Longitudinal data analysis for biomedical and behavioral sciences This innovative book sets forth and describes methods for the analysis of longitudinaldata, emphasizing applications to problems in the biomedical and behavioral sciences. Reflecting the growing importance and use of longitudinal data across many areas of research, the text is designed to help users of statistics better analyze and understand this type of data. Much of the material from the book grew out of a course taught by Dr. Hedeker on longitudinal data analysis. The material is, therefore, thoroughly classroom tested and includes a number of features designed to help readers better understand and apply the material. Statistical procedures featured within the text include: * Repeated measures analysis of variance * Multivariate analysis of variance for repeated measures * Random-effects regression models (RRM) * Covariance-pattern models * Generalized-estimating equations (GEE) models * Generalizations of RRM and GEE for categorical outcomes Practical in their approach, the authors emphasize the applications of the methods, using real-world examples for illustration. Some syntax examples are provided, although the authors do not generally focus on software in this book. Several datasets and computer syntax examples are posted on this title's companion Web site. The authors intend to keep the syntax examples current as new versions of the software programs emerge. This text is designed for both undergraduate and graduate courses in longitudinal data analysis. Instructors can take advantage of overheads and additional course materials available online for adopters. Applied statisticians in biomedicine and the social sciences can also use the book as a convenient reference.
Author(s): Donald Hedeker, Robert D. Gibbons
Series: Wiley Series in Probability and Statistics
Edition: 1
Publisher: Wiley-Interscience
Year: 2006
Language: English
Pages: 360
Title ......Page 1
Date-line ......Page 2
Contents ......Page 4
Preface ......Page 10
Acknowledgments ......Page 14
Acronyms ......Page 15
1.1 Advantages of Longitudinal Studies ......Page 17
1.2 Challenges of Longitudinal Data Analysis ......Page 18
1.3 Some General Notation ......Page 19
1.4 Data Layout ......Page 20
1.6 General Approaches ......Page 21
1.7.1 Change Score Analysis ......Page 23
1.7.2 Analysis of Covariance of Post-test Scores ......Page 24
1.7.4 Example ......Page 25
1.8 Summary ......Page 28
2 ANOVA Approaches to Longitudinal Data ......Page 29
2.1.1 Design ......Page 30
2.1.2 Decomposing the Time Effect ......Page 33
2.1.2.1 Trend Analysis—Orthogonal Polynomial Contrasts ......Page 34
2.1.2.4 Contrasting Each Timepoint to the Mean of Subsequent Timepoints—Helmert Contrasts ......Page 35
2.1.2.6 Multiple Comparisons ......Page 36
2.2 Multiple-Sample Repeated Measures ANOVA ......Page 37
2.2.2 Testing for Subject Effect ......Page 39
2.2.3.1 Orthogonal Polynomial Partition of SS ......Page 40
2.2.4 Compound Symmetry and Sphericity ......Page 41
2.2.4.1 Sphericity ......Page 42
2.3 Illustration ......Page 43
2.4 Summary ......Page 45
3 MANOVA Approaches to Longitudinal Data ......Page 47
3.1 Data Layout for ANOVA versus MANOVA ......Page 48
3.2.1 Growth Curve Analysis—Polynomial Representation ......Page 50
3.2.2 Extracting Univariate Repeated Measures ANOVA Results ......Page 53
3.2.4 Tests of Specific Time Elements ......Page 54
3.3 MANOVA of Repeated Measures— s Sample Case ......Page 55
3.3.2 Multivariate Tests ......Page 57
3.4 Illustration ......Page 58
3.5 Summary ......Page 61
4.1 Introduction ......Page 63
4.2 A Simple Linear Regression Model ......Page 64
4.3 Random Intercept MRM ......Page 65
4.3.2 Compound Symmetry and Intraclass Correlation ......Page 67
4.3.4 Psychiatric Dataset ......Page 68
4.3.5 Random Intercept Model Example ......Page 71
4.4 Random Intercept and Trend MRM ......Page 72
4.4.1 Random Intercept and Trend Example ......Page 74
4.4.2 Coding of Time ......Page 75
4.4.2.1 Example ......Page 77
4.4.3 Effect of Diagnosis on Time Trends ......Page 78
4.5 Matrix Formulation ......Page 80
4.5.1 Fit of Variance-Covariance Matrix ......Page 82
4.5.2 Model with Time-Varying Covariates ......Page 85
4.5.2.1 Within and Between-Subjects Effects for Time-Varying Covariates ......Page 88
4.5.2.2 Time Interactions with Time-Varying Covariates ......Page 90
4.6 Estimation ......Page 92
4.7 Summary ......Page 95
5.2 Curvilinear Trend Model ......Page 97
