Longitudinal and Panel Data: Analysis and Applications in the Social Sciences

✍ Scribed by Edward W. Frees

• Year: 2004
• Tongue: English
• Leaves: 485
• Category: Library

✦ Synopsis

Focusing on an analysis of models and data that arise from repeated observations of a cross-section of individuals, households or firms, this book also covers important applications within business, economics, education, political science and other social science disciplines. The author introduces the foundations of longitudinal and panel data analysis at a level suitable for quantitatively oriented social science graduate students as well as individual researchers. He emphasizes mathematical and statistical fundamentals but also demonstrates substantive applications from across the social sciences. These applications are enhanced by real-world data sets and software programs in SAS and Stata.

✦ Table of Contents

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Intended Audience and Level......Page 11
Organization......Page 12
Statistical Software......Page 15
Approach......Page 16
Acknowledgments......Page 18
Statistical Modeling......Page 19
Defining Longitudinal and Panel Data......Page 20
Some Notation......Page 21
Prevalence of Longitudinal and Panel Data Analysis......Page 22
Dynamic Relationships......Page 23
Historical Approach......Page 24
Longitudinal Data as Repeated Cross-Sectional Studies......Page 25
Heterogeneity......Page 26
Omitted Variables......Page 27
Efficiency of Estimators......Page 28
Drawbacks: Attrition......Page 29
Types of Inference......Page 30
Social Science Statistical Modeling......Page 31
Modeling Issues......Page 32
1.4 Historical Notes......Page 33
Data......Page 36
Basic Models......Page 37
Parameters of Interest......Page 40
Subject and Time Heterogeneity......Page 41
Data Exploration Techniques......Page 42
Basic Added-Variable Plot......Page 43
Trellis Plot......Page 48
Least-Squares Estimation......Page 49
ANOVA Table and Standard Errors......Page 51
Large-Sample Properties of Estimators......Page 55
2.4.1 Pooling Test......Page 56
Correlations and Added-Variable Plots......Page 58
2.4.3 Influence Diagnostics......Page 59
2.4.4 Cross-Sectional Correlation......Page 60
Calibration of Cross-Sectional Correlation Test Statistics......Page 61
2.4.5 Heteroscedasticity......Page 63
2.5.1 Serial Correlation......Page 64
Temporal Covariance Matrix......Page 65
2.5.2 Subject-Specific Slopes......Page 67
Sampling and Model Assumptions......Page 68
2.5.3 Robust Estimation of Standard Errors......Page 69
Further Reading......Page 70
2A.1 Basic Fixed-Effects Model: Ordinary Least-Squares Estimation......Page 71
2A.2 Fixed-Effects Models: Generalized Least-Squares Estimation......Page 72
Observation-Level Diagnostic Statistic......Page 73
2A.4 Cross-Sectional Correlation: Shortcut Calculations......Page 74
Section 2.1......Page 75
Section 2.3......Page 76
Section 2.4......Page 79
Section 2.5......Page 81
Empirical Exercises......Page 83
Sampling and Inference......Page 90
Traditional ANOVA Setup......Page 91
Sampling and Model Assumptions......Page 93
Time-Constant Variables......Page 95
Generalized Least-Squares Estimation......Page 96
Feasible GLS Estimator......Page 97
Pooling Test......Page 98
3.2 Example: Income Tax Payments......Page 99
3.3.1 Linear Mixed-Effects Model......Page 104
Repeated Measures Design......Page 106
Random-Coefficients Model......Page 107
Variations of the Random-Coefficients Model......Page 108
Group Effects......Page 109
3.3.2 Mixed Linear Models......Page 110
3.4 Inference for Regression Coefficients......Page 112
Matrix Inversion Formula......Page 113
Maximum Likelihood Estimation......Page 114
Robust Estimation of Standard Errors......Page 115
Testing Hypotheses......Page 116
3.5.1 Maximum Likelihood Estimation......Page 118
3.5.2 Restricted Maximum Likelihood......Page 119
Starting Values......Page 121
3.5.3 MIVQUEs......Page 123
Further Reading......Page 124
3A.1 Independence of Residuals and Least-Squares Estimators......Page 125
3A.2 Restricted Likelihoods......Page 126
Special Case: Testing the Importance of a Subset of Regression Coefficients......Page 128
Section 3.1......Page 131
Section 3.4......Page 135
Section 3.5......Page 138
Empirical Exercises......Page 139
4.1 Estimators versus Predictors......Page 143
Shrinkage Estimator......Page 144
Types of Predictors......Page 146
