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简介
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.
目录
Preface p. xiii
Acknowledgments p. xvii
Acronyms p. xix
Introduction p. 1
Advantages of Longitudinal Studies p. 1
Challenges of Longitudinal Data Analysis p. 2
Some General Notation p. 3
Data Layout p. 4
Analysis Considerations p. 5
General Approaches p. 5
The Simplest Longitudinal Analysis p. 7
Change Score Analysis p. 7
Analysis of Covariance of Post-test Scores p. 8
ANCOVA of Change Scores p. 9
Example p. 9
Summary p. 12
ANOVA Approaches to Longitudinal Data p. 13
Single-Sample Repeated Measures ANOVA p. 14
Design p. 14
Decomposing the Time Effect p. 17
Trend Analysis-Orthogonal Polynomial Contrasts p. 18
Change Relative to Baseline-Reference Cell Contrasts p. 19
Consecutive Time Comparisons-Profile Contrasts p. 19
Contrasting Each Timepoint to the Mean of Subsequent Timepoints-Helmert Contrasts p. 19
Contrasting Each Timepoint to the Mean of Others-Deviation Contrasts p. 20
Multiple Comparisons p. 20
Multiple-Sample Repeated Measures ANOVA p. 21
Testing for Group by Time Interaction p. 23
Testing for Subject Effect p. 23
Contrasts for Time Effects p. 24
Orthogonal Polynomial Partition of SS p. 24
Compound Symmetry and Sphericity p. 25
Sphericity p. 26
Illustration p. 27
Summary p. 29
MANOVA Approaches to Longitudinal Data p. 31
Data Layout for ANOVA versus MANOVA p. 32
MANOVA for Repeated Measurements p. 34
Growth Curve Analysis-Polynomial Representation p. 34
Extracting Univariate Repeated Measures ANOVA Results p. 37
Multivariate Test of the Time Effect p. 38
Tests of Specific Time Elements p. 38
MANOVA of Repeated Measures- s Sample Case p. 39
Extracting Univariate Repeated Measures ANOVA Results p. 41
Multivariate Tests p. 41
Illustration p. 42
Summary p. 45
Mixed-Effects Regression Models for Continuous Outcomes p. 47
Introduction p. 47
A Simple Linear Regression Model p. 48
Random Intercept MRM p. 49
Incomplete Data Across Time p. 51
Compound Symmetry and Intraclass Correlation p. 51
Inference p. 52
Psychiatric Dataset p. 52
Random Intercept Model Example p. 55
Random Intercept and Trend MRM p. 56
Random Intercept and Trend Example p. 58
Coding of Time p. 59
Example p. 61
Effect of Diagnosis on Time Trends p. 62
Matrix Formulation p. 64
Fit of Variance-Covariance Matrix p. 66
Model with Time-Varying Covariates p. 69
Within and Between-Subjects Effects for Time-Varying Covariates p. 72
Time Interactions with Time-Varying Covariates p. 74
Estimation p. 76
ML Bias in Estimation of Variance Parameters p. 79
Summary p. 79
Mixed-Effects Polynomial Regression Models p. 81
Introduction p. 81
Curvilinear Trend Model p. 81
Curvilinear Trend Example p. 83
Orthogonal Polynomials p. 86
Model Representations p. 89
Orthogonal Polynomial Trend Example p. 90
Translating Parameters p. 91
Higher-Order Polynomial Models p. 94
Cubic Trend Example p. 96
Summary p. 99
Covariance Pattern Models p. 101
Introduction p. 101
Covariance Pattern Models p. 102
Compound Symmetry Structure p. 102
First-Order Autoregressive Structure p. 103
Toeplitz or Banded Structure p. 103
Unstructured Form p. 104
Random-Effects Structure p. 104
Model Selection p. 105
Example p. 105
Summary p. 111
Mixed Regression Models with Autocorrelated Errors p. 113
Introduction p. 113
