Ecological Inference: New Methodological Strategies (Analytical Methods for Social Research)

Cover......Page 1
Half-title......Page 3
Series-title......Page 4
Title......Page 5
Copyright......Page 6
Contents......Page 7
Contributors......Page 9
Preface......Page 11
1 Prior and Likelihood Choices in the Analysis of Ecological Data......Page 13
0.1.2 Deterministic and Statistical Approaches......Page 14
0.1.2.1 Extracting Deterministic Information: The Method of Bounds......Page 15
0.1.3 Extracting Both Deterministic and Statistical Information: King’s EI Approach......Page 16
0.1.4 King, Rosen, and Tanner’s Hierarchical Model......Page 20
0.2 NEW SOURCES OF INFORMATION IN ECOLOGICAL INFERENCE......Page 21
REFERENCES......Page 23
1.1 INTRODUCTION......Page 25
1.2 THE FUNDAMENTAL DIFFICULTY OF ECOLOGICAL INFERENCE......Page 27
1.3 LIKELIHOOD FUNCTION......Page 32
1.4 PRIORS......Page 37
1.5.1 Derivation of the Posterior Distribution......Page 40
1.5.2 Markov Chain Monte Carlo Algorithms......Page 41
1.5.3 Auxiliary Variables Scheme......Page 42
1.5.4 Rejection Algorithm for Individual Tables......Page 43
1.6 A SIMPLE EXAMPLE......Page 44
1.7.1 County 150......Page 45
1.7.2 County 50......Page 54
BASELINE MODELS......Page 55
HIERARCHICAL MODELS......Page 57
1.8 DISCUSSION......Page 58
APPENDIX......Page 60
REFERENCES......Page 61
2.1 INTRODUCTION......Page 63
2.2 INFORMATION LOST BY AGGREGATION......Page 64
2.3.2 Analysis Using Individual-Level Data......Page 66
2.3.3 Analysis Using Aggregate Data......Page 68
2.4 USING AGGREGATE AND UNIT-LEVEL DATA......Page 72
2.5 EXAMPLE......Page 73
2.6 DISCUSSION......Page 79
REFERENCES......Page 80
INTRODUCTION......Page 81
HOW ECOLOGICAL ANALYSIS KILLED ECOLOGICAL INFERENCE......Page 82
ENTER THE METHOD OF BOUNDS......Page 85
IF IT IS SO USEFUL, THEN WHY ALL THE CRITICISM?”......Page 88
Why King’s Method Performs Better with Poor Data......Page 89
Why King’s Method Performed Poorly with Horrible Data......Page 90
APPLYING EI WITH INFORMATIVE DATA OR CONTEXTUAL KNOWLEDGE......Page 92
County-Level Racial Voting Behavior......Page 93
Precinct-Level Racial Voting Behavior......Page 97
Moving Beyond Aggregate Data......Page 102
CONCLUSION......Page 104
REFERENCES......Page 105
4.1 INTRODUCTION......Page 109
4.2 KING’S EI MODEL......Page 110
4.2.1 MCMC Estimation of EI......Page 112
4.2.2 Ecological Inference in Several Elections at Once......Page 113
4.3 ESTIMATING THE TRUNCATED BIVARIATE NORMAL PARAMETERS WHEN THE DEGREE OF TRUNCATION IS LARGE......Page 115
4.4.1 Validating the SUEI Model......Page 117
4.4.2 Investigating SUEI Efficiency Gains......Page 120
4.5 TURNOUT BY RACE IN VIRGINIA ELECTIONS......Page 124
4.6 DISCUSSION......Page 132
REFERENCES......Page 133
5.1 INTRODUCTION......Page 135
5.1.1 Background......Page 136
5.1.2 Proposed Methods......Page 137
5.2 ANALYZING THE LINK BETWEEN INDIVIDUAL BEHAVIOR AND BEHAVIOR RECORDED AT THE AGGREGATE LEVEL......Page 138
5.2.1 Tomographic Plots......Page 140
5.3 A SIMPLE DISTANCE MINIMIZATION ALGORITHM FOR ECOLOGICAL INFERENCE: METHOD I......Page 141
5.4.1 Adapting our Previous Distance Minimization Algorithm for Use in (m, b) Space Rather than (betab, betaw) Space: Method II......Page 145
5.4.3 Defining the Cone of Feasible Values......Page 146
5.5 COMPARING THE KING ECOLOGICAL INFERENCE ESTIMATES AND THOSE OF OUR SIMPLIFIED APPROACHES......Page 148
5.5.1 Weighting by Informativeness......Page 149
5.6 DISCUSSION......Page 151
APPENDIX 1. PROOF OF THEOREM 1......Page 152
APPENDIX 2. AREA CALCULATIONS FOR METHOD III......Page 153
REFERENCES......Page 154
6.1 INTRODUCTION......Page 156
6.2 DATA......Page 157
6.3 USING ECOLOGICAL INFERENCE TO ESTIMATE MALE AND FEMALE TURNOUT......Page 159
6.4 NONSAMPLE INFORMATION AND ECOLOGICAL INFERENCE......Page 161
6.5 INTRODUCING PRIOR INFORMATION......Page 162
6.6 FINDINGS......Page 164
6.6.1 Implications of Changes in the Expected Mean of Male Turnout......Page 165
6.6.2 Implications of Changes in the Precision of the Expected Mean Male Turnout......Page 166
6.6.3 Implications of Changes in the Parameters of the Gamma Distribution......Page 167
6.7 USING MCD-LEVEL ASSUMPTIONS TO IMPROVE ESTIMATES......Page 168