4.3 Best Linear Unbiased Predictors......Page 147
BLUPs as Predictors......Page 148
4.4.1 Linear Mixed-Effects Model......Page 151
4.4.2 Linear Combinations of Global Parameters and Subject-Specific Effects......Page 152
4.4.3 BLUP Residuals......Page 153
4.4.4 Predicting Future Observations......Page 154
4.5.1 Sources and Characteristics of Data......Page 156
4.5.2 In-Sample Model Specification......Page 161
4.5.3 Out-of-Sample Model Specification......Page 162
4.5.4 Forecasts......Page 164
4.6 Bayesian Inference......Page 165
4.7 Credibility Theory......Page 170
4.7.1 Credibility Theory Models......Page 171
4.7.2 Credibility Rate-Making......Page 172
Further Reading......Page 174
4A.2 Best Linear Unbiased Predictor......Page 175
4A.3 BLUP Variance......Page 176
Section 4.2......Page 177
Section 4.4......Page 178
Empirical Exercises......Page 181
5.1 Cross-Sectional Multilevel Models......Page 184
5.1.1 Two-Level Models......Page 185
Extended Two-Level Models......Page 187
Motivation for Multilevel Models......Page 189
5.1.2 Multiple-Level Models......Page 190
5.1.3 Multilevel Modeling in Other Fields......Page 191
5.2.1 Two-Level Models......Page 192
Growth-Curve Models......Page 193
5.2.2 Multiple-Level Models......Page 197
5.3 Prediction......Page 198
Two-Level Models......Page 199
Multiple-Level Models......Page 200
5.4 Testing Variance Components......Page 202
Appendix 5A High-Order Multilevel Models......Page 205
Section 5.3......Page 209
Section 5.4......Page 211
Empirical Exercise......Page 213
Appendix 5A......Page 216
6.1 Stochastic Regressors in Nonlongitudinal Settings......Page 217
6.1.1 Endogenous Stochastic Regressors......Page 218
6.1.2 Weak and Strong Exogeneity......Page 220
6.1.3 Causal Effects......Page 222
6.1.4 Instrumental Variable Estimation......Page 223
6.2.1 Longitudinal Data Models without Heterogeneity Terms......Page 226
6.2.2 Longitudinal Data Models with Heterogeneity Terms and Strictly Exogenous Regressors......Page 227
Fixed-Effects Estimation......Page 230
6.3 Longitudinal Data Models with Heterogeneity Terms and Sequentially Exogenous Regressors......Page 231
Estimation Difficulties......Page 232
6.4 Multivariate Responses......Page 239
6.4.1 Multivariate Regression......Page 240
6.4.2 Seemingly Unrelated Regressions......Page 241
6.4.3 Simultaneous-Equations Models......Page 243
Seemingly Unrelated Regression Models with Error Components......Page 246
Simultaneous-Equations Models with Error Components......Page 247
6.5.1 Cross-Sectional Models......Page 249
Mean Parameters......Page 250
Identification Issues......Page 251
Estimation Techniques......Page 252
6.5.2 Longitudinal Data Applications......Page 254
Growth-Curve Models......Page 256
Appendix 6A Linear Projections......Page 258
7.1 Heterogeneity......Page 260
Two Approaches to Modeling Heterogeneity......Page 261
Theoretical Identification with Heterogeneity May Be Impossible......Page 262
Estimation of Regression Coefficients without Complete Identification Is Possible......Page 263
7.2 Comparing Fixed- and Random-Effects Estimators......Page 265
7.2.1 A Special Case......Page 268
7.2.2 General Case......Page 270
Correlated-Effects Model......Page 272
7.3 Omitted Variables......Page 274
7.3.1 Models of Omitted Variables......Page 276
7.3.2 Augmented Regression Estimation......Page 279
7.4.1 Incomplete and Rotating Panels......Page 281
Missing-Data Models......Page 283
7.4.3 Nonignorable Missing Data......Page 286
Heckman Two-Stage Procedure......Page 287
Hausman and Wise Procedure......Page 288
EM Algorithm......Page 289
Section 7.2......Page 290
8.1 Introduction......Page 295
8.2.1 Covariance Structures......Page 298
8.2.2 Nonstationary Structures......Page 299
8.2.3 Continuous-Time Correlation Models......Page 301
8.3 Cross-Sectional Correlations and Time-Series Cross-Section Models......Page 304
8.4.1 The Model......Page 306
8.4.2 Estimation......Page 308
8.4.3 Forecasting......Page 310
8.5 Kalman Filter Approach......Page 313
8.5.1 Transition Equations......Page 314
8.5.2 Observation Set......Page 315
8.5.3 Measurement Equations......Page 316
8.5.4 Initial Conditions......Page 317
8.5.5 The Kalman Filter Algorithm......Page 318
Likelihood Equations......Page 319
8.6 Example: Capital Asset Pricing Model......Page 320
8A.2 Estimation......Page 330
Likelihood Equations......Page 331
8A.3 Prediction......Page 332
