Models for Discrete Longitudinal Data

Author: Geert Molenberghs,Geert Verbeke

Publisher: Springer Science & Business Media

ISBN: 9780387251448

Category: Mathematics

Page: 687

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The linear mixed model has become the main parametric tool for the analysis of continuous longitudinal data, as the authors discussed in their 2000 book. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The authors received the American Statistical Association's Excellence in Continuing Education Award based on short courses on longitudinal and incomplete data at the Joint Statistical Meetings of 2002 and 2004.
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Linear Mixed Models for Longitudinal Data

Author: Geert Verbeke,Geert Molenberghs

Publisher: Springer Science & Business Media

ISBN: 9780387950273

Category: Mathematics

Page: 568

View: 560

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This book provides a comprehensive treatment of linear mixed models for continuous longitudinal data. Next to model formulation, this edition puts major emphasis on exploratory data analysis for all aspects of the model, such as the marginal model, subject-specific profiles, and residual covariance structure. Further, model diagnostics and missing data receive extensive treatment. Sensitivity analysis for incomplete data is given a prominent place. Most analyses were done with the MIXED procedure of the SAS software package, but the data analyses are presented in a software-independent fashion.
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Mixed-Effects Regression Models in Linguistics

Author: Dirk Speelman,Kris Heylen,Dirk Geeraerts

Publisher: Springer

ISBN: 3319698303

Category: Social Science

Page: 146

View: 6823

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When data consist of grouped observations or clusters, and there is a risk that measurements within the same group are not independent, group-specific random effects can be added to a regression model in order to account for such within-group associations. Regression models that contain such group-specific random effects are called mixed-effects regression models, or simply mixed models. Mixed models are a versatile tool that can handle both balanced and unbalanced datasets and that can also be applied when several layers of grouping are present in the data; these layers can either be nested or crossed. In linguistics, as in many other fields, the use of mixed models has gained ground rapidly over the last decade. This methodological evolution enables us to build more sophisticated and arguably more realistic models, but, due to its technical complexity, also introduces new challenges. This volume brings together a number of promising new evolutions in the use of mixed models in linguistics, but also addresses a number of common complications, misunderstandings, and pitfalls. Topics that are covered include the use of huge datasets, dealing with non-linear relations, issues of cross-validation, and issues of model selection and complex random structures. The volume features examples from various subfields in linguistics. The book also provides R code for a wide range of analyses.
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Dynamic Mixed Models for Familial Longitudinal Data

Author: Brajendra C. Sutradhar

Publisher: Springer Science & Business Media

ISBN: 9781441983428

Category: Mathematics

Page: 494

View: 2494

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This book provides a theoretical foundation for the analysis of discrete data such as count and binary data in the longitudinal setup. Unlike the existing books, this book uses a class of auto-correlation structures to model the longitudinal correlations for the repeated discrete data that accommodates all possible Gaussian type auto-correlation models as special cases including the equi-correlation models. This new dynamic modelling approach is utilized to develop theoretically sound inference techniques such as the generalized quasi-likelihood (GQL) technique for consistent and efficient estimation of the underlying regression effects involved in the model, whereas the existing ‘working’ correlations based GEE (generalized estimating equations) approach has serious theoretical limitations both for consistent and efficient estimation, and the existing random effects based correlations approach is not suitable to model the longitudinal correlations. The book has exploited the random effects carefully only to model the correlations of the familial data. Subsequently, this book has modelled the correlations of the longitudinal data collected from the members of a large number of independent families by using the class of auto-correlation structures conditional on the random effects. The book also provides models and inferences for discrete longitudinal data in the adaptive clinical trial set up. The book is mathematically rigorous and provides details for the development of estimation approaches under selected familial and longitudinal models. Further, while the book provides special cares for mathematics behind the correlation models, it also presents the illustrations of the statistical analysis of various real life data. This book will be of interest to the researchers including graduate students in biostatistics and econometrics, among other applied statistics research areas. Brajendra Sutradhar is a University Research Professor at Memorial University in St. John’s, Canada. He is an elected member of the International Statistical Institute and a fellow of the American Statistical Association. He has published about 110 papers in statistics journals in the area of multivariate analysis, time series analysis including forecasting, sampling, survival analysis for correlated failure times, robust inferences in generalized linear mixed models with outliers, and generalized linear longitudinal mixed models with bio-statistical and econometric applications. He has served as an associate editor for six years for Canadian Journal of Statistics and for four years for the Journal of Environmental and Ecological Statistics. He has served for 3 years as a member of the advisory committee on statistical methods in Statistics Canada. Professor Sutradhar was awarded 2007 distinguished service award of Statistics Society of Canada for his many years of services to the society including his special services for society’s annual meetings.
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Multivariate Statistical Modelling Based on Generalized Linear Models

