## Applied Longitudinal Data Analysis: Modeling Change and Event OccurrenceChange is constant in everyday life. Infants crawl and then walk, children learn to read and write, teenagers mature in myriad ways, the elderly become frail and forgetful. Beyond these natural processes and events, external forces and interventions instigate and disrupt change: test scores may rise after a coaching course, drug abusers may remain abstinent after residential treatment. By charting changes over time and investigating whether and when events occur, researchers reveal the temporal rhythms of our lives. Applied Longitudinal Data Analysis is a much-needed professional book for empirical researchers and graduate students in the behavioral, social, and biomedical sciences. It offers the first accessible in-depth presentation of two of today's most popular statistical methods: multilevel models for individual change and hazard/survival models for event occurrence (in both discrete- and continuous-time). Using clear, concise prose and real data sets from published studies, the authors take you step by step through complete analyses, from simple exploratory displays that reveal underlying patterns through sophisticated specifications of complex statistical models.Applied Longitudinal Data Analysis offers readers a private consultation session with internationally recognized experts and represents a unique contribution to the literature on quantitative empirical methods.Visit http://www.ats.ucla.edu/stat/examples/alda.htm for: DT Downloadable data sets DT Library of computer programs in SAS, SPSS, Stata, HLM, MLwiN, and more DT Additional material for data analysis |

