1 A Framework for Investigating Change over Time 3
1.1 When Might You Study Change over Time? 4
1.2 Distinguishing Between Two Types of Questions about Change 7
1.3 Three Important Features of a Study of Change 9
2 Exploring Longitudinal Data on Change 16
2.1 Creating a Longitudinal Data Set 17
2.2 Descriptive Analysis of Individual Change over Time 23
2.3 Exploring Differences in Change across People 33
2.4 Improving the Precision and Reliability of OLS-Estimated Rates of Change: Lessons for Research Design 41
3 Introducing the Multilevel Model for Change 45
3.1 What Is the Purpose of the Multilevel Model for Change? 46
3.2 The Level-1 Submodel for Individual Change 49
3.3 The Level-2 Submodel for Systematic Interindividual Differences in Change 57
3.4 Fitting the Multilevel Model for Change to Data 63
3.5 Examining Estimated Fixed Effects 68
3.6 Examining Estimated Variance Components 72
4 Doing Data Analysis with the Multilevel Model for Change 75
4.1 Example: Changes in Adolescent Alcohol Use 76
4.2 The Composite Specification of the Multilevel Model for Change 80
4.3 Methods of Estimation, Revisited 85
4.4 First Steps: Fitting Two Unconditional Multilevel Models for Change 92
4.5 Practical Data Analytic Strategies for Model Building 104
4.6 Comparing Models Using Deviance Statistics 116
4.7 Using Wald Statistics to Test Composite Hypotheses About Fixed Effects 122
4.8 Evaluating the Tenability of a Model''s Assumptions 127
4.9 Model-Based (Empirical Bayes) Estimates of the Individual Growth Parameters 132
5 Treating TIME More Flexibly 138
5.1 Variably Spaced Measurement Occasions 139
5.2 Varying Numbers of Measurement Occasions 146
5.3 Time-Varying Predictors 159
5.4 Recentering the Effect of TIME 181
6 Modeling Discontinuous and Nonlinear Change 189
6.1 Discontinuous Individual Change 190
6.2 Using Transformations to Model Nonlinear Individual Change 208
6.3 Representing Individual Change Using a Polynomial Function of TIME 213
6.4 Truly Nonlinear Trajectories 223
7 Examining the Multilevel Model''s Error Covariance Structure 243
7.1 The "Standard" Specification of the Multilevel Model for Change 243
7.2 Using the Composite Model to Understand Assumptions about the Error Covariance Matrix 246
7.3 Postulating an Alternative Error Covariance Structure 256
8 Modeling Change Using Covariance Structure Analysis 266
8.1 The General Covariance Structure Model 266
8.2 The Basics of Latent Growth Modeling 280
8.3 Cross-Domain Analysis of Change 295
8.4 Extensions of Latent Growth Modeling 299
9 A Framework for Investigating Event Occurrence 305
9.1 Should You Conduct a Survival Analysis? The "Whether" and "When" Test 306
9.2 Framing a Research Question About Event Occurrence 309
9.3 Censoring: How Complete Are the Data on Event Occurrence? 315
10 Describing Discrete-Time Event Occurrence Data 325
10.1 The Life Table 326
10.2 A Framework for Characterizing the Distribution of Discrete-Time Event Occurrence Data 330
10.3 Developing Intuition About Hazard Functions, Survivor Functions, and Median Lifetimes 339
10.4 Quantifying the Effects of Sampling Variation 348
10.5 A Simple and Useful Strategy for Constructing the Life Table 351
11 Fitting Basic Discrete-Time Hazard Models 357
11.1 Toward a Statistical Model for Discrete-Time Hazard 358
11.2 A Formal Representation of the Population Discrete-Time Hazard Model 369
11.3 Fitting a Discrete-Time Hazard Model to Data 378
11.4 Interpreting Parameter Estimates 386
11.5 Displaying Fitted Hazard and Survivor Functions 391
11.6 Comparing Models Using Deviance Statistics and Information Criteria 397
11.7 Statistical Inference Using Asymptotic Standard Errors 402
12 Extending the Discrete-Time Hazard Model 407
12.1 Alternative Specifications for the "Main Effect of TIME" 408
12.2 Using the Complementary Log-Log Link to Specify a Discrete-Time Hazard Model 419
12.3 Time-Varying Predictors 426
12.4 The Linear Additivity Assumption: Uncovering Violations and Simple Solutions 443
12.5 The Proportionality Assumption: Uncovering Violations and Simple Solutions 451
12.6 The No Unobserved Heterogeneity Assumption: No Simple Solution 461
12.7 Residual Analysis 463
13 Describing Continuous-Time Event Occurrence Data 468
13.1 A Framework for Characterizing the Distribution of Continuous-Time Event Data 469
13.2 Grouped Methods for Estimating Continuous-Time Survivor and Hazard Functions 475
13.3 The Kaplan-Meier Method of Estimating the Continuous-Time Survivor Function 483
13.4 The Cumulative Hazard Function 488
13.5 Kernel-Smoothed Estimates of the Hazard Function 494
13.6 Developing an Intuition about Continuous-Time Survivor, Cumulative Hazard, and Kernel-Smoothed Hazard Functions 497
14 Fitting Cox Regression Models 503
14.1 Toward a Statistical Model for Continuous-Time Hazard 503
14.2 Fitting the Cox Regression Model to Data 516
14.3 Interpreting the Results of Fitting the Cox Regression Model to Data 523
14.4 Nonparametric Strategies for Displaying the Results of Model Fitting 535
15 Extending the Cox Regression Model 543
15.1 Time-Varying Predictors 544
15.2 Nonproportional Hazards Models via Stratification 556
15.3 Nonproportional Hazards Models via Interactions with Time 562
15.4 Regression Diagnostics 570
15.5 Competing Risks 586
15.6 Late Entry into the Risk Set 595
Notes 607
References 613
Index 627
