An Introduction to Generalized Linear Models, Third Edition

An Introduction to Generalized Linear Models, Third Edition

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Description

Continuing to emphasize numerical and graphical methods, An Introduction to Generalized Linear Models, Third Edition provides a cohesive framework for statistical modeling. This new edition of a bestseller has been updated with Stata, R, and WinBUGS code as well as three new chapters on Bayesian analysis. 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. Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons. It includes examples and exercises with complete data sets for nearly all the models covered.show more

Product details

  • Electronic book text | 320 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • English
  • Revised
  • 3rd Revised edition
  • 101 Tables, black and white; 59 Illustrations, black and white
  • 1584889519
  • 9781584889519

Table of contents

Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions Generalized Linear Models Dose Response Models General Logistic Regression Model Goodness-of-Fit Statistics Residuals Other Diagnostics Example: Senility and WAIS Nominal and Ordinal Logistic Regression Introduction Multinomial Distribution Nominal Logistic Regression Ordinal Logistic Regression General Comments Poisson Regression and Log-Linear Models Introduction Poisson Regression Examples of Contingency Tables Probability Models for Contingency Tables Log-Linear Models Inference for Log-Linear Models Numerical Examples Remarks Survival Analysis Introduction Survivor Functions and Hazard Functions Empirical Survivor Function Estimation Inference Model Checking Example: Remission Times Clustered and Longitudinal Data Introduction Example: Recovery from Stroke Repeated Measures Models for Normal Data Repeated Measures Models for Non-Normal Data Multilevel Models Stroke Example Continued Comments Bayesian Analysis Frequentist and Bayesian Paradigms Priors Distributions and Hierarchies in Bayesian Analysis WinBUGS Software for Bayesian Analysis Methods Why Standard Inference Fails Monte Carlo Integration Markov Chains Bayesian Inference Diagnostics of Chain Convergence Bayesian Model Fit: The DIC Example Bayesian Analyses Introduction Binary Variables and Logistic Regression Nominal Logistic Regression Latent Variable Model Survival Analysis Random Effects Longitudinal Data Analysis Some Practical Tips for WinBUGS Software References Index Exercises appear at the end of each chapter.show more

Review quote

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) 53The 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 Praise for the Second Edition: The second edition ... is successful in filling a void in the otherwise sparse literature on the subject of generalized linear models at the introductory level ... a wide range of research applications are covered and ample workings are also provided to aid the reader in statistical calculations ... I would highly recommend this text ... . -Kerrie Nelson, Statistics in Medicine, Vol. 23show more