Richly Parameterized Linear Models - James S. Hodges

Richly Parameterized Linear Models
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Autor: James S. Hodges

 Wydawnictwo: Chapman Hall
ISBN: 9781439866832
EAN:
Format: ...
Oprawa: twarda
Stron: 469
Data wydania: 2013-11-01
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A First Step toward a Unified Theory of Richly Parameterized Linear Models Using mixed linear models to analyze data often leads to results that are mysterious, inconvenient, or wrong. Further compounding the problem, statisticians lack a cohesive resource to acquire a systematic, theory-based understanding of models with random effects. Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects takes a first step in developing a full theory of richly parameterized models, which would allow statisticians to better understand their analysis results. The author examines what is known and unknown about mixed linear models and identifies research opportunities. The first two parts of the book cover an existing syntax for unifying models with random effects. The text explains how richly parameterized models can be expressed as mixed linear models and analyzed using conventional and Bayesian methods. In the last two parts, the author discusses oddities that can arise when analyzing data using these models. He presents ways to detect problems and, when possible, shows how to mitigate or avoid them. The book adapts ideas from linear model theory and then goes beyond that theory by examining the information in the data about the mixed linear model's covariance matrices. Each chapter ends with two sets of exercises. Conventional problems encourage readers to practice with the algebraic methods and open questions motivate readers to research further. Supporting materials, including datasets for most of the examples analyzed, are available on the author's website. "Hodges' book is a really recommendable reference for mixed models users. Use of random effects models has exponentially grown during the last few decades mainly due to the availability of software making the fit of these models possible. Such software has made mixed models available to a wide community of users, thus complex analyses with complex covariance structures have filled both applied and theoretical journals. Nevertheless, as masterfully described within this book, the hypotheses underneath these models, and the corresponding covariance structures, are not harmless at all but, on the contrary, they may have a large impact on their fit. Hodges' monograph explores and highlights the repercussion of many aspects involved in the definition of most mixed models that are usually unknown or, even worse, ignored. Hodges makes us aware of these issues that should be kept very in mind by any mixed models user and illustrates them with lots of real case studies. This is an extremely clarifying tool for those who usually work with GLMMs in general. Mathematical details underlying GLMMs are usually overwhelming ... Hodges makes a journey to the grounds of linear mixed models, where mathematical detail is more accessible, providing a deep insight also of use in GLMMs. The approach described in this book yields some intuition about what can be happening underneath the complex GLMMs that are usually used in practice." -Miguel Martinez Beneito, Foundation for the Promotion of Health and Biomedical Research in the Valencian Region "I recommend this text to any student/researcher who is interested in mixed models. The book is written in an enthralling and engaging style and is overflowing with interesting observations, has a unique spin, and is very thought provoking. Over the past 20 years there has been a tendency toward the fitting of more and more complex models, with the potential negative implications of this endeavor (which I will loosely term 'overfitting') being lost amid the enthusiasm for bigger and allegedly 'more realistic' models. Those with such tendencies would definitely benefit from studying this book in order to gain insight into the unexpected consequences that some mixed model choices can have. All of the model types appearing in title are covered in great detail, including coverage of diagnostics for mixed models.

Książka "Richly Parameterized Linear Models"
James S. Hodges