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Publisher:

Chapman & Hall/CRC

Publication Date:

2014

Number of Pages:

431

Format:

Hardcover

Series:

Texts in Statistical Science

Price:

89.95

ISBN:

9781439866832

Category:

Monograph

We do not plan to review this book.

*Mixed Linear Models: Syntax, Theory, and Methods *

**An Opinionated Survey of Methods for Mixed Linear Models**

Mixed linear models in the standard formulation

Conventional analysis of the mixed linear model

Bayesian analysis of the mixed linear model

Conventional and Bayesian approaches compared

A few words about computing

**Two More Tools: Alternative Formulation, Measures of Complexity**

Alternative formulation: The "constraint-case" formulation

Measuring the complexity of a mixed linear model fit

*Richly Parameterized Models as Mixed Linear Models*

Penalized Splines as Mixed Linear Models

Penalized splines: Basis, knots, and penalty

More on basis, knots, and penalty

Mixed linear model representation

**Additive Models and Models with Interactions **

Additive models as mixed linear models

Models with interactions

**Spatial Models as Mixed Linear Models**

Geostatistical models

Models for areal data

Two-dimensional penalized splines

**Time-Series Models as** **Mixed Linear Models**

Example: Linear growth model

Dynamic linear models in some generality

Example of a multi-component DLM

**Two Other Syntaxes for Richly Parameterized Models**

Schematic comparison of the syntaxes

Gaussian Markov random fields

Likelihood inference for models with unobservables

*From Linear Models to Richly Parameterized Models: Mean Structure *

Adapting Diagnostics from Linear Models

Preliminaries

Added variable plots

Transforming variables

Case influence

Residuals

**Puzzles from Analyzing Real Datasets**

Four puzzles

Overview of the next three chapters

**A Random Effect Competing with a Fixed Effect **

Slovenia data: Spatial confounding

Kids and crowns: Informative cluster size

**Differential Shrinkage**

The simplified model and an overview of the results

Details of derivations

Conclusion: What might cause differential shrinkage?

**Competition between Random Effects **

Collinearity between random effects in three simpler models

Testing hypotheses on the optical-imaging data and DLM models

Discussion

**Random Effects Old and New **

Old-style random effects

New-style random effects

Practical consequences

Conclusion

*Beyond Linear Models: Variance Structure *

Mysterious, Inconvenient, or Wrong Results from Real Datasets

Periodontal data and the ICAR model

Periodontal data and the ICAR with two classes of neighbor pairs

Two very different smooths of the same data

Misleading zero variance estimates

Multiple maxima in posteriors and restricted likelihoods

Overview of the remaining chapters

**Re-Expressing the Restricted Likelihood: Two-Variance Models**

The re-expression

Examples

A tentative collection of tools

**Exploring the Restricted Likelihood for Two-Variance Models**

Which *v _{j} *tell us about which variance?

Two mysteries explained

**Extending the Re-Expressed Restricted Likelihood**

Restricted likelihoods that can and can’t be re-expressed

Expedients for restricted likelihoods that can’t be re-expressed

**Zero Variance Estimates **

Some observations about zero variance estimates

Some thoughts about tools

**Multiple Maxima in the Restricted Likelihood and Posterior**

Restricted likelihoods with multiple local maxima

Posteriors with multiple modes

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