Antedependence Models for Longitudinal Data (Chapman & Hall CRC Monographs on Statistics & Applied Probability)

✍ Scribed by Dale L. Zimmerman, Vicente A. Núñez-Antón

• Publisher: Chapman and Hall/CRC
• Year: 2009
• Tongue: English
• Leaves: 279
• Edition: 1
• Category: Library

✦ Synopsis

The First Book Dedicated to This Class of Longitudinal Models Although antedependence models are particularly useful for modeling longitudinal data that exhibit serial correlation, few books adequately cover these models. By gathering results scattered throughout the literature, Antedependence Models for Longitudinal Data offers a convenient, systematic way to learn about antedependence models. Illustrated with numerous examples, the book also covers some important statistical inference procedures associated with these models. After describing unstructured and structured antedependence models and their properties, the authors discuss informal model identification via simple summary statistics and graphical methods. They then present formal likelihood-based procedures for normal antedependence models, including maximum likelihood and residual maximum likelihood estimation of parameters as well as likelihood ratio tests and penalized likelihood model selection criteria for the model’s covariance structure and mean structure. The authors also compare the performance of antedependence models to other models commonly used for longitudinal data. With this book, readers no longer have to search across widely scattered journal articles on the subject. The book provides a thorough treatment of the properties and statistical inference procedures of various antedependence models.

✦ Table of Contents

Cover Page
......Page 1
Title Page
......Page 2
Antedependence Models for Longitudinal Data......Page 6
Contents......Page 9
Preface......Page 14
1.1 Longitudinal data......Page 17
1.2 Classical methods of analysis......Page 21
1.3 Parametric modeling......Page 23
1.4 Antedependence models, in brief......Page 26
1.5 A motivating example......Page 27
1.6 Overview of the book......Page 30
1.7.1 Cattle growth data......Page 31
1.7.2 100-km race data......Page 32
1.7.3 Speech recognition data......Page 34
1.7.4 Fruit fly mortality data......Page 37
2.1 Antedependent random variables......Page 43
2.2 Antecorrelation and partial antecorrelation......Page 46
2.3.1 Precision matrix characterization......Page 50
2.3.2 Autoregressive characterization......Page 55
2.3.3 Marginal characterization......Page 59
2.4 Some results on determinants and traces......Page 62
2.5 The first-order case......Page 63
2.6 Variable-order antedependence......Page 68
2.7 Other conditional independence models......Page 72
CHAPTER 3: Structured Antedependence Models......Page 75
3.1 Stationary autoregressive models......Page 76
3.2 Heterogeneous autoregressive models......Page 79
3.3 Integrated autoregressive models......Page 80
3.4 Integrated antedependence models......Page 81
3.5 Unconstrained linear models......Page 83
3.6 Power law models......Page 85
3.7 Variable-order SAD models......Page 90
3.8 Nonlinear stationary autoregressive models......Page 92
3.9.1 Vanishing correlation (banded) models......Page 93
3.9.2 Random coefficient models......Page 95
CHAPTER 4: Informal Model Identification......Page 98
4.1 Identifying mean structure......Page 99
4.2 Identifying covariance structure: Summary statistics......Page 101
4.3 Identifying covariance structure: Graphical methods......Page 107
4.3.1 Marginal structure......Page 109
4.3.2 Intervenor-adjusted structure......Page 112
4.3.4 Autoregressive structure......Page 121
4.4 Concluding remarks......Page 123
5.1.1 Model......Page 126
5.1.2 Estimability......Page 129
5.2 Estimation in the general case......Page 131
5.3.1 Saturated mean......Page 135
5.3.2 Multivariate regression mean......Page 147
5.3.3 Arbitrary linear mean......Page 153
5.4 Unstructured antedependence: Unbalanced data......Page 157
5.4.1 Monotone missing data, saturated mean......Page 159
5.4.2 Monotone missing data, multivariate regression mean......Page 162
5.4.3 Monotone missing data, arbitrary linear mean......Page 165
5.4.4 Other missing data patterns......Page 166
5.5 Structured antedependence models......Page 169
5.5.1 Marginal formulation......Page 171
5.5.2 Intervenor-adjusted formulation......Page 174
5.5.4 Autoregressive formulation......Page 175
5.6 Concluding remarks......Page 179
CHAPTER 6: Testing Hypotheses on the Covariance Structure......Page 182
6.1.1 Partial correlations......Page 183
6.1.2 Intervenor-adjusted partial correlations......Page 185
6.1.3 Autoregressive coefficients......Page 186
6.2 Testing for the order of antedependence......Page 187
Simulation results......Page 193
6.3 Testing for structured antedependence......Page 197
6.4 Testing for homogeneity across groups......Page 199
6.5 Penalized likelihood criteria......Page 203
6.6 Concluding remarks......Page 208
CHAPTER 7: Testing Hypotheses on the Mean Structure......Page 209
7.1 One-sample case......Page 210
7.2 Two-sample case......Page 219
7.3 Multivariate regression mean......Page 222
7.4 Other situations......Page 226
7.5 Penalized likelihood criteria......Page 229
7.6 Concluding remarks......Page 231
8.1 A coherent parametric modeling approach......Page 233
8.2 Case study #1: Cattle growth data......Page 235
8.3 Case study #2: 100-km race data......Page 238
8.4 Case study #3: Speech recognition data......Page 243
8.5 Case study #4: Fruit fly mortality data......Page 245
8.6 Other studies......Page 247
8.7 Discussion......Page 248
9.1.1 Nonparametric methods......Page 251
9.1.3 Bayesian methods......Page 252
9.2 Nonlinear mean structure......Page 254
9.3 Discrimination under antedependence......Page 255
9.4 Multivariate antedependence models......Page 256
9.5 Spatial antedependence models......Page 257
9.6 Antedependence models for discrete data......Page 259
Appendix 1: Some Matrix Results
......Page 263
Proof of Theorem 2.5......Page 267
Proof of Theorem 2.6......Page 269
References
......Page 272

✦ Subjects

Математика;Теория вероятностей и математическая статистика;Математическая статистика;