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Introduction to Generalized Linear Models 4th edition [Pehme köide]

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(Queensland University of Technology, Kelvin Grove, Australia), (University of Queensland, Herston, Australia)
  • Formaat: Paperback / softback, 392 pages, kõrgus x laius: 234x156 mm, kaal: 730 g, 114 Tables, black and white; 73 Line drawings, black and white; 73 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Texts in Statistical Science
  • Ilmumisaeg: 13-Apr-2018
  • Kirjastus: CRC Press
  • ISBN-10: 1138741515
  • ISBN-13: 9781138741515
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Introduction to Generalized Linear Models 4th editionSuurem pilt
  • Formaat: Paperback / softback, 392 pages, kõrgus x laius: 234x156 mm, kaal: 730 g, 114 Tables, black and white; 73 Line drawings, black and white; 73 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Texts in Statistical Science
  • Ilmumisaeg: 13-Apr-2018
  • Kirjastus: CRC Press
  • ISBN-10: 1138741515
  • ISBN-13: 9781138741515
Teised raamatud teemal:
Teised raamatud sellest sooduspakkumisest: Taylor & Francis teadusraamatud International Student Editions hindadega
Püsilink: https://www.kriso.ee/db/9781138741515.html
Märksõnad:
An Introduction to Generalized Linear Models, Fourth Edition provides a cohesive framework for statistical modelling, with an emphasis on numerical and graphical methods. This new edition of a bestseller has been updated with new sections on non-linear associations, strategies for model selection, and a Postface on good statistical practice.

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.











Introduces GLMs in a way that enables readers to understand the unifying structure that underpins them





Discusses common concepts and principles of advanced GLMs, including nominal and ordinal regression, survival analysis, non-linear associations and longitudinal analysis





Connects Bayesian analysis and MCMC methods to fit GLMs





Contains numerous examples from business, medicine, engineering, and the social sciences





Provides the example code for R, Stata, and WinBUGS to encourage implementation of the methods





Offers the data sets and solutions to the exercises online





Describes the components of good statistical practice to improve scientific validity and reproducibility of results.

Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons.

Arvustused

Praise for the Third Edition:

Overall, this new edition remains a highly useful and compact introduction to a large number of seemingly disparate regression models. Depending on the background of the audience, it will be suitable for upper-level undergraduate or beginning post-graduate courses. Christian Kleiber, Statistical Papers (2012) 53

The comments of Lang in his review of the second edition, that This relatively short book gives a nice introductory overview of the theory underlying generalized linear modelling. can equally be applied to the new edition. three new chapters on Bayesian analysis are also added. suitable for experienced professionals needing to refresh their knowledge . Pharmaceutical Statistics, 2011

The chapters are short and concise, and the writing is clear explanations are fundamentally sound and aimed well at an upper-level undergrad or early graduate student in a statistics-related field. This is a very worthwhile book: a good class text and a practical reference for applied statisticians.

Biometrics

This book promises in its introductory section to provide a unifying framework for many statistical techniques. It accomplishes this goal easily. Furthermore, the text covers important topics that are frequently overlooked in introductory courses, such as models for ordinal outcomes. This book is an excellent resource, either as an introduction to or a reminder of the technical aspects of generalized linear models and provides a wealth of simple yet useful examples and data sets. Journal of Biopharmaceutical Statistics, Issue 2

This book aims to provide an overview of the key issues in generalized linear models (GLMs), including assumptions, estimation methods, different link functions, and a Bayesian approach. Applications of the book concern different types of data, such as continuous, categorical, count, correlated, and time-to-event data. The book contains theoretical and applicable examples of different type of GLMs. The first five chapters introduce the basics of linear models and the relations between different distributions. The following chapters explain GLMs in respect to different types of link function. One of the most important features of the book is the statistical software codes in each chapter, which make it more practical, as well as the last chapter that focuses on examples of Bayesian analysis. - Morteza Hajihosseini in ISCB, June 2019

