This book takes a first step in developing a full theory of richly parameterized models, which would allow statisticians to better understand their analysis results.
This book takes a first step in developing a full theory of richly parameterized models, which would allow statisticians to better understand their analysis results.
Mixed Linear Models: Syntax, Theory, and Methods: An Opinionated Survey of Methods for Mixed Linear Models. Two More Tools: Alternative Formulation, Measures of Complexity. Richly Parameterized Models as Mixed Linear Models: Penalized Splines as Mixed Linear Models. Additive Models and Models with Interactions. Spatial Models as Mixed Linear Models. Time-Series Models as Mixed Linear Models. Two Other Syntaxes for Richly Parameterized Models. From Linear Models to Richly Parameterized Models: Mean Structure: Adapting Diagnostics from Linear Models. Puzzles from Analyzing Real Datasets. A Random Effect Competing with a Fixed Effect. Differential Shrinkage. Competition between Random Effects. Random Effects Old and New. Beyond Linear Models: Variance Structure: Mysterious, Inconvenient, or Wrong Results from Real Datasets. Re-Expressing the Restricted Likelihood: Two-Variance Models. Exploring the Restricted Likelihood for Two-Variance Models. Extending the Re-Expressed Restricted Likelihood. Zero Variance Estimates. Multiple Maxima in the Restricted Likelihood and Posterior.
Mixed Linear Models: Syntax, Theory, and Methods: An Opinionated Survey of Methods for Mixed Linear Models. Two More Tools: Alternative Formulation, Measures of Complexity. Richly Parameterized Models as Mixed Linear Models: Penalized Splines as Mixed Linear Models. Additive Models and Models with Interactions. Spatial Models as Mixed Linear Models. Time-Series Models as Mixed Linear Models. Two Other Syntaxes for Richly Parameterized Models. From Linear Models to Richly Parameterized Models: Mean Structure: Adapting Diagnostics from Linear Models. Puzzles from Analyzing Real Datasets. A Random Effect Competing with a Fixed Effect. Differential Shrinkage. Competition between Random Effects. Random Effects Old and New. Beyond Linear Models: Variance Structure: Mysterious, Inconvenient, or Wrong Results from Real Datasets. Re-Expressing the Restricted Likelihood: Two-Variance Models. Exploring the Restricted Likelihood for Two-Variance Models. Extending the Re-Expressed Restricted Likelihood. Zero Variance Estimates. Multiple Maxima in the Restricted Likelihood and Posterior.
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