Statistical Models and Causal Inference: A Dialogue with the Social Sciences

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 13
Editors’ Introduction: Inference and Shoe Leather......Page 15
Notes......Page 18
Part I Statistical Modeling: Foundations and Limitations......Page 19
1 Issues in the Foundations of Statistics: Probability and Statistical Models......Page 21
1.2 The objectivist position......Page 22
1.3 The subjectivist position......Page 23
1.3.1 Probability and relative frequency......Page 24
1.4 A critique of the subjectivist position......Page 25
1.4.1 Other arguments for the Bayesian position......Page 26
1.5.1 Examples......Page 29
1.5.3 Statistical models and the problem of induction......Page 33
Notes......Page 34
Acknowledgments......Page 39
2.1 Introduction......Page 41
2.2 Treating the data as a population......Page 43
2.3 Assuming a real population and an imaginary sampling mechanism......Page 44
2.5 When the statistical issues are substantive......Page 45
2.6.1 Violations of independence......Page 47
2.7.1 Spatial dependence......Page 49
2.7.3 Time series models......Page 50
2.7.4 Meta-analysis......Page 51
2.7.5 Observational studies and experiments......Page 55
2.8 Recommendations for practice......Page 56
Notes......Page 58
3.1 Introduction......Page 63
3.2 Some examples from Epidemiology......Page 65
3.3 Some examples from the Social Sciences......Page 71
3.4 Summary of the position......Page 73
3.5 Can technical fixes rescue the models?......Page 75
3.6 Other literature......Page 77
Acknowledgments......Page 80
Part II Studies in Political Science, Public Policy, and Epidemiology......Page 81
4.1 Introduction......Page 83
4.2 The census......Page 84
4.3 Demographic analysis......Page 85
4.4 DSE—Dual System Estimator......Page 86
4.5 Small-area estimation......Page 87
4.6 State shares......Page 89
4.8 Census 2000......Page 90
4.9 The adjustment decision for Census 2000......Page 91
4.10 Gross or net?......Page 93
4.11 Heterogeneity in 2000......Page 94
4.12 Loss function analysis......Page 97
4.13 Pointers to the literature......Page 98
4.15 Other countries......Page 99
Note......Page 100
5.1 Introduction......Page 101
5.3 Empirical results......Page 105
5.4 Diagnostics......Page 106
5.7 Counting success......Page 107
5.9 Other literature......Page 108
5.10 Some details......Page 109
5.11 The extended model......Page 112
5.12 Identifiability and other a priori arguments......Page 113
5.13 Summary and conclusions......Page 114
6.1 Introduction......Page 115
6.2 Model comparisons......Page 116
6.3 Diagnostics......Page 118
6.5 Making the data available......Page 121
6.6 Summary and conclusions......Page 122
7.1 Introduction......Page 123
7.2 The paradox......Page 124
7.3 Case selection......Page 125
7.A.2 Simple random samples......Page 128
7.A.4 Samples and inductive inference......Page 129
7.A.7 The odds ratio......Page 130
Notes......Page 131
Acknowledgments......Page 132
8.1 Introduction......Page 133
8.2.1 Symmetryand equallylik elyoutcomes......Page 134
8.2.4 The principle of insufficient reason......Page 135
8.2.6 Mathematical probability: Kolmogorov’s axioms......Page 137
8.2.7 Probabilitymodels......Page 138
8.3 The USGS earthquake forecast......Page 139
8.4 A view from the past......Page 142
Notes......Page 144
9 Salt and Blood Pressure: Conventional Wisdom Reconsidered......Page 149
9.2 The Intersalt study......Page 150
9.3 Units for salt and blood pressure......Page 152
9.4 Patterns in the Intersalt data......Page 153
9.6 The protocol......Page 157
9.7 Human experiments......Page 159
9.8 Publication bias......Page 161
9.9 DASH—Dietary Approaches to Stop Hypertension......Page 162
9.10 Health effects of salt......Page 163
9.11 Back to Intersalt......Page 164
9.12 The salt epidemiologists respond......Page 165
Acknowledgments......Page 167
10.1 Introduction......Page 169
10.2 The swine flu vaccine and GBS......Page 171
10.3 The Manko case......Page 174
10.3.1 Completeness of reporting......Page 176
10.3.3 Individual differences......Page 177
Notes......Page 179
Acknowledgments......Page 184
11 Survival Analysis: An Epidemiological Hazard?......Page 187
11.2 Hazard rates......Page 188