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### Contents

A Framework for Investigating Change over Time | 3 |

11 When Might You Study Change over Time? | 4 |

12 Distinguishing Between Two Types of Questions about Change | 7 |

13 Three Important Features of a Study of Change | 9 |

Exploring Longitudinal Data on Change | 16 |

21 Creating a Longitudinal Data Set | 17 |

22 Descriptive Analysis of Individual Change over Time | 23 |

23 Exploring Differences in Change across People | 33 |

92 Framing a Research Question about Event Occurrence | 309 |

How Complete Are the Data on Event Occurrence? | 315 |

Describing DiscreteTime Event Occurrence Data | 325 |

101 The Life Table | 326 |

102 A Framework for Characterizing the Distribution of DiscreteTime Event Occurrence Data | 330 |

103 Developing Intuition About Hazard Functions Survivor Functions and Median Lifetimes | 339 |

104 Quantifying the Effects of Sampling Variation | 348 |

105 A Simple and Useful Strategy for Constructing the Life Table | 351 |

Lessons for Research Design | 41 |

Introducing the Multilevel Model for Change | 45 |

31 What Is the Purpose of the Multilevel Model for Change? | 46 |

32 The Level1 Submodel for Individual Change | 49 |

33 The Level2 Submodel for Systematic Interindividual Differences in Change | 57 |

34 Fitting the Multilevel Model for Change to Data | 63 |

35 Examining Estimated Fixed Effects | 68 |

36 Examining Estimated Variance Components | 72 |

Doing Data Analysis with the Multilevel Model for Change | 75 |

Changes in Adolescent Alcohol Use | 76 |

42 The Composite Specification of the Multilevel Model for Change | 80 |

43 Methods of Estimation Revisited | 85 |

Fitting Two Unconditional Multilevel Models for Change | 92 |

45 Practical Data Analytic Strategies for Model Building | 104 |

46 Comparing Models Using Deviance Statistics | 116 |

47 Using Wald Statistics to Test Composite Hypotheses About Fixed Effects | 122 |

48 Evaluating the Tenability of a Models Assumptions | 127 |

49 ModelBased Empirical Bayes Estimates of the Individual Growth Parameters | 132 |

Treating TIME More Flexibly | 138 |

51 Variably Spaced Measurement Occasions | 139 |

52 Varying Numbers of Measurement Occasions | 146 |

53 TimeVarying Predictors | 159 |

54 Recentering the Effect of TIME | 181 |

Modeling Discontinuous and Nonlinear Change | 189 |

61 Discontinuous Individual Change | 190 |

62 Using Transformations to Model Nonlinear Individual Change | 208 |

63 Representing Individual Change Using a Polynomial Function of TIME | 213 |

64 Truly Nonlinear Trajectories | 223 |

Examining the Multilevel Models Error Covariance Structure | 243 |

Assumptions about the Error Covariance Matrix | 246 |

73 Postulating an Alternative Error Covariance Structure | 256 |

Modeling Change Using Covariance Structure Analysis | 266 |

82 The Basics of Latent Growth Modeling | 280 |

83 CrossDomain Analysis of Change | 295 |

84 Extensions of Latent Growth Modeling | 299 |

PART II | 303 |

A Framework for Investigating Event Occurrence | 305 |

91 Should You Conduct a Survival Analysis? The Whether and When Test | 306 |

Fitting Basic DiscreteTime Hazard Models | 357 |

111 Toward a Statistical Model for DiscreteTime Hazard | 358 |

112 A Formal Representation of the Population DiscreteTime Hazard Model | 369 |

113 Fitting a DiscreteTime Hazard Model to Data | 378 |

114 Interpreting Parameter Estimates | 386 |

115 Displaying Fitted Hazard and Survivor Functions | 391 |

116 Comparing Models Using Deviance Statistics and Information Criteria | 397 |

117 Statistical Inference Using Asymptotic Standard Errors | 402 |

Extending the DiscreteTime Hazard Model | 407 |

121 Alternative Specifications for the Main Effect of TIME | 408 |

122 Using the Complementary LogLog Link to Specify a DiscreteTime Hazard Model | 419 |

123 TimeVarying Predictors | 426 |

Uncovering Violations and Simple Solutions | 443 |

Uncovering Violations and Simple Solutions | 451 |

No Simple Solution | 461 |

127 Residual Analysis | 463 |

Describing ContinuousTime Event Occurrence Data | 468 |

131 A Framework for Characterizing the Distribution of ContinuousTime Event Data | 469 |

132 Grouped Methods for Estimating ContinuousTime Survivor and Hazard Functions | 475 |

133 The KaplanMeier Method of Estimating the ContinuousTime Survivor Function | 483 |

134 The Cumulative Hazard Function | 488 |

135 KernelSmoothed Estimates of the Hazard Function | 494 |

Survivor Cumulative Hazard and KernelSmoothed Hazard Functions | 497 |

Fitting Cox Regression Models | 503 |

142 Fitting the Cox Regression Model to Data | 516 |

143 Interpreting the Results of Fitting the Cox Regression Model to Data | 523 |

144 Nonparametric Strategies for Displaying the Results of Model Fitting | 535 |

Extending the Cox Regression Model | 543 |

151 TimeVarying Predictors | 544 |

152 Nonproportional Hazards Models via Stratification | 556 |

153 Nonproportional Hazards Models via Interactions with Time | 562 |

154 Regression Diagnostics | 570 |

155 Competing Risks | 586 |

156 Late Entry into the Risk Set | 595 |

Notes | 607 |

613 | |

627 | |

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### Common terms and phrases

adolescents alcohol ALCUSE assess asymptote average censored change trajectory compute covariance matrix Cox model Cox regression model cumulative hazard functions data collection describe deviance statistic dictors discrete-time hazard model error covariance event occurrence examine fitted hazard fixed effects goodness-of-fit grade hazard ratio homoscedasticity hypothesized identical includes individual change individual growth parameters initial status interaction interpretation interval Kaplan-Meier estimate level-2 residuals level-2 submodel likelihood likelihood function linear main effect measurement median lifetime methods metric model fitting model for change multilevel model null hypothesis odds outcome panel of figure parameter estimates parenting transitions PEER period person person-period data set plots polynomial population postulate predictor values rate of change represent researchers residual variance results of fitting risk scores risk set sample specification standard errors statistical model strategies substantive predictors survival analysis survivor function time-invariant time-varying predictors tion variable variance components waves of data

### Popular passages

Page 615 - DA (1996). Temporal tempering: An event history analysis of the process of voluntary turnover.

### References to this book

A First Course in Structural Equation Modeling Tenko Raykov,George A. Marcoulides No preview available - 2006 |