MRMs with AC Errors p. 114
AR(1) Errors p. 116
MA(1) Errors p. 118
ARMA(1,1) Errors p. 119
Toeplitz Errors p. 119
Nonstationary AR(1) Errors p. 120
Model Selection p. 121
Example p. 122
Summary p. 129
Generalized Estimating Equations (GEE) Models p. 131
Introduction p. 131
Generalized Linear Models (GLMs) p. 132
Generalized Estimating Equations (GEE) models p. 134
Working Correlation Forms p. 135
GEE Estimation p. 136
Example p. 138
Generalized Wald Tests for Model Comparison p. 141
Model Fit of Observed Proportions p. 144
Summary p. 146
Mixed-Effects Regression Models for Binary Outcomes p. 149
Introduction p. 149
Logistic Regression Model p. 150
Probit Regression Models p. 153
Threshold Concept p. 154
Mixed-Effects Logistic Regression Model p. 155
Intraclass Correlation p. 158
More General Mixed-Effects Models p. 158
Heterogeneous Variance Terms p. 158
Multilevel Representation p. 160
Response Functions p. 161
Estimation p. 162
Estimation of Random Effects and Probabilities p. 165
Multiple Random Effects p. 166
Integration over the Random-Effects Distribution p. 167
Illustration p. 170
Fixed-Effects Logistic Regression Model p. 173
Random Intercept Logistic Regression Model p. 175
Random Intercept and Trend Logistic Regression Model p. 181
Summary p. 186
Mixed-Effects Regression Models for Ordinal Outcomes p. 187
Introduction p. 187
Mixed-Effects Proportional Odds Model p. 188
Partial Proportional Odds p. 191
Models with Scaling Terms p. 194
Intraclass Correlation and Partitioning of Between- and Within-Cluster Variance p. 195
Survival Analysis Models p. 196
Intraclass Correlation p. 199
Estimation p. 199
Psychiatric Example p. 202
Health Services Research Example p. 212
Summary p. 216
Mixed-Effects Regression Models for Nominal Data p. 219
Mixed-Effects Multinomial Regression Model p. 220
Intraclass Correlation p. 222
Parameter Estimation p. 222
Health Services Research Example p. 223
Competing Risk Survival Models p. 229
Waiting for Organ Transplantation p. 229
Summary p. 238
Mixed-effects Regression Models for Counts p. 239
Poisson Regression Model p. 240
Modified Poisson Models p. 241
The ZIP Model p. 242
Mixed-Effects Models for Counts p. 244
Mixed-Effects Poisson Regression Model p. 244
Estimation of Random Effects p. 246
Mixed-Effects ZIP Regression Model p. 247
Illustration p. 251
Summary p. 256
Mixed-Effects Regression Models for Three-Level Data p. 257
Three-Level Mixed-Effects Linear Regression Model p. 258
Illustration p. 260
Three-Level Mixed-Effects Nonlinear Regression Models p. 265
Three-Level Mixed-Effects Probit Regression p. 265
Three-Level Logistic Regression Model for Dichotomous Outcomes p. 268
Illustration p. 268
More General Outcomes p. 273
Ordinal Outcomes p. 275
Nominal Outcomes p. 276
Count Outcomes p. 277
Summary p. 278
Missing Data in Longitudinal Studies p. 279
Introduction p. 279
Missing Data Mechanisms p. 280
Missing Completely at Random (MCAR) p. 281
Missing at Random (MAR) p. 281
Missing Not at Random (MNAR) p. 282
Models and Missing Data Mechanisms p. 283
MCAR Simulations p. 283
MAR and MNAR Simulations p. 285
Testing MCAR p. 289
Example p. 293
Models for Nonignorable Missingness p. 295
Selection Models p. 295
Mixed-Effects Selection Models p. 296
Example p. 297
Pattern-Mixture Models p. 302
Example p. 304
Summary p. 312
