Multivariate Statistical Modelling Based on Generalized Linear Models

To get the data sets discussed in this book, using R: install.packages("Fahrmeir")Classical statistical models for regression, time series and longitudinal data provide well-established tools for approximately normally distributed vari-ables. Enhanced by the availability of software packages these models dom-inated the field of applications for a long time. With the introduction of generalized linear models (GLM) a much more flexible instrument for sta-tistical modelling has been created. The broad class of GLM's includes some of the classicallinear models as special cases but is particularly suited for categorical discrete or nonnegative responses. The last decade has seen various extensions of GLM's: multivariate and multicategorical models have been considered, longitudinal data analysis has been developed in this setting, random effects and nonparametric pre-dictors have been included. These extended methods have grown around generalized linear models but often are no longer GLM's in the original sense. The aim of this book is to bring together and review a large part of these recent advances in statistical modelling. Although the continuous case is sketched sometimes, thoughout the book the focus is on categorical data. The book deals with regression analysis in a wider sense including not only cross-sectional analysis but also time series and longitudinal data situations. We do not consider problems of symmetrical nature, like the investigation of the association structure in a given set of variables. For example, log-linear models for contingency tables, which can be treated as special cases of GLM's are totally omitted. The estimation approach that is primarily considered in this book is likelihood-based. Classical statistical models for regression, time series and longitudinal data provide well-established tools for approximately normally distributed vari­ ables. Enhanced by the availability of software packages these models dom­ inated the field of applications for a long time. With the introduction of generalized linear models (GLM) a much more flexible instrument for sta­ tistical modelling has been created. The broad class of GLM's includes some of the classicallinear models as special cases but is particularly suited for categorical discrete or nonnegative responses. The last decade has seen various extensions of GLM's: multivariate and multicategorical models have been considered, longitudinal data analysis has been developed in this setting, random effects and nonparametric pre­ dictors have been included. These extended methods have grown around generalized linear models but often are no longer GLM's in the original sense. The aim of this book is to bring together and review a large part of these recent advances in statistical modelling. Although the continuous case is sketched sometimes, thoughout the book the focus is on categorical data. The book deals with regression analysis in a wider sense including not only cross-sectional analysis but also time series and longitudinal data situations. We do not consider problems of symmetrical nature, like the investigation of the association structure in a given set of variables. For example, log-linear models for contingency tables, which can be treated as special cases of GLM's are totally omitted. The estimation approach that is primarily considered in this book is likelihood-based. This book is concerned with the use of generalized linear models for univariate and multivariate regression analysis. Its emphasis is to provide a detailed introductory survey of the subject based on the analysis of real data drawn from a variety of subjects including the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account to have on their desks. "The basic aim of the authors is to bring together and review a large part of recent advances in statistical modelling of multivariate and multicategorical models within the generalized linear models framework. Based on well-chosen sets of data, these new developments are introduced to a not necessarily expert audience. Completeness was not an aim. The result is a self-contained, well-written text offering the applied researcher a useful insight into the applicability of the general linear model methodology." P.A.L. Embrechts, ETH-Zentrum, Z rich, Switzerland "The authors give a detailed introductory survey of the subject based on the analysis of real data drawn from a variety of subjects, including the biological sciences, economics, and the social sciences. Technical details and proofs are deferred to an appendix in order to provide an accessible account for nonexperts. The appendix serves as a reference or brief tutorial for the concepts of the EM algorithm, numerical integration, MCMC, and others.". "In the new edition, Bayesian concepts, which are of growing importance in statistics, are treated more extensively. The chapter on nonparametric and semiparametric generalized regression has been rewritten totally, random effects models now cover nonparametric maximum likelihood and fully Bayesian approaches, and state-space and hidden Markov models have been supplemented with an extension to models that can accommodate for spatial and spatiotemporal data.". "The authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, this book is ideally suited for applied statisticians, graduate students of statistics, and students and researchers with a strong interest in statistics and data analysis from econometrics, biometrics, and the social sciences."--BOOK JACKET. Front Matter....Pages i-xxiv Introduction....Pages 1-13 Modelling and analysis of cross—sectional data: a review of univariate generalized linear models....Pages 15-62 Models for multicategorical responses: multivariate extensions of generalized linear models....Pages 63-118 Selecting and checking models....Pages 119-149 Semi— and nonparametric approaches to regression analysis....Pages 151-185 Fixed parameter models for time series and longitudinal data....Pages 187-218 Random effects models....Pages 219-255 State space models....Pages 257-303 Survival models....Pages 305-344 Back Matter....Pages 345-426