Advanced Linear Modeling

1. Front Matter

   Pages i-xxiii

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2. Nonparametric Regression

   • Ronald Christensen

   Pages 1-58

3. Penalized Estimation

   • Ronald Christensen

   Pages 59-85

4. Reproducing Kernel Hilbert Spaces

   • Ronald Christensen

   Pages 87-123

5. Covariance Parameter Estimation

   • Ronald Christensen

   Pages 125-159

6. Mixed Models and Variance Components

   • Ronald Christensen

   Pages 161-194

7. Frequency Analysis of Time Series

   • Ronald Christensen

   Pages 195-246

8. Time Domain Analysis

   • Ronald Christensen

   Pages 247-319

9. Linear Models for Spatial Data: Kriging

   • Ronald Christensen

   Pages 321-355

10. Multivariate Linear Models: General

    • Ronald Christensen

    Pages 357-388

11. Multivariate Linear Models: Applications

    • Ronald Christensen

    Pages 389-422

12. Generalized Multivariate Linear Models and Longitudinal Data

    • Ronald Christensen

    Pages 423-455

13. Discrimination and Allocation

    • Ronald Christensen

    Pages 457-501

14. Binary Discrimination and Regression

    • Ronald Christensen

    Pages 503-531

15. Principal Components, Classical Multidimensional Scaling, and Factor Analysis

    • Ronald Christensen

    Pages 533-574

16. Back Matter

    Pages 575-608

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Now in its third edition, this companion volume to Ronald Christensen’s Plane Answers to Complex Questions uses three fundamental concepts from standard linear model theory—best linear prediction, projections, and Mahalanobis distance— to extend standard linear modeling into the realms of Statistical Learning and Dependent Data.  
This new edition features a wealth of new and revised content.  In Statistical Learning it delves into nonparametric regression, penalized estimation (regularization), reproducing kernel Hilbert spaces, the kernel trick, and support vector machines.  For Dependent Data it uses linear model theory to examine general linear models, linear mixed models, time series, spatial data, (generalized) multivariate linear models, discrimination, and dimension reduction.  While numerous references to Plane Answers are made throughout the volume, Advanced Linear Modeling can be used on its own given a solid background in linear models.  Accompanying R code for the analyses is available online.

• ANOVA
• Excel
• Factor analysis
• STATISTICA
• Time series
• data analysis
• mathematical statistics
• heteroscedasticity
• mixed models
• multivariate models

“This book is in my opinion a very valuable resource for researchers since it presents the theoretical foundations of linear models in a unified way while discussing a number of applications. … This book is definitely worth considering for anyone looking for an extensive and thorough treatment of advanced topics in linear modeling.” (Fabio Mainardi, MAA Reviews, May 23, 2021)

• Department of Mathematics and Statistics, University of New Mexico, Albuquerque, USA

  Ronald Christensen

Ronald Christensen is a Professor of Statistics at the University of New Mexico, Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics, former Chair of the ASA Section on Bayesian Statistical Science and former Editor of The American Statistician. His book publications include Plane Answers to Complex Questions (Springer 2011), Log-Linear Models and Logistic Regression (Springer 1997), Analysis of Variance, Design, and Regression (1996, 2016), and  Bayesian Ideas and Data Analysis (2010, with Johnson, Branscum and Hanson).

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