall book.". - Includes bibliographical references and index |
| Beschreibung: | XV, 376 Seiten Diagramme 24 cm |
| ISBN: | 9781138741683 9781138741515 |
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Datensatz im Suchindex
| _version_ | 1804178953642967040 |
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| adam_text | Contents Preface xv 1 Introduction 1.1 Background 1.2 Scope 1.3 Notation 1.4 Distributionsrelated to the Normal distribution 1.4.1 Normal distributions 1.4.2 Chi-squared distribution 1.4.3 t-distribution 1.4.4 F-distribution 1.4.5 Some relationships between distributions 1.5 Quadratic forms 1.6 Estimation 1.6.1 Maximum likelihood estimation 1.6.2 Example: Poisson distribution 1.6.3 Least squares estimation 1.6.4 Comments on estimation 1.6.5 Example: Tropical cyclones 1.7 Exercises 1 1 1 6 8 8 9 10 10 11 11 13 13 15 15 16 17 17 2 Model Fitting 2.1 Introduction 2.2 Examples 2.2.1 Chronic medical conditions 2.2.2 Example: Birthweight and gestational age 2.3 Some principles of statistical modelling 2.3.1 Exploratory data analysis 2.3.2 Model formulation 2.3.3 Parameter estimation 21 21 21 21 25 35 35 36 36 vii
Vlil 2.4 2.5 2.3.4 Residuals and model checking 2.3.5 Inference and interpretation 2.3.6 Further reading Notation and coding for explanatory variables 2.4.1 Example: Means for two groups 2.4.2 Example: Simple linear regression for two groups 2.4.3 Example: Alternative formulations for comparing the means of two groups 2.4.4 Example: Ordinal explanatory variables Exercises 36 39 40 40 41 42 42 43 44 3 Exponential Family and Generalized Linear Models 3.1 Introduction 3.2 Exponential family of distributions 3.2.1 Poisson distribution 3.2.2 Normal distribution 3.2.3 Binomial distribution 3.3 Properties of distributions in the exponentialfamily 3.4 Generalized linear models 3.5 Examples 3.5.1 Normal linear model 3.5.2 Historical linguistics 3.5.3 Mortality rates 3.6 Exercises 49 49 50 51 52 52 53 56 58 58 58 59 61 4 Estimation 4.1 Introduction 4.2 Example: Failure times for pressure vessels 4.3 Maximum likelihood estimation 4.4 Poisson regression example 4.5 Exercises 65 65 65 70 73 76 5 Inference 5.1 Introduction 5.2 Sampling distribution for score statistics 5.2.1 Example: Score statistic for the Normal distribution 5.2.2 Example: Score statistic for the Binomial distribution 5.3 Taylor series approximations 5.4 Sampling distribution for maximum likelihood estimators 79 79 81 82 82 83 84
ix 5.4.1 5.5 5.6 5.7 5.8 6 Example: Maximum likelihood estimators for the Normal linear model Log-likelihood ratio statistic Sampling distribution for the deviance 5.6.1 Example: Deviance for a Binomial model 5.6.2 Example: Deviance for a Normallinear model 5.6.3 Example: Deviance for a Poisson model Hypothesis testing 5.7.1 Example: Hypothesis testing fora Normal linear model Exercises Normal Linear Models 6.1 Introduction 6.2 Basic results 6.2.1 Maximum likelihood estimation 6.2.2 Least squares estimation 6.2.3 Deviance 6.2.4 Hypothesis testing 6.2.5 Orthogonality 6.2.6 Residuals 6.2.7 Other diagnostics 6.3 Multiple linear regression 6.3.1 Example: Carbohydrate diet 6.3.2 Coefficient of determination, Ŕ2 6.3.3 Model selection 6.3.4 Collinearity 6.4 Analysis of variance 6.4.1 One-factor analysis of variance 6.4.2 Two-factor analysis of variance 6.5 Analysis of covariance 6.6 General linear models 6.7 Non-linear associations 6.7.1 PLOS Medicine journal data 6.8 Fractional polynomials 6.9 Exercises 85 86 87 88 89 91 92 94 95 97 97 98 98 98 99 99 100 101 102 104 104 108 111 118 119 119 126 132 135 137 138 141 143
x 7 Binary Variables and Logistic Regression 7.1 Probability distributions 7.2 Generalized linear models 7.3 Dose response models 7.3.1 Example: Beetle mortality 7.4 General logistic regression model 7.4.1 Example: Embryogénie anthers 7.5 Goodness of fit statistics 7.6 Residuals 7.7 Other diagnostics 7.8 Example: Senility and WAIS 7.9 Odds ratios and prevalence ratios 7.10 Exercises 149 149 150 151 154 158 159 162 166 167 168 171 174 8 Nominal and Ordinal Logistic Regression 8.1 Introduction 8.2 Multinomial distribution 8.3 Nominal logistic regression 8.3.1 Example: Car preferences 8.4 Ordinal logistic regression 8.4.1 Cumulative logit model 8.4.2 Proportional odds model 8.4.3 Adjacent categories logit model 8.4.4 Continuation ratio logit model 8.4.5 Comments 8.4.6 Example: Car preferences 8.5 General comments 8.6 Exercises 179 179 180 181 183 188 189 189 190 191 192 192 193 194 9 Poisson Regression and Log-Linear Models 9.1 Introduction 9.2 Poisson regression 9.2.1 Example of Poisson regression:British doctors’ smoking and coronarydeath 9.3 Examples of contingency tables 9.3.1 Example: Cross-sectional study ofmalignant melanoma 9.3.2 Example: Randomized controlled trialof influenza vaccine 197 197 198 201 204 205 206