Forecasting......Page 334
Linear Probability Models......Page 336
Using Nonlinear Functions of Explanatory Variables......Page 337
Threshold Interpretation......Page 338
Random-Utility Interpretation......Page 339
Logistic Regression......Page 340
Logistic Regression Parameter Interpretation......Page 341
9.1.2 Inference for Logistic and Probit Regression Models Parameter Estimation......Page 342
9.1.3 Example: Income Tax Payments and Tax Preparers......Page 344
9.2 Random-Effects Models......Page 347
Random-Effects Likelihood......Page 348
Multilevel Model Extensions......Page 350
Maximum Likelihood Estimation......Page 353
Conditional Maximum Likelihood Estimation......Page 355
Conditional Likelihood Estimation......Page 356
GEE Estimators for the Random-Effects Binary Dependent-Variable Model......Page 357
GEE Estimation Procedure......Page 358
Further Reading......Page 361
9A.1 Consistency of Likelihood Estimators......Page 362
Computing the Distribution of Sums of Nonidentically, Independently Distributed Bernoulli Random Variables......Page 363
Computing the Conditional Maximum Likelihood Estimator......Page 364
Section 9.1......Page 365
10.1 Homogeneous Models......Page 368
10.1.1 Linear Exponential Families of Distributions......Page 369
10.1.2 Link Functions......Page 370
Maximum Likelihood Estimation for Canonical Links......Page 371
Maximum Likelihood Estimation for General Links......Page 372
Overdispersion......Page 373
10.2 Example: Tort Filings......Page 374
Marginal Models......Page 378
Generalized Estimating Equations......Page 380
GEEs with Unknown Variance Components......Page 381
Robust Estimation of Standard Errors......Page 382
10.4 Random-Effects Models......Page 384
Random-Effects Likelihood......Page 385
Serial Correlation and Overdispersion......Page 386
Computational Considerations......Page 388
10.5.1 Maximum Likelihood Estimation for Canonical Links......Page 389
10.5.2 Conditional Maximum Likelihood Estimation for Canonical Links......Page 391
10.5.3 Poisson Distribution......Page 392
10.6 Bayesian Inference......Page 394
10A.1 Moment-Generating Function......Page 398
10A.2 Sufficiency......Page 400
10A.3 Conjugate Distributions......Page 401
10A.4 Marginal Distributions......Page 402
Exercises and Extensions......Page 404
11.1 Homogeneous Models......Page 405
11.1.1 Statistical Inference......Page 406
Parameter Interpretations......Page 407
11.1.3 Multinomial (Conditional) Logit......Page 409
11.1.4 Random-Utility Interpretation......Page 412
11.1.6 Generalized Extreme-Value Distribution......Page 414
11.2 Multinomial Logit Models with Random Effects......Page 416
Relation with Nonlinear Random-Effects Poisson Model......Page 417
11.3 Transition (Markov) Models......Page 418
Unordered Categorical Response......Page 419
Higher Order Markov Models......Page 426
11.4 Survival Models......Page 429
Appendix 11A Conditional Likelihood Estimation for Multinomial Logit Models with Heterogeneity Terms......Page 433
A.1 Basic Terminology......Page 435
A.3 Additional Definitions......Page 436
A.4 Matrix Decompositions......Page 437
A.5 Partitioned Matrices......Page 438
A.6 Kronecker (Direct) Product......Page 439
B.2 Multivariate Normal Distribution......Page 440
B.4 Conditional Distributions......Page 441
C.1 Characteristics of Likelihood Functions......Page 442
C.2 Maximum Likelihood Estimators......Page 443
C.3 Iterated Reweighted Least Squares......Page 444
C.5 Quasi-Likelihood......Page 445
C.6 Estimating Equations......Page 446
C.7 Hypothesis Tests......Page 449
C.8 Goodness-of-Fit Statistics......Page 450
C.9 Information Criteria......Page 451
D.1 Basic State Space Model......Page 452
D.2 Kalman Filter Algorithm......Page 453
D.4 Extended State Space Model and Mixed Linear Models......Page 454
D.5 Likelihood Equations for Mixed Linear Models......Page 455
Appendix E Symbols and Notation......Page 457
Appendix F Selected Longitudinal and Panel Data Sets......Page 463
Biological Sciences Longitudinal Data References (B)......Page 469
Econometrics Panel Data References (E)......Page 470
Educational Science and Psychology References (EP)......Page 473
Other Social Science References (O)......Page 474
Statistical Longitudinal Data References (S)......Page 476
General Statistics References (G)......Page 478
Index......Page 481

✦ Subjects

Финансово-экономические дисциплины;Статистический анализ экономических данных;