Linear and Generalized Linear Mixed Models and Their Applications

Author: Jiming Jiang
Publisher: Springer Science & Business Media
ISBN: 9780387479460
Release Date: 2007-05-30
Genre: Mathematics

This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.

Correlated Data Analysis Modeling Analytics and Applications

Author: Peter X. -K. Song
Publisher: Springer Science & Business Media
ISBN: 9780387713939
Release Date: 2007-06-30
Genre: Mathematics

This book covers recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to cover a broader range of data types than the traditional generalized linear models. The reader is provided with a systematic treatment for the topic of estimating functions, and both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to the discussions on marginal models and mixed-effects models, this book covers new topics on joint regression analysis based on Gaussian copulas.

Wahrscheinlichkeitstheorie und Stochastische Prozesse

Author: Michael Mürmann
Publisher: Springer-Verlag
ISBN: 9783642381607
Release Date: 2013-11-22
Genre: Mathematics

Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

Modern Mathematical Tools and Techniques in Capturing Complexity

Author: Leandro Pardo
Publisher: Springer
ISBN: 9783642208539
Release Date: 2011-05-26
Genre: Technology & Engineering

Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately. This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations. Several researchers, colleagues, friends and students of Professor María Luisa Menéndez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work.

Large Sample Techniques for Statistics

Author: Jiming Jiang
Publisher: Springer Science & Business Media
ISBN: 9781441968272
Release Date: 2010-06-30
Genre: Mathematics

In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 “standard” situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson’s? -test—the asymptotic distri- 2 2 bution of Pearson’s? -test is not always? (e.g., Moore 1978).

Statistics for High Dimensional Data

Author: Peter Bühlmann
Publisher: Springer Science & Business Media
ISBN: 9783642201929
Release Date: 2011-06-08
Genre: Mathematics

Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.

Dynamic Mixed Models for Familial Longitudinal Data

Author: Brajendra C. Sutradhar
Publisher: Springer Science & Business Media
ISBN: 1441983422
Release Date: 2011-01-27
Genre: Mathematics

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.

Generalized Linear Models

Author: Dipak K. Dey
Publisher: CRC Press
ISBN: 0824790340
Release Date: 2000-05-25
Genre: Mathematics

This volume describes how to conceptualize, perform, and critique traditional generalized linear models (GLMs) from a Bayesian perspective and how to use modern computational methods to summarize inferences using simulation. Introducing dynamic modeling for GLMs and containing over 1000 references and equations, Generalized Linear Models considers parametric and semiparametric approaches to overdispersed GLMs, presents methods of analyzing correlated binary data using latent variables. It also proposes a semiparametric method to model link functions for binary response data, and identifies areas of important future research and new applications of GLMs.

Statistics Applied to Clinical Studies

Author: Ton J. Cleophas
Publisher: Springer Science & Business Media
ISBN: 9789400728622
Release Date: 2012-02-09
Genre: Medical

Thanks to the omnipresent computer, current statistics can include data files of many thousands of values, and can perform any exploratory analysis in less than seconds. This development, however fascinating, generally does not lead to simple results. We should not forget that clinical studies are, mostly, for confirming prior hypotheses based on sound arguments, and the simplest tests provide the best power and are adequate for such studies. In the past few years the authors of this 5th edition, as teachers and research supervisors in academic and top-clinical facilities, have been able to closely observe the latest developments in the field of clinical data analysis, and they have been able to assess their performance. In this 5th edition the 47 chapters of the previous edition have been maintained and upgraded according to the current state of the art, and 20 novel chapters have been added after strict selection of the most valuable and promising novel methods. The novel methods are explained using practical examples and step-by-step analyses readily accessible for non-mathematicians. All of the novel chapters have been internationally published by the authors in peer-reviewed journal, including the American Journal of Therapeutics, the European Journal of Clinical Investigation, The International journal of Clinical Pharmacology and therapeutics, and other journals, and permission is granted by all of them to use this material in the current book. We should add that the authors are well-qualified in their fields of knowledge. Professor Zwinderman is president-elect of the International Society of Biostatistics, and Professor Cleophas is past-president of the American College of Angiology. From their expertise they should be able to make adequate selections of modern methods for clinical data analysis for the benefit of physicians, students, and investigators. The authors, although from a different discipline, one clinician and one statistician, have been working and publishing together for over 10 years, and their research of statistical methodology can be characterized as a continued effort to demonstrate that statistics is not mathematics but rather a discipline at the interface of biology and mathematics. They firmly believe that any reader can benefit from this clinical approach to statistical data analysis.

