### 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.

#### Review

Hodges describes mixed liner models using normal distributions andsome richly parametrized models that can be expressed this way and can be analyzed using conventional and Bayesian methods for mixedlinear models. Then he explains why fitting a particular model to a particular dataset produces the result it does, how the result wouldchange if either the model or the dataset were altered, and how to choose which model to use for a particular dataset. Finally hepresents a set of unsolved, poorly solved, and recently solved problems, most from his own work.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Hodges describes mixed liner models using normal distributions andsome richly parametrized models that can be expressed this way and can be analyzed using conventional and Bayesian methods for mixedlinear models. Then he explains why fitting a particular model to a particular dataset produces the result it does, how the result wouldchange if either the model or the dataset were altered, and how to choose which model to use for a particular dataset. Finally hepresents a set of unsolved, poorly solved, and recently solved problems, most from his own work.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Hodges describes mixed liner models using normal distributions andsome richly parametrized models that can be expressed this way and can be analyzed using conventional and Bayesian methods for mixedlinear models. Then he explains why fitting a particular model to a particular dataset produces the result it does, how the result wouldchange if either the model or the dataset were altered, and how to choose which model to use for a particular dataset. Finally hepresents a set of unsolved, poorly solved, and recently solved problems, most from his own work.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Hodges describes mixed liner models using normal distributions andsome richly parametrized models that can be expressed this way and can be analyzed using conventional and Bayesian methods for mixedlinear models. Then he explains why fitting a particular model to a particular dataset produces the result it does, how the result wouldchange if either the model or the dataset were altered, and how to choose which model to use for a particular dataset. Finally hepresents a set of unsolved, poorly solved, and recently solved problems, most from his own work.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Hodges describes mixed liner models using normal distributions andsome richly parametrized models that can be expressed this way and can be analyzed using conventional and Bayesian methods for mixedlinear models. Then he explains why fitting a particular model to a particular dataset produces the result it does, how the result wouldchange if either the model or the dataset were altered, and how to choose which model to use for a particular dataset. Finally hepresents a set of unsolved, poorly solved, and recently solved problems, most from his own work.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Hodges describes mixed liner models using normal distributions andsome richly parametrized models that can be expressed this way and can be analyzed using conventional and Bayesian methods for mixedlinear models. Then he explains why fitting a particular model to a particular dataset produces the result it does, how the result wouldchange if either the model or the dataset were altered, and how to choose which model to use for a particular dataset. Finally hepresents a set of unsolved, poorly solved, and recently solved problems, most from his own work.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Review

Hodges describes mixed liner models using normal distributions andsome richly parametrized models that can be expressed this way and can be analyzed using conventional and Bayesian methods for mixedlinear models. Then he explains why fitting a particular model to a particular dataset produces the result it does, how the result wouldchange if either the model or the dataset were altered, and how to choose which model to use for a particular dataset. Finally hepresents a set of unsolved, poorly solved, and recently solved problems, most from his own work.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

#### Synopsis

"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"--