## Mixed Models: Theory and ApplicationsA rigorous, self-contained examination of mixed model theory and application Mixed modeling is one of the most promising and exciting areas of statistical analysis, enabling the analysis of nontraditional, clustered data that may come in the form of shapes or images. This book provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as applications such as the analysis of tumor regrowth, shape, and image. Paying special attention to algorithms and their implementations, the book discusses: - Modeling of complex clustered or longitudinal data
- Modeling data with multiple sources of variation
- Modeling biological variety and heterogeneity
- Mixed model as a compromise between the frequentist and Bayesian approaches
- Mixed model for the penalized log-likelihood
- Healthy Akaike Information Criterion (HAIC)
- How to cope with parameter multidimensionality
- How to solve ill-posed problems including image reconstruction problems
- Modeling of ensemble shapes and images
- Statistics of image processing
Major results and points of discussion at the end of each chapter along with "Summary Points" sections make this reference not only comprehensive but also highly accessible for professionals and students alike in a broad range of fields such as cancer research, computer science, engineering, and industry. |

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### Contents

1 Introduction Why Mixed Models? | 1 |

2 MLE for LME Model | 45 |

3 Statistical Properties of the LME Model | 117 |

4 Growth Curve Model and Generalizations | 183 |

5 Metaanalysis Model | 247 |

6 Nonlinear Marginal Model | 291 |

7 Generalized Linear Mixed Models | 329 |

8 Nonlinear Mixed Effects Model | 431 |