11.3 The Kaplan-Meier estimator......Page 190
11.4 An application of the Kaplan-Meier estimator......Page 192
11.5 The proportional-hazards model in brief......Page 193
11.5.1 A mathematical diversion......Page 195
11.6 An application of the proportional-hazards model......Page 196
11.6.1 The crucial questions......Page 198
11.7.1 Nurses’ Health Study: Observational......Page 199
11.7.2 Women’s Health Initiative: Experimental......Page 200
11.7.3 Were the observational studies right, or the experiments?......Page 201
11.8 Simulations......Page 202
11.8.1 The model works......Page 203
11.8.2 The model does not work......Page 204
11.10 What is the bottom line?......Page 206
11.11 Where do we go from here?......Page 207
11.A Appendix: The delta method in more detail......Page 208
Acknowledgments......Page 210
Part III New Developments: Progress or Regress?......Page 211
12.1 Introduction......Page 213
12.2 Asymptotics for multiple-regression estimators......Page 218
12.3 Asymptotic nominal variances......Page 221
12.4 The gain from adjustment......Page 222
12.5 Finite-sample results......Page 224
12.6 Recommendations for practice......Page 227
12.A Technical appendix......Page 228
Acknowledgments......Page 236
13.1 Introduction......Page 237
13.2.1 The intention-to-treat principle......Page 238
13.3.1 Interpreting the coefficients in the model......Page 239
13.3.3 What if the logit model is right?......Page 240
13.4 A plug-in estimator for the log odds......Page 242
13.5 Simulations......Page 243
13.6 Extensions and implications......Page 245
13.7 Literature review......Page 246
13.8 Sketch of proofs......Page 248
13.8.2 Summing up......Page 258
13.9 An inequality......Page 259
Acknowledgments......Page 260
14 The Grand Leap......Page 261
Notes......Page 269
15 On Specifying Graphical Models for Causation, and the Identification Problem......Page 273
15.1 A first example: Simple regression......Page 274
15.2 Conditionals......Page 277
15.3 Two linear regressions......Page 278
15.4 Simultaneous equations......Page 280
15.5 Nonlinear models: Figure 15.1 revisited......Page 283
15.6 Technical notes......Page 284
15.7 More complicated examples......Page 285
15.8 Parametric nonlinear models......Page 288
15.9 Concomitants......Page 289
15.10 The story behind Figures 15.3 and 15.4......Page 290
15.11 Models and kernels revisited......Page 292
15.12 Literature review......Page 293
Acknowledgments......Page 296
16 Weighting Regressions by Propensity Scores......Page 297
16.1 Simulation #1......Page 299
16.2 Results for Simulation #2......Page 303
16.4 Discussion......Page 305
16.5 Literature review......Page 307
16.6 Theory......Page 309
16.8 Contrasts......Page 310
16.9 Contrasts vs structural equations......Page 311
Acknowledgments......Page 312
17.1 Introduction......Page 313
17.2 Robust standard errors......Page 317
17.4 A possible extension......Page 318
17.6 The linear case......Page 319
17.8 What about Huber?......Page 320
17.9 Summary and conclusions......Page 321
Acknowledgments......Page 322
18.1 Introduction......Page 323
18.2 Aprobit response model with an endogenous regressor......Page 324
18.3 Aprobit model with endogenous sample selection......Page 329
18.4 Numerical issues......Page 331
18.5 Implications for practice......Page 332
18.6 Motivating the estimator......Page 333
18.7 Identifiability......Page 334
18.8 Some relevant literature......Page 338
Acknowledgments......Page 339
19.1. Introduction......Page 341
19.2. Specific models......Page 348
19.3. Discussion......Page 350
19.5. Recommendations......Page 351
Acknowledgments......Page 352
Part IV Shoe Leather Revisited......Page 353
20 On Types of Scientific Inquiry: The Role of Qualitative Reasoning......Page 355
20.1 Jenner and vaccination......Page 356
20.2 Semmelweis and puerperal fever......Page 358
20.3 Snow and cholera......Page 359
20.4 Eijkman and beriberi......Page 362
20.5 Goldberger and pellagra......Page 365
20.6 McKay and fluoridation......Page 366
20.7 Flemingand penicillin......Page 367
20.8 Gregg and German measles......Page 368
20.10 Conclusions......Page 369
20.11 Further reading......Page 370
Acknowledgments......Page 374
References and Further Reading......Page 375
Index......Page 411