Preface xv
1 Introduction
1(20)
1.1 Background
1(1)
1.2 Scope
1(5)
1.3 Notation
6(2)
1.4 Distributions related to the Normal distribution
8(3)
1.4.1 Normal distributions
8(1)
1.4.2 Chi-squared distribution
9(1)
1.4.3 t-distribution
10(1)
1.4.4 F-distribution
10(1)
1.4.5 Some relationships between distributions
11(1)
1.5 Quadratic forms
11(2)
1.6 Estimation
13(4)
1.6.1 Maximum likelihood estimation
13(2)
1.6.2 Example: Poisson distribution
15(1)
1.6.3 Least squares estimation
15(1)
1.6.4 Comments on estimation
16(1)
1.6.5 Example: Tropical cyclones
17(1)
1.7 Exercises
17(4)
2 Model Fitting
21(28)
2.1 Introduction
21(1)
2.2 Examples
21(14)
2.2.1 Chronic medical conditions
21(4)
2.2.2 Example: Birthweight and gestational age
25(10)
2.3 Some principles of statistical modelling
35(5)
2.3.1 Exploratory data analysis
35(1)
2.3.2 Model formulation
36(1)
2.3.3 Parameter estimation
36(1)
2.3.4 Residuals and model checking
36(3)
2.3.5 Inference and interpretation
39(1)
2.3.6 Further reading
40(1)
2.4 Notation and coding for explanatory variables
40(4)
2.4.1 Example: Means for two groups
41(1)
2.4.2 Example: Simple linear regression for two groups
42(1)
2.4.3 Example: Alternative formulations for comparing the means of two groups
42(1)
2.4.4 Example: Ordinal explanatory variables
43(1)
2.5 Exercises
44(5)
3 Exponential Family and Generalized Linear Models
49(16)
3.1 Introduction
49(1)
3.2 Exponential family of distributions
50(3)
3.2.1 Poisson distribution
51(1)
3.2.2 Normal distribution
52(1)
3.2.3 Binomial distribution
52(1)
3.3 Properties of distributions in the exponential family
53(3)
3.4 Generalized linear models
56(2)
3.5 Examples
58(3)
3.5.1 Normal linear model
58(1)
3.5.2 Historical linguistics
58(1)
3.5.3 Mortality rates
59(2)
3.6 Exercises
61(4)
4 Estimation
65(14)
4.1 Introduction
65(1)
4.2 Example: Failure times for pressure vessels
65(5)
4.3 Maximum likelihood estimation
70(3)
4.4 Poisson regression example
73(3)
4.5 Exercises
76(3)
5 Inference
79(18)
5.1 Introduction
79(2)
5.2 Sampling distribution for score statistics
81(2)
5.2.1 Example: Score statistic for the Normal distribution
82(1)
5.2.2 Example: Score statistic for the Binomial distribution
82(1)
5.3 Taylor series approximations
83(1)
5.4 Sampling distribution for maximum likelihood estimators
84(2)
5.4.1 Example: Maximum likelihood estimators for the Normal linear model
85(1)
5.5 Log-likelihood ratio statistic
86(1)
5.6 Sampling distribution for the deviance
87(5)
5.6.1 Example: Deviance for a Binomial model
88(1)
5.6.2 Example: Deviance for a Normal linear model
89(2)
5.6.3 Example: Deviance for a Poisson model
91(1)
5.7 Hypothesis testing
92(3)
5.7.1 Example: Hypothesis testing for a Normal linear model
94(1)
5.8 Exercises
95(2)
6 Normal Linear Models
97(52)
6.1 Introduction
97(1)
6.2 Basic results
98(6)
6.2.1 Maximum likelihood estimation
98(1)
6.2.2 Least squares estimation
98(1)
6.2.3 Deviance
99(1)
6.2.4 Hypothesis testing
99(1)
6.2.5 Orthogonality
100(1)
6.2.6 Residuals
101(1)
6.2.7 Other diagnostics
102(2)
6.3 Multiple linear regression
104(15)
6.3.1 Example: Carbohydrate diet
104(4)
6.3.2 Coefficient of determination, R2
108(3)
6.3.3 Model selection
111(7)
6.3.4 Collinearity
118(1)
6.4 Analysis of variance
119(13)
6.4.1 One-factor analysis of variance
119(7)
6.4.2 Two-factor analysis of variance
126(6)
6.5 Analysis of covariance
132(3)
6.6 General linear models
135(2)
6.7 Non-linear associations
137(4)
6.7.1 PLOS Medicine journal data
138(3)
6.8 Fractional polynomials
141(2)
6.9 Exercises
143(6)
7 Binary Variables and Logistic Regression
149(30)
7.1 Probability distributions
149(1)
7.2 Generalized linear models
150(1)
7.3 Dose response models
151(7)
7.3.1 Example: Beetle mortality
154(4)
7.4 General logistic regression model
158(4)
7.4.1 Example: Embryogenic anthers
159(3)
7.5 Goodness of fit statistics
162(4)
7.6 Residuals
166(1)
7.7 Other diagnostics
167(1)
7.8 Example: Senility and WAIS
168(3)
7.9 Odds ratios and prevalence ratios
171(3)
7.10 Exercises
174(5)
8 Nominal and Ordinal Logistic Regression
179(18)
8.1 Introduction