Author: Ludwig Fahrmeir,Gerhard Tutz

Publisher: Springer Science & Business Media

ISBN: 1489900101

Category: Mathematics

Page: 426

View: 9360

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Concerned with the use of generalised linear models for univariate and multivariate regression analysis, this is a detailed introductory survey of the subject, based on the analysis of real data drawn from a variety of subjects such as 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.
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Bayesian Hierarchical Models

With Applications Using R, Second Edition

Author: Peter D. Congdon

Publisher: CRC Press

ISBN: 0429532903

Category: Mathematics

Page: 550

View: 5095

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An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website
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Unified Methods for Censored Longitudinal Data and Causality

Author: Mark J. van der Laan,M. J. Laan,James M Robins

Publisher: Springer Science & Business Media

ISBN: 9780387955568

Category: Mathematics

Page: 397

View: 1120

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These techniques include estimation of regression parameters in the familiar (multivariate) generalized linear regression and multiplicative intensity models. They go beyond standard statistical approaches by incorporating all the observed data to allow for informative censoring, to obtain maximal efficiency, and by developing estimators of causal effects.
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Advances and Challenges in Parametric and Semi-parametric Analysis for Correlated Data

Proceedings of the 2015 International Symposium in Statistics

Author: Brajendra C. Sutradhar

Publisher: Springer

ISBN: 331931260X

Category: Mathematics

Page: 256

View: 4622

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This proceedings volume contains eight selected papers that were presented in the International Symposium in Statistics (ISS) 2015 On Advances in Parametric and Semi-parametric Analysis of Multivariate, Time Series, Spatial-temporal, and Familial-longitudinal Data, held in St. John’s, Canada from July 6 to 8, 2015. The main objective of the ISS-2015 was the discussion on advances and challenges in parametric and semi-parametric analysis for correlated data in both continuous and discrete setups. Thus, as a reflection of the theme of the symposium, the eight papers of this proceedings volume are presented in four parts. Part I is comprised of papers examining Elliptical t Distribution Theory. In Part II, the papers cover spatial and temporal data analysis. Part III is focused on longitudinal multinomial models in parametric and semi-parametric setups. Finally Part IV concludes with a paper on the inferences for longitudinal data subject to a challenge of important covariates selection from a set of large number of covariates available for the individuals in the study.
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Quasi-Least Squares Regression

Author: Justine Shults,Joseph M. Hilbe

Publisher: CRC Press

ISBN: 1420099930

Category: Mathematics

Page: 221

View: 621

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Drawing on the authors’ substantial expertise in modeling longitudinal and clustered data, Quasi-Least Squares Regression provides a thorough treatment of quasi-least squares (QLS) regression—a computational approach for the estimation of correlation parameters within the framework of generalized estimating equations (GEEs). The authors present a detailed evaluation of QLS methodology, demonstrating the advantages of QLS in comparison with alternative methods. They describe how QLS can be used to extend the application of the traditional GEE approach to the analysis of unequally spaced longitudinal data, familial data, and data with multiple sources of correlation. In some settings, QLS also allows for improved analysis with an unstructured correlation matrix. Special focus is given to goodness-of-fit analysis as well as new strategies for selecting the appropriate working correlation structure for QLS and GEE. A chapter on longitudinal binary data tackles recent issues raised in the statistical literature regarding the appropriateness of semi-parametric methods, such as GEE and QLS, for the analysis of binary data; this chapter includes a comparison with the first-order Markov maximum-likelihood (MARK1ML) approach for binary data. Examples throughout the book demonstrate each topic of discussion. In particular, a fully worked out example leads readers from model building and interpretation to the planning stages for a future study (including sample size calculations). The code provided enables readers to replicate many of the examples in Stata, often with corresponding R, SAS, or MATLAB® code offered in the text or on the book’s website.
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