Regression

Author: Ludwig Fahrmeir
Publisher: Springer-Verlag
ISBN: 9783642018374
Release Date: 2009-08-27
Genre: Business & Economics

In dem Band beschreiben die Autoren erstmals klassische Regressionsansätze und moderne nicht- und semiparametrische Methoden in einer integrierten und anwendungsorientierten Form. Um Lesern die Analyse eigener Fragestellungen zu ermöglichen, demonstrieren sie die praktische Anwendung der Konzepte und Methoden anhand ausführlicher Fallstudien. Geeignet für Studierende der Statistik sowie für Wissenschaftler und Praktiker, zum Beispiel in den Wirtschafts- und Sozialwissenschaften, der Bioinformatik und -statistik, Ökonometrie und Epidemiologie.

Modern Phylogenetic Comparative Methods and Their Application in Evolutionary Biology

Author: László Zsolt Garamszegi
Publisher: Springer
ISBN: 9783662435502
Release Date: 2014-07-29
Genre: Science

Phylogenetic comparative approaches are powerful analytical tools for making evolutionary inferences from interspecific data and phylogenies. The phylogenetic toolkit available to evolutionary biologists is currently growing at an incredible speed, but most methodological papers are published in the specialized statistical literature and many are incomprehensible for the user community. This textbook provides an overview of several newly developed phylogenetic comparative methods that allow to investigate a broad array of questions on how phenotypic characters evolve along the branches of phylogeny and how such mechanisms shape complex animal communities and interspecific interactions. The individual chapters were written by the leading experts in the field and using a language that is accessible for practicing evolutionary biologists. The authors carefully explain the philosophy behind different methodologies and provide pointers – mostly using a dynamically developing online interface – on how these methods can be implemented in practice. These “conceptual” and “practical” materials are essential for expanding the qualification of both students and scientists, but also offer a valuable resource for educators. Another value of the book are the accompanying online resources (available at: http://www.mpcm-evolution.com), where the authors post and permanently update practical materials to help embed methods into practice.

Linear Models

Author: Calyampudi R. Rao
Publisher: Springer Science & Business Media
ISBN: 9780387227528
Release Date: 2006-04-06
Genre: Mathematics

An up-to-date account of the theory and applications of linear models, for use as a textbook in statistics at graduate level as well as an accompanying text for other courses in which linear models play a part. The authors present a unified theory of inference from linear models with minimal assumptions, not only through least squares theory, but also using alternative methods of estimation and testing based on convex loss functions and general estimating equations. Highlights include: - a special emphasis on sensitivity analysis and model selection; - a chapter devoted to the analysis of categorical data based on logic, loglinear, and logistic regression models; - a chapter devoted to incomplete data sets; - an extensive appendix on matrix theory; - a chapter devoted to the analysis of categorical data based on a unified presentation of generalized linear models including GEE-methods for correlated response; - a chapter devoted to incomplete data sets including regression diagnostics to identify Non-MCAR-processes The material covered is thus invaluable not only to graduates, but also to researchers and consultants in statistics.

Machine Learning in Medicine

Author: Ton J. Cleophas
Publisher: Springer Science & Business Media
ISBN: 9789400758247
Release Date: 2013-02-12
Genre: Medical

Machine learning is a novel discipline concerned with the analysis of large and multiple variables data. It involves computationally intensive methods, like factor analysis, cluster analysis, and discriminant analysis. It is currently mainly the domain of computer scientists, and is already commonly used in social sciences, marketing research, operational research and applied sciences. It is virtually unused in clinical research. This is probably due to the traditional belief of clinicians in clinical trials where multiple variables are equally balanced by the randomization process and are not further taken into account. In contrast, modern computer data files often involve hundreds of variables like genes and other laboratory values, and computationally intensive methods are required. This book was written as a hand-hold presentation accessible to clinicians, and as a must-read publication for those new to the methods.