Richly Parameterized Linear Models (Chapman & Hall/CRC Texts in Statistical Science)

Product Description A First Step toward a Unified Theory of Richly Parameterized Linear ModelsUsing 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. Review "Richly Parameterized Linear Models is a strong addition to the literature on mixed models, offering a much more unified treatment and broader scope than many existing texts. … The book also provides an excellent treatment of diagnostics for mixed models. … The literature on mixed models has expanded in recent decades, often in disparate ways. Richly Parameterized Linear Models provides a step toward unifying this growing area of research and serves as an excellent resource for applied researchers with experience and interest in mixed models."―Journal of the American Statistical Association, Vol. 110, 2015"This is a thought-provoking book that stimulates discussion and further research. … It is a refreshing idea to concentrate on poorly understood ‘mysteries’ in the class of linear mixed models. … If you have ever encountered similar issues in linear mixed models, you will appreciate this book. Furthermore, if you are looking for new scientific challenges, then you will find a large resource of still open questions and useful references. Graduate students will develop a deeper understanding of the linear mixed model and critical thinking in the application of this model class. … We recommend this book, as it will stimulate further research, leading to deeper insight into richly parametrized linear models."―Biometrical Journal, 2015"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 extre