Bibliography p. 313
Topic Index p. 335
Acknowledgments p. xvii
Acronyms p. xix
Introduction p. 1
Advantages of Longitudinal Studies p. 1
Challenges of Longitudinal Data Analysis p. 2
Some General Notation p. 3
Data Layout p. 4
Analysis Considerations p. 5
General Approaches p. 5
The Simplest Longitudinal Analysis p. 7
Change Score Analysis p. 7
Analysis of Covariance of Post-test Scores p. 8
ANCOVA of Change Scores p. 9
Example p. 9
Summary p. 12
ANOVA Approaches to Longitudinal Data p. 13
Single-Sample Repeated Measures ANOVA p. 14
Design p. 14
Decomposing the Time Effect p. 17
Trend Analysis-Orthogonal Polynomial Contrasts p. 18
Change Relative to Baseline-Reference Cell Contrasts p. 19
Consecutive Time Comparisons-Profile Contrasts p. 19
Contrasting Each Timepoint to the Mean of Subsequent Timepoints-Helmert Contrasts p. 19
Contrasting Each Timepoint to the Mean of Others-Deviation Contrasts p. 20
Multiple Comparisons p. 20
Multiple-Sample Repeated Measures ANOVA p. 21
Testing for Group by Time Interaction p. 23
Testing for Subject Effect p. 23
Contrasts for Time Effects p. 24
Orthogonal Polynomial Partition of SS p. 24
Compound Symmetry and Sphericity p. 25
Sphericity p. 26
Illustration p. 27
Summary p. 29
MANOVA Approaches to Longitudinal Data p. 31
Data Layout for ANOVA versus MANOVA p. 32
MANOVA for Repeated Measurements p. 34
Growth Curve Analysis-Polynomial Representation p. 34
Extracting Univariate Repeated Measures ANOVA Results p. 37
Multivariate Test of the Time Effect p. 38
Tests of Specific Time Elements p. 38
MANOVA of Repeated Measures- s Sample Case p. 39
Extracting Univariate Repeated Measures ANOVA Results p. 41
Multivariate Tests p. 41
Illustration p. 42
Summary p. 45
Mixed-Effects Regression Models for Continuous Outcomes p. 47
Introduction p. 47
A Simple Linear Regression Model p. 48
Random Intercept MRM p. 49
Incomplete Data Across Time p. 51
Compound Symmetry and Intraclass Correlation p. 51
Inference p. 52
Psychiatric Dataset p. 52
Random Intercept Model Example p. 55
Random Intercept and Trend MRM p. 56
Random Intercept and Trend Example p. 58
Coding of Time p. 59
Example p. 61
Effect of Diagnosis on Time Trends p. 62
Matrix Formulation p. 64
Fit of Variance-Covariance Matrix p. 66
Model with Time-Varying Covariates p. 69
Within and Between-Subjects Effects for Time-Varying Covariates p. 72
Time Interactions with Time-Varying Covariates p. 74
Estimation p. 76
ML Bias in Estimation of Variance Parameters p. 79
Summary p. 79
Mixed-Effects Polynomial Regression Models p. 81
Introduction p. 81
Curvilinear Trend Model p. 81
Curvilinear Trend Example p. 83
Orthogonal Polynomials p. 86
Model Representations p. 89
Orthogonal Polynomial Trend Example p. 90
Translating Parameters p. 91
Higher-Order Polynomial Models p. 94
Cubic Trend Example p. 96
Summary p. 99
Covariance Pattern Models p. 101
Introduction p. 101
Covariance Pattern Models p. 102
Compound Symmetry Structure p. 102
First-Order Autoregressive Structure p. 103
Toeplitz or Banded Structure p. 103
Unstructured Form p. 104
Random-Effects Structure p. 104
Model Selection p. 105
Example p. 105
Summary p. 111
Mixed Regression Models with Autocorrelated Errors p. 113
Introduction p. 113
MRMs with AC Errors p. 114
AR(1) Errors p. 116
MA(1) Errors p. 118
ARMA(1,1) Errors p. 119
