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Mixed Models: Theory and Applications

Mixed Models: Theory and Applications

Eugene Demidenko

ISBN: 978-0-471-72843-6 January 2005 704 Pages


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.


1. Introduction: Why Mixed Models?

2. MLE for LME Model.

3. Statistical Properties of the LME Model.

4. Growth Curve Model and Generalizations.

5. Meta-analysis Model.

6. Nonlinear Marginal Model.

7. Generalized Linear Mixed Models.

8. Nonlinear Mixed Effects Model.

9. Diagnostics and Influence Analysis.

10. Tumor Regrowth Curves.

11. Statistical Analysis of Shape.

12. Statistical Image Analysis.

13. Appendix: Useful Facts and Formulas.



"…this book will serve to greatly complement the growing number of texts dealing with mixed models and I highly recommend including it in one's personal library." (Journal of the American Statistical Association, December 2006)

"…an excellent book and it thoroughly covers new developments in mixed models in addition to the classical mixed model approaches." (Biometrics, March 2006)

"Statisticians would like very much to read this book." (Journal of Statistical Computation and Simulation, January 2006)

"…I recommend this book and congratulate the author for his dedication…" (Annals of Biomedical Engineering, October 2005)

"…has a wealth of information. I recommend this book to anyone working in mixed models." (Journal of Biopharmaceutical Statistics, July/August 2005)

"…a very welcome addition and…a good companion to other mixed models texts…" (Statistical Methods in Medical Research, Vol. 14, 2005)

"…intended for professionals and students in a broad range of fields such as cancer research, computer science, engineering and industry." (Zentralblatt Math, Vol.1055, No.06, 2005)

"The book is useful for statisticians who are interested in mathematical statistics and those who are interested in applications." (Mathematical Reviews, 2005e)

"Written with the statistician/mathematician in mind, the computer engineer will find the content also useful." (E-STREAMS, February 2005)