xi 9.3.3 9.4 9.5 9.6 9.7 9.8 9.9 Example: Case-control studyof gastric andduodenal ulcers and aspirin use Probability models for contingency tables 9.4.1 Poisson model 9.4.2 Multinomial model 9.4.3 Product multinomial models Log-linear models Inference for log-linear models Numerical examples 9.7.1 Cross-sectional study of malignantmelanoma 9.7.2 Case-control study of gastricand duodenalulcer and aspirin use Remarks Exercises 207 209 209 209 210 210 212 212 212 215 216 217 10 Survival Analysis 10.1 Introduction 10.2 Survivor functions and hazard functions 10.2.1 Exponential distribution 10.2.2 Proportional hazards models 10.2.3 Weibull distribution 10.3 Empirical survivor function 10.3.1 Example: Remission times 10.4 Estimation 10.4.1 Example: Exponential model 10.4.2 Example: Weibull model 10.5 Inference 10.6 Model checking 10.7 Example: Remission times 10.8 Exercises 223 223 225 226 227 228 230 231 233 234 235 236 236 238 240 11 Clustered and Longitudinal Data 11.1 Introduction 11.2 Example: Recovery from stroke 11.3 Repeated measures models for Normaldata 11.4 Repeated measures models for non-Normal data 11.5 Multilevel models 11.6 Stroke example continued 11.7 Comments 11.8 Exercises 245 245 247 253 257 259 262 265 266
Xli 12 Bayesian Analysis 12.1 Frequentist and Bayesian paradigms 12.1.1 Alternative definitions of p-values and confidence intervals 12.1.2 Bayes’ equation 12.1.3 Parameterspace 12.1.4 Example: Schistosoma japonicum 12.2 Priors 12.2.1 Informative priors 12.2.2 Example: Sceptical prior 12.2.3 Example: Overdoses amongst released prisoners 12.3 Distributions and hierarchies in Bayesian analysis 12.4 WinBUGS software for Bayesian analysis 12.5 Exercises 271 271 271 272 273 273 275 276 276 279 281 281 284 13 Markov Chain Monte Carlo Methods 13.1 Why standard inference fails 13.2 Monte Carlo integration 13.3 Markov chains 13.3.1 The Metropolis-Hastings sampler 13.3.2 The Gibbs sampler 13.3.3 Comparing a Markov chain to classical maximum likelihood estimation 13.3.4 Importance of parameterization 13.4 Bayesian inference 13.5 Diagnostics of chain convergence 13.5.1 Chain history 13.5.2 Chain autocorrelation 13.5.3 Multiple chains 13.6 Bayesian model fit: the deviance information criterion 13.7 Exercises 287 287 287 289 291 293 14 Example Bayesian Analyses 14.1 Introduction 14.2 Binary variables and logistic regression 14.2.1 Prevalence ratios for logistic regression 14.3 Nominal logistic regression 14.4 Latent variable model 14.5 Survival analysis 14.6 Random effects 315 315 316 319 322 324 326 328 295 299 300 302 302 304 305 306 308
XIII 14.7 Longitudinal data analysis 14.8 Bayesian model averaging 14.8.1 Example: Stroke recovery 14.8.2 Example: PLOS Medicine journal data 14.9 Some practical tips for WinBUGS 14.10 Exercises 331 338 340 340 342 344 Postface 347 Appendix 355 Software 357 References 359 Index 371
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| record_format | marc |
| series2 | Chapman & Hall/CRC texts in statistical science series |
| spelling | Dobson, Annette J. 1945- (DE-588)14077954X aut An introduction to generalized linear models by Annette J. Dobson and Adrian G. Barnett Generalized linear models Fourth edition Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2018] 2018 XV, 376 Seiten Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC texts in statistical science series "A Chapman & Hall book.". - Includes bibliographical references and index Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers Normal, Poisson, and Binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods. Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf Lineares Modell (DE-588)4134827-8 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Verallgemeinertes lineares Modell (DE-588)4124382-1 s Statistik (DE-588)4056995-0 s Modellierung (DE-588)4170297-9 s DE-604 Lineares Modell (DE-588)4134827-8 s 1\p DE-604 Modelltheorie (DE-588)4114617-7 s 2\p DE-604 Barnett, Adrian G. (DE-588)136168019 aut Erscheint auch als Online-Ausgabe 978-1-315-18278-0 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030616995&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dobson, Annette J. 1945- Barnett, Adrian G. An introduction to generalized linear models Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Lineares Modell (DE-588)4134827-8 gnd Modellierung (DE-588)4170297-9 gnd Modelltheorie (DE-588)4114617-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4124382-1 (DE-588)4134827-8 (DE-588)4170297-9 (DE-588)4114617-7 (DE-588)4056995-0 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | An introduction to generalized linear models |
| title_alt | Generalized linear models |
| title_auth | An introduction to generalized linear models |
| title_exact_search | An introduction to generalized linear models |
| title_full | An introduction to generalized linear models by Annette J. Dobson and Adrian G. Barnett |
| title_fullStr | An introduction to generalized linear models by Annette J. Dobson and Adrian G. Barnett |
| title_full_unstemmed | An introduction to generalized linear models by Annette J. Dobson and Adrian G. Barnett |
| title_short | An introduction to generalized linear models |
| title_sort | an introduction to generalized linear models |
| topic | Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Lineares Modell (DE-588)4134827-8 gnd Modellierung (DE-588)4170297-9 gnd Modelltheorie (DE-588)4114617-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Linear models (Statistics) Verallgemeinertes lineares Modell Lineares Modell Modellierung Modelltheorie Statistik Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030616995&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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