Toeplitz Errors p. 119
Nonstationary AR(1) Errors p. 120
Model Selection p. 121
Example p. 122
Summary p. 129
Generalized Estimating Equations (GEE) Models p. 131
Introduction p. 131
Generalized Linear Models (GLMs) p. 132
Generalized Estimating Equations (GEE) models p. 134
Working Correlation Forms p. 135
GEE Estimation p. 136
Example p. 138
Generalized Wald Tests for Model Comparison p. 141
Model Fit of Observed Proportions p. 144
Summary p. 146
Mixed-Effects Regression Models for Binary Outcomes p. 149
Introduction p. 149
Logistic Regression Model p. 150
Probit Regression Models p. 153
Threshold Concept p. 154
Mixed-Effects Logistic Regression Model p. 155
Intraclass Correlation p. 158
More General Mixed-Effects Models p. 158
Heterogeneous Variance Terms p. 158
Multilevel Representation p. 160
Response Functions p. 161
Estimation p. 162
Estimation of Random Effects and Probabilities p. 165
Multiple Random Effects p. 166
Integration over the Random-Effects Distribution p. 167
Illustration p. 170
Fixed-Effects Logistic Regression Model p. 173
Random Intercept Logistic Regression Model p. 175
Random Intercept and Trend Logistic Regression Model p. 181
Summary p. 186
Mixed-Effects Regression Models for Ordinal Outcomes p. 187
Introduction p. 187
Mixed-Effects Proportional Odds Model p. 188
Partial Proportional Odds p. 191
Models with Scaling Terms p. 194
Intraclass Correlation and Partitioning of Between- and Within-Cluster Variance p. 195
Survival Analysis Models p. 196
Intraclass Correlation p. 199
Estimation p. 199
Psychiatric Example p. 202
Health Services Research Example p. 212
Summary p. 216
Mixed-Effects Regression Models for Nominal Data p. 219
Mixed-Effects Multinomial Regression Model p. 220
Intraclass Correlation p. 222
Parameter Estimation p. 222
Health Services Research Example p. 223
Competing Risk Survival Models p. 229
Waiting for Organ Transplantation p. 229
Summary p. 238
Mixed-effects Regression Models for Counts p. 239
Poisson Regression Model p. 240
Modified Poisson Models p. 241
The ZIP Model p. 242
Mixed-Effects Models for Counts p. 244
Mixed-Effects Poisson Regression Model p. 244
Estimation of Random Effects p. 246
Mixed-Effects ZIP Regression Model p. 247
Illustration p. 251
Summary p. 256
Mixed-Effects Regression Models for Three-Level Data p. 257
Three-Level Mixed-Effects Linear Regression Model p. 258
Illustration p. 260
Three-Level Mixed-Effects Nonlinear Regression Models p. 265
Three-Level Mixed-Effects Probit Regression p. 265
Three-Level Logistic Regression Model for Dichotomous Outcomes p. 268
Illustration p. 268
More General Outcomes p. 273
Ordinal Outcomes p. 275
Nominal Outcomes p. 276
Count Outcomes p. 277
Summary p. 278
Missing Data in Longitudinal Studies p. 279
Introduction p. 279
Missing Data Mechanisms p. 280
Missing Completely at Random (MCAR) p. 281
Missing at Random (MAR) p. 281
Missing Not at Random (MNAR) p. 282
Models and Missing Data Mechanisms p. 283
MCAR Simulations p. 283
MAR and MNAR Simulations p. 285
Testing MCAR p. 289
Example p. 293
Models for Nonignorable Missingness p. 295
Selection Models p. 295
Mixed-Effects Selection Models p. 296
Example p. 297
Pattern-Mixture Models p. 302
Example p. 304
Summary p. 312
Bibliography p. 313
Topic Index p. 335
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