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Richly Parameterized Linear Models - Additive, Time Series, and Spatial Models Using Random Effects (Paperback)
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Richly Parameterized Linear Models - Additive, Time Series, and Spatial Models Using Random Effects (Paperback)
Series: Chapman & Hall/CRC Texts in Statistical Science
Expected to ship within 10 - 15 working days
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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.
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