This book discusses the theory of a growth curve model (GCM) with particular emphasis on statistical diagnostics, which is mainly based on recent work on diagnostics made by the authors and their collaborators. This book is intended for researchers who are working in the area of theoretical studies related to the GCM as well as multivariate statistical diagnostics, and for applied statisticians working in application of the GCM to practical areas.

Preface

Acronyms

Notation

Chapter 1

Introduction

1.1 General Remarks

 1.1.1 Statistical Diagnostics

 1.1.2 Outliers and Influential Observation

1.2 Statistical Diagnostics in Multivariate Analysis

 1.2.1 Multiple Outliers in Multivariate Data

 1.2.2 Statistical diagnostics in multivariate models

1.3 Growth Curve Model (GCM)

 1.3.1 A Brief Review

 1.3.2 Covariance Structure Selection

1.4 Summary

 1.4.1 Statistical Inference

 1.4.2 Diagnostics Within a Iikelihood Framework

 1.4.3 Diagnostics Within a Bayesian Framework

1.5 Preliminary Results

 1.5.1 Matrix Operation and Matrix Derivative

 1.5.2 Matrix-variate Normal and t Distributions

1.6 Further Readings

Chapter 2

Generalized Least Square Estimation

2.1 General Remarks

 2.1.1 Model Definition

 2.1.2 Practical Examples

2.2 Generalized Least Square Estimation

2.2.1 Generalized Least Square Estimate (GLSE)

2.2.2 Best Linear Unbiased Estimate (BLUE)

2.2.3 Illustrative Examples

2.3 Admissible Estimate of Regression Coefficient

2.3.1 Admissibility

2.3.2 Necessary and Sufficient Condition

2.4 Bibliographical Notes

Chapter 3

Maximum Likelihood Estimation

3.1 Maximum Likelihood Estimation

3.1.1 Maximum Likelihood Estimate (MLE)

3.1.2 Expectation and Variance-covariance

3.1.3 Illustrative Examples

3.2 Rao's Simple Covariance Structure (SCS)

 3.2.1 Condition That the MLE Is Identical to the GLSE

 3.2.2 Estimates of Dispersion Components

 3.2.3 Illustrative Examples

3.3 Restricted Maximum Likelihood Estimation

 3.3.1 Restricted Maximum Likelihood (REMLs) estimate

 3.3.2 REMLs Estimates in the GCM

 3.3.3 Illustrative Examples

3.4 Bibliographical Notes

Chapter 4

Discordant Outlier and Influential Observation

4.1 General Remarks

 4.1.1 Discordant Outlier-Generating Model

 4.1.2 Influential Observation

4.2 Discordant Outlier Detection in the GCM with SCS

 4.2.1 Multiple Individual Deletion Model (MIDM)

 4.2.2 Mean Shift Regression Model (MSRM)

 4.2.3 Multiple Discordant Outlier Detection

 4.2.4 Illustrative Examples

4.3 Influential Observation in the GCM with SCS

 4.3.1 Generalized Cook-type Distance

 4.3.2 Confidence Ellipsoid's Volume

 4.3.3 Influence Assessment on Linear Combination

 4.3.4 Illustrative Examples

4.4 Discordant Outlier Detection in the GCM with UC

 4.4.1 "Multiple Individual Deletion Model (MIDM)

 4.4.2 Mean Shift Regression Model (MSRM)

 4.4.3 Multiple Discordant Outlier Detection

 4.4.4 Illustrative Examples

4.5 Influential Observation in the GCM with UC

4.5.1 Generalized Cook-type Distance

4.5.2 Confidence Ellipsoid's Volume

4.5.3 Influence Assessment on Linear Combination

4.5.4 Illustrative Examples

4.6 Bibliographical Notes

Chapter 5

Likelihood-Based Local Influence

5.1 General Remarks

 5.1.1 Background

 5.1.2 Local Influence Analysis

5.2 Local Influence Assessment in the GCM with SCS

 5.2.1 Observed Information Matrix

 5.2.2 Hessian Matrix

 5.2.3 Covariance-Weighted Perturbation

 5.2.4 Illustrative Examples

5.3 Local Influence Assessment in the GCM with UC

 5.3.1 Observed Information Matrix

 5.3.2 Hessian Matrix

 5.3.3 Covariance-Weighted Perturbation

 5.3.4 Illustrative Examples

5.4 Bibliographical Notes

Chapter 6

Bayesian Influence Assessment

6.1 General Remarks

 6.1.1 Bayesian Influence Analysis

 6.1.2 Kullback-Leibler Divergence

6.2 Bayesian Influence Analysis in the GCM with SCS

 6.2.1 Posterior Distribution

 6.2.2 Bayesian Influence Measurement

 6.2.3 Illustrative Examples

6.3 Bayesian Influence Analysis in the GCM with UC

 6.3.1 Posterior Distribution

 6.3.2 Bayesian Influence Measurement

 6.3.3 Illustrative Examples

6.4 Bibliographical Notes

Chapter 7

Bayesian Local Influence

7.1 General Remarks

 7.1.1 Bayesian Local Influence

 7.1.2 Bayesian Hessian Matrix

7.2 Bayesian Local Influence in the GCM with SCS

 7.2.1 Bayesian Hessian Matrix

 7.2.2 Covariance-Weighted Perturbation

 7.2.3 Illustrative Examples

7.3 Bayesian Local Influence in the GCM with UC

 7.3.1 Bayesian Hessian Matrix

 7.3.2 Covariance-Weighted Perturbation

 7.3.3 Illustrative Examples

7.4 Bibliographical Notes

Appendix

Data sets used in this book

References

Author Index

Subject Index