Generalized Inference in Repeated Measures by AOL Time Warner, Weerahandi, Samaradasa;

Short description:

A complete guide to powerful and practical statistical modeling using MANOVA

Numerous statistical applications are time dependent. Virtually all biomedical, pharmaceutical, and industrial experiments demand repeated measurements over time. The same holds true for market research and analysis.

Long description:

A complete guide to powerful and practical statistical modeling using MANOVA

Numerous statistical applications are time dependent. Virtually all biomedical, pharmaceutical, and industrial experiments demand repeated measurements over time. The same holds true for market research and analysis. Yet conventional methods, such as the Repeated Measures Analysis of Variance (Rm ANOVA), do not always yield exact solutions, obliging practitioners to settle for asymptotic results and approximate solutions. Generalized inference in Multivariate Analysis of Variance (MANOVA), mixed models, and growth curves offer exact methods of data analysis under milder conditions without deviating from the conventional philosophy of statistical inference.

Generalized Inference in Repeated Measures is a concise, self-contained guide to the use of these innovative solutions, presenting them as extensions of-rather than alternatives to-classical methods of statistical evaluation. Requiring minimal prior knowledge of statistical concepts in the evaluation of linear models, the book provides exact parametric methods for each application considered, with solutions presented in terms of generalized p-values. Coverage includes:

• New concepts in statistical inference, with special focus on generalized p-values and generalized confidence intervals
  
  
• One-way and two-way ANOVA, in cases of equal and unequal variances
  
  
• Basic and higher-way mixed models, including testing and estimation of fixed effects and variance components
  
  
• Multivariate populations, including basic inference, comparison, and analysis of variance
  
  
• Basic, widely used repeated measures models including crossover designs and growth curves
  

With a comprehensive set of formulas, illustrative examples, and exercises in each chapter, Generalized Inference in Repeated Measures is ideal as both a comprehensive reference for research professionals and a text for students.

A complete guide to powerful and practical statistical modeling using MANOVA

Numerous statistical applications are time dependent. Virtually all biomedical, pharmaceutical, and industrial experiments demand repeated measurements over time. The same holds true for market research and analysis. Yet conventional methods, such as the Repeated Measures Analysis of Variance (Rm ANOVA), do not always yield exact solutions, obliging practitioners to settle for asymptotic results and approximate solutions. Generalized inference in Multivariate Analysis of Variance (MANOVA), mixed models, and growth curves offer exact methods of data analysis under milder conditions without deviating from the conventional philosophy of statistical inference.

Generalized Inference in Repeated Measures is a concise, self-contained guide to the use of these innovative solutions, presenting them as extensions of-rather than alternatives to-classical methods of statistical evaluation. Requiring minimal prior knowledge of statistical concepts in the evaluation of linear models, the book provides exact parametric methods for each application considered, with solutions presented in terms of generalized p-values. Coverage includes:

• New concepts in statistical inference, with special focus on generalized p-values and generalized confidence intervals
  
  
• One-way and two-way ANOVA, in cases of equal and unequal variances
  
  
• Basic and higher-way mixed models, including testing and estimation of fixed effects and variance components
  
  
• Multivariate populations, including basic inference, comparison, and analysis of variance
  
  
• Basic, widely used repeated measures models including crossover designs and growth curves
  

With a comprehensive set of formulas, illustrative examples, and exercises in each chapter, Generalized Inference in Repeated Measures is ideal as both a comprehensive reference for research professionals and a text for students.

"I enjoyed reading this book and recommend [it] highly to the statistics community." (Journal of Statistical Computation and Simulation, March 2006)

"Researchers, teachers, students, and practitioners will definitely find this book very valuable." (Technometrics, May 2005)

"?this is an important work that summarizes and illustrates the work of the author and his colleagues." (Journal of Quality Technology, April 2005)

"I enjoyed reading this book and recommend [it] highly to the statistics community." (Journal of Statistical Computation and Simulation, March 2006)

"Researchers, teachers, students, and practitioners will definitely find this book very valuable." (Technometrics, May 2005)

"?this is an important work that summarizes and illustrates the work of the author and his colleagues." (Journal of Quality Technology, April 2005)

Table of Contents:

Preface.

1. Exact Generalized Inference.

1.1 Introduction.

1.2 Test Statistics and p-Values.

1.3 Test Variables and Generalized p-Values.

1.4 Substitution Method.

1.5 Fixed Level Testing.

1.6 Generalized Confidence Intervals.

1.7 Substitution Method in Interval Estimation.

1.8 Generalized p-Values Based Intervals.

2. Methods in Analysis of Variance.

2.1 Introduction.

2.2 Comparing Two Population Means.

2.3 Case of Unequal Variances.

2.4 One-Way ANOVA.

2.5 Multiple Comparisons: Case of Equal Variances.

2.6 Multiple Comparisons: Case of Unequal Variances.

2.7 Two-Way ANOVA Under Equal Variances.

2.8 Two-Way ANOVA Under Heteroscedasticity.

2.9 Two-Factor Nested Design.

3. Introduction to Mixed Models.

3.1 Introduction.

3.2 Random Effects One-Way ANOVA.

3.3 Inference About Variance Components.

3.4 Fixed Level Testing.

3.5 Inference About the Mean.

3.6 Two-Way Mixed Model without Replicates.

4. Higher-Way Mixed Models.

4.1 Introduction.

4.2 Canonical Form of the Problem.

4.3 Testing Fixed Effects.

4.4 Estimating Variance Components.

4.5 Testing Variance Components.

4.6 Confidence Intrvals.

4.7 Functions of Variance Components.

5. Multivariate Populations.

5.1 Introduction.

5.2 Multivariate Normal Populations.

5.3 Inferences About the Mean Vector.

5.4 Inferences About Linear Functions of ?.

5.5 Multivariate Regression.

6. Multivariate Analysis of Variance.

6.1 Introduction.

6.2 Comparing Two Multivariate Populations.

6.3 Multivariate Behrens?Fisher Problem.

6.4 MANOVA with Equal Covariances.

6.5 MANOVA with Unequal Covariances.

7. Mixed Models in Repeated Measures.

7.1 Introduction.

7.2 Mixed Models for One Group.

7.3 Analysis of Data from Two Factors.

7.4 ANOVA Under Equal Error Variances.

7.5 Other Two-Factors Models.

7.6 Regression and RM ANCOVA.

8. Repeated Measures Under Heteroscedasticity.

8.1 Introduction.

8.2 Two-Factor Model with Unequal Group Variances.

8.3 Point Estimation.

8.4 Testing Fixed Effects.

8.5 Multiple Comparisons.

8.6 Inference on Variance Components.

8.7 RM ANCOVA Under Heteroscedasticity.

9. Crossover Designs.

9.1 Introduction.

9.2 Two-Sequence Design.

9.3 Comparing Teatments.

9.4 Four-Sequence Design.

9.5 Distributional Results.

9.6 Testing and Interval Estimation.

10. Growth Curves.

10.1 Introduction.

10.2 Growth Curve Models.

10.3 Infewrence with Unstructured Covariances.

10.4 Inferences on General Linear Contrasts.

10.5 Simultaneous Confidence Intervals.

10.6 Mixed Models in Growth Curves.

10.7 Exact Infernece Under Structured Covariances.

10.8 Comparing Growth Curves.

10.9 Case of Unequal Group Variances.

Appendix A: Univariate Technical Arguments.

Appendix B: Multivariate Technical Arguments.

References.