179(1)
8.2 Multinomial distribution
180(1)
8.3 Nominal logistic regression
181(7)
8.3.1 Example: Car preferences
183(5)
8.4 Ordinal logistic regression
188(5)
8.4.1 Cumulative logit model
189(1)
8.4.2 Proportional odds model
189(1)
8.4.3 Adjacent categories logit model
190(1)
8.4.4 Continuation ratio logit model
191(1)
8.4.5 Comments
192(1)
8.4.6 Example: Car preferences
192(1)
8.5 General comments
193(1)
8.6 Exercises
194(3)
9 Poisson Regression and Log-Linear Models
197(26)
9.1 Introduction
197(1)
9.2 Poisson regression
198(6)
9.2.1 Example of Poisson regression: British doctors' smoking and coronary death
201(3)
9.3 Examples of contingency tables
204(5)
9.3.1 Example: Cross-sectional study of malignant melanoma
205(1)
9.3.2 Example: Randomized controlled trial of influenza vaccine
206(1)
9.3.3 Example: Case-control study of gastric and duodenal ulcers and aspirin use
207(2)
9.4 Probability models for contingency tables
209(1)
9.4.1 Poisson model
209(1)
9.4.2 Multinomial model
209(1)
9.4.3 Product multinomial models
210(1)
9.5 Log-linear models
210(2)
9.6 Inference for log-linear models
212(1)
9.7 Numerical examples
212(4)
9.7.1 Cross-sectional study of malignant melanoma
212(3)
9.7.2 Case-control study of gastric and duodenal ulcer and aspirin use
215(1)
9.8 Remarks
216(1)
9.9 Exercises
217(6)
10 Survival Analysis
223(22)
10.1 Introduction
223(2)
10.2 Survivor functions and hazard functions
225(5)
10.2.1 Exponential distribution
226(1)
10.2.2 Proportional hazards models
227(1)
10.2.3 Weibull distribution
228(2)
10.3 Empirical survivor function
230(3)
10.3.1 Example: Remission times
231(2)
10.4 Estimation
233(3)
10.4.1 Example: Exponential model
234(1)
10.4.2 Example: Weibull model
235(1)
10.5 Inference
236(1)
10.6 Model checking
236(2)
10.7 Example: Remission times
238(2)
10.8 Exercises
240(5)
11 Clustered and Longitudinal Data
245(26)
11.1 Introduction
245(2)
11.2 Example: Recovery from stroke
247(6)
11.3 Repeated measures models for Normal data
253(4)
11.4 Repeated measures models for non-Normal data
257(2)
11.5 Multilevel models
259(3)
11.6 Stroke example continued
262(3)
11.7 Comments
265(1)
11.8 Exercises
266(5)
12 Bayesian Analysis
271(16)
12.1 Frequentist and Bayesian paradigms
271(4)
12.1.1 Alternative definitions of p-values and confidence intervals
271(1)
12.1.2 Bayes' equation
272(1)
12.1.3 Parameter space
273(1)
12.1.4 Example: Schistosoma japonicum
273(2)
12.2 Priors
275(6)
12.2.1 Informative priors
276(1)
12.2.2 Example: Sceptical prior
276(3)
12.2.3 Example: Overdoses amongst released prisoners
279(2)
12.3 Distributions and hierarchies in Bayesian analysis
281(1)
12.4 WinBUGS software for Bayesian analysis
281(3)
12.5 Exercises
284(3)
13 Markov Chain Monte Carlo Methods
287(28)
13.1 Why standard inference fails
287(1)
13.2 Monte Carlo integration
287(2)
13.3 Markov chains
289(11)
13.3.1 The Metropolis-Hastings sampler
291(2)
13.3.2 The Gibbs sampler
293(2)
13.3.3 Comparing a Markov chain to classical maximum likelihood estimation
295(4)
13.3.4 Importance of parameterization
299(1)
13.4 Bayesian inference
300(2)
13.5 Diagnostics of chain convergence
302(4)
13.5.1 Chain history
302(2)
13.5.2 Chain autocorrelation
304(1)
13.5.3 Multiple chains
305(1)
13.6 Bayesian model fit: the deviance information criterion
306(2)
13.7 Exercises
308(7)
14 Example Bayesian Analyses
315(32)
14.1 Introduction
315(1)
14.2 Binary variables and logistic regression
316(6)
14.2.1 Prevalence ratios for logistic regression
319(3)
14.3 Nominal logistic regression
322(2)
14.4 Latent variable model
324(2)
14.5 Survival analysis
326(2)
14.6 Random effects
328(3)
14.7 Longitudinal data analysis
331(7)
14.8 Bayesian model averaging
338(4)
14.8.1 Example: Stroke recovery
340(1)
14.8.2 Example: PLOS Medicine journal data
340(2)
14.9 Some practical tips for WinBUGS
342(2)
14.10 Exercises
344(3)
Postface 347(8)
Appendix 355(2)
Software 357(2)
References 359(12)
Index 371
Annette J. Dobson is Professor of Biostatistics at the Univesity of Queensland.

Adrian G. Barnett is a professor at the Queensland University of Technology.