Mixed Models: Theory and Applications

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John Wiley & Sons, Jan 28, 2005 - Mathematics - 704 pages
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A 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
9 Diagnostics and Influence Analysis
481
10 Tumor Regrowth Curves
531
11 Statistical Analysis of Shape
567
12 Statistical Image Analysis
595
13 Appendix Useful Facts and Formulas
643
References
665
Index
697
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About the author (2005)

EUGENE DEMIDENKO, PhD, is presently Associate Professor of Biostatistics and Epidemiology at the Dartmouth (NH) Medical School. He received his PhD in Mathematics and Statistics from the Central Institute of Economics and Mathematics of the Academy of Sciences of the USSR. His research interests cover a broad range of theoretical and computational statistics as applicable to bioengineering and cancer-related areas. He has served as an invited lecturer to several institutes/academies around the world.

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