5.2.1 Curvilinear Trend Example ......Page 99
5.3 Orthogonal Polynomials ......Page 102
5.3.1 Model Representations ......Page 105
5.3.2 Orthogonal Polynomial Trend Example ......Page 106
5.3.3 Translating Parameters ......Page 107
5.3.4 Higher-Order Polynomial Models ......Page 110
5.3.5 Cubic Trend Example ......Page 112
5.4 Summary ......Page 115
6.1 Introduction ......Page 117
6.2.1 Compound Symmetry Structure ......Page 118
6.2.3 Toeplitz or Banded Structure ......Page 119
6.2.5 Random-Effects Structure ......Page 120
6.4 Example ......Page 121
6.5 Summary ......Page 127
7.1 Introduction ......Page 129
7.2 MRMs with AC Errors ......Page 130
7.2.1 AR(1) Errors ......Page 132
7.2.2 MA(1) Errors ......Page 134
7.2.4 Toeplitz Errors ......Page 135
7.2.5 Nonstationary AR(1) Errors ......Page 136
7.3 Model Selection ......Page 137
7.4 Example ......Page 138
7.5 Summary ......Page 145
8.1 Introduction ......Page 147
8.2 Generalized Linear Models (GLMs) ......Page 148
8.3 Generalized Estimating Equations (GEE) models ......Page 150
8.3.1 Working Correlation Forms ......Page 151
8.4 GEE Estimation ......Page 152
8.5 Example ......Page 154
8.5.1 Generalized Wald Tests for Model Comparison ......Page 157
8.5.2 Model Fit of Observed Proportions ......Page 160
8.6 Summary ......Page 162
9.1 Introduction ......Page 165
9.2 Logistic Regression Model ......Page 166
9.3 Probit Regression Models ......Page 169
9.4 Threshold Concept ......Page 170
9.5 Mixed-Effects Logistic Regression Model ......Page 171
9.5.3 Heterogeneous Variance Terms ......Page 174
9.5.4 Multilevel Representation ......Page 176
9.5.5 Response Functions ......Page 177
9.6 Estimation ......Page 178
9.6.1 Estimation of Random Effects and Probabilities ......Page 181
9.6.2 Multiple Random Effects ......Page 182
9.6.3 Integration over the Random-Effects Distribution ......Page 183
9.7 Illustration ......Page 186
9.7.1 Fixed-Effects Logistic Regression Model ......Page 189
9.7.2 Random Intercept Logistic Regression Model ......Page 191
9.7.3 Random Intercept and Trend Logistic Regression Model ......Page 197
9.8 Summary ......Page 202
10.1 Introduction ......Page 203
10.2 Mixed-Effects Proportional Odds Model ......Page 204
10.2.1 Partial ProportionalOdds ......Page 207
10.2.2 Models with Scaling Terms ......Page 210
10.2.2.1 Intraclass Correlation and Partitioning of Between- and Within-Cluster Variance ......Page 211
10.2.3 Survival Analysis Models ......Page 212
10.2.4 Estimation ......Page 215
10.3 Psychiatric Example ......Page 218
10.4 Health Services Research Example ......Page 228
10.5 Summary ......Page 232
11 Mixed-Effects Regression Models for Nominal Data ......Page 235
11.1 Mixed-Effects Multinomial Regression Model ......Page 236
11.1.2 Parameter Estimation ......Page 238
11.2 Health Services Research Example ......Page 239
11.3.1 Waiting for Organ Transplantation ......Page 245
11.4 Summary ......Page 254
12 Mixed-effects Regression Models for Counts ......Page 255
12.1 Poisson Regression Model ......Page 256
12.2 Modified Poisson Models ......Page 257
12.3 The ZIP Model ......Page 258
12.4.1 Mixed-Effects Poisson Regression Model ......Page 260
12.4.2 Estimation of Random Effects ......Page 262
12.4.3 Mixed-Effects ZIP Regression Model ......Page 263
12.5 Illustration ......Page 267
12.6 Summary ......Page 272
13 Mixed-Effects Regression Models for Three-Level Data ......Page 273
13.1 Three-Level Mixed-Effects Linear Regression Model ......Page 274
13.1.1 Illustration ......Page 276
13.2.1 Three-Level Mixed-Effects Probit Regression ......Page 281
13.2.3 Illustration ......Page 284
13.2.4 More General Outcomes ......Page 289
13.2.4.1 Ordinal Outcomes ......Page 291
13.2.4.2 Nominal Outcomes ......Page 292
13.2.4.3 Count Outcomes ......Page 293
13.3 Summary ......Page 294
14.1 Introduction ......Page 295
14.2 Missing Data Mechanisms ......Page 296
14.2.2 Missing at Random (MAR) ......Page 297
14.2.3 Missing Not at Random (MNAR) ......Page 298
14.3.1 MCAR Simulations ......Page 299
14.3.2 MAR and MNAR Simulations ......Page 301
14.4 Testing MCAR ......Page 305
14.4.1 Example ......Page 309
14.5.1 Selection Models ......Page 311
14.5.1.1 Mixed-Effects Selection Models ......Page 312
14.5.1.2 Example ......Page 313
14.5.2 Pattern-Mixture Models ......Page 318
14.5.2.1 Example ......Page 320
14.6 Summary ......Page 328
Bibliography ......Page 329
Topic Index......Page 351
Wiley Series in Probability and Statistics......Page 354
