Generalized Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models

This book presents some of the most recent developments and classical methods in Multivariate Analysis of Variance (MANOVA), Repeated Measures, and Growth Curves. It attempts to deal with the problem of poor approximations by offering more exact methods for data analysis. Through examples such as following the change in consumer demand of a product over time and analyzing data from clinical trials, Exact Methods in MANOVA, Mixed Models, and Repeated Measures shows readers how these methods are more useful and more accurate in predicting results.

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.