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Other titles in the Chapman & Hall/CRC Texts in Statistical Science series:
Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects (Chapman & Hall/CRC Texts in Statistical Science)by James S. Hodges
Synopses & Reviews
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.
"This book covers a wide range of statistical models, including hierarchical, hierarchical generalized linear, linear mixed, dynamic linear, smoothing, spatial, and longitudinal. It presents a framework for expressing these richly parameterized models together as well as tools for exploring and interpreting the results of fitting the models to data. It extends the standard theory of linear models and illustrates the advantages and disadvantages of various theories. The book also examines surprising or undesirable results arising in the use of the models to analyze real data sets from collaborative research"--
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