6.8 CONCLUSION......Page 172
REFERENCES......Page 173
7.1 INTRODUCTION......Page 174
7.2 NOTATION AND BASIC INVERSE MODEL......Page 175
7.2.1 Modeling Voting Behavior as an Inverse Problem......Page 176
7.3.1 Choosing the Criterion Function......Page 178
7.3.2 Solution to a Pure Inverse Problem......Page 180
7.3.3 Incorporating Bounds on the Conditional Probabilities......Page 181
7.3.4.1 Incorporating Bounds on the Characteristics of the Noise......Page 182
7.3.4.2 The Solution......Page 183
7.3.5 Remarks......Page 184
7.4 RECOVERING INFORMATION ON INDIVIDUAL BEHAVIOR......Page 185
7.4.1 Moment-Based Model Formulation......Page 186
7.4.2 The Discrete Choice Voter Response Model......Page 188
7.4.2.1 Remarks......Page 190
7.5 IMPLICATIONS......Page 191
Information-Theoretic Formulation......Page 192
Variants of King’s Ohio Voter Problem......Page 194
Moment-Based Formulation......Page 197
REFERENCES......Page 198
8.1 INTRODUCTION......Page 200
8.2.1 Binary Transition Model......Page 202
8.2.2.1 Maximum Likelihood Estimation......Page 205
8.2.2.3 Markov Chain Monte Carlo Simulation......Page 207
8.3.1 PC Penetration in Dutch Households......Page 208
8.3.2.1 Maximum Likelihood......Page 209
8.3.2.2 Parametric Bootstrap......Page 211
8.3.3 Dynamic Panel Model......Page 212
8.3.4 Samples of Independent Observations......Page 214
8.4 SUMMARY......Page 215
REFERENCES......Page 216
9.1 INTRODUCTION......Page 219
9.2.1 Likelihood......Page 220
9.2.2 Prior Specification......Page 221
9.3 MODEL FITTING......Page 223
9.4 SIMULATED DATA EXAMPLES......Page 224
9.5 APPLICATION: VOTER REGISTRATION IN LOUISIANA, 1975–1988......Page 228
9.6 DISCUSSION......Page 236
REFERENCES......Page 243
10.1 INTRODUCTION......Page 245
10.2 THE MODIFIABLE AREAL UNIT PROBLEM......Page 246
10.3 SPATIAL STATISTICS AND THE CHANGE-OF-SUPPORT PROBLEM......Page 247
10.4.1 Spatial Smoothing of Aggregated Data......Page 249
10.4.2 Case Study: Georgia Health Care District 9......Page 251
REFERENCES......Page 255
11.1 INTRODUCTION......Page 257
11.2 CONTEXTUAL EFFECTS AND GLOBAL RELATIONSHIPS......Page 258
11.3 LINEAR RELATIONSHIPS AND NON-LINEAR SPACES......Page 259
11.4.1 Contiguity......Page 261
11.4.2 Distance Weights: GWR......Page 262
11.5 THE PROCEDURE......Page 264
11.6 A SIMPLE MONTE CARLO TEST OF THE GW-AR APPROACH TO ECOLOGICAL INFERENCE......Page 265
11.7 AN ECOLOGICAL INFERENCE OF THE PERONIST TURNOUT IN 1999 IN THE CITY OF BUENOS AIRES......Page 270
11.8 CONCLUDING REMARKS......Page 274
The Winbugs Model......Page 275
REFERENCES......Page 276
12.1 INTRODUCTION......Page 278
12.2 NOTATION AND PROBLEM FORMULATION......Page 279
12.3 SPATIALLY STRUCTURED REGISTRATION PROBABILITIES......Page 281
12.4.1.2 Stage 2......Page 283
12.4.1.3 Stage 3......Page 286
12.4.2 Simulation from the Prior......Page 287
12.4.3 Implementation......Page 295
12.5 SIMULATIONS......Page 296
12.6.1 Analysis Based on Internal Data......Page 299
12.6.2 Analysis Based Solely on Margins......Page 304
12.7 DISCUSSION......Page 308
12.A.2 Autocorrelation Statistics......Page 310
12.A.3 WinBUGS Code......Page 311
REFERENCES......Page 312
13.1 INTRODUCTION......Page 315
13.2 ECOLOGICAL INFERENCE IN EPIDEMIOLOGY......Page 317
13.3 STATISTICAL MODEL......Page 318
13.4 SOURCES OF ECOLOGICAL BIAS......Page 321
13.4.1 Unmeasured Confounding......Page 325
13.4.3 Parameters That Vary between Areas......Page 327
13.5.1 Ecological Bias in Epidemiology......Page 328
13.5.2 Overdispersion and Random Effects......Page 329
13.5.4 Sensitivity to an Unmeasured Confounder......Page 331
13.6.1 Ecological Inference for 2×2 Tables......Page 334
13.6.2 Fractions versus Probabilities......Page 335
13.6.3 Probabilities That Vary between Areas......Page 336
13.7 RELATIONSHIP BETWEEN MODELS IN EPIDEMIOLOGY AND SOCIAL SCIENCE......Page 339
13.8 CONCLUSIONS......Page 341
REFERENCES......Page 342
INTRODUCTION......Page 345
Electoral Politics and Background......Page 347
A Model of Voting Behavior in Italy’s Mixed-Member System......Page 348
Formal Statement of the Model......Page 349
Reexpressing the Estimation Problem......Page 351
Reducing the Parameter Space......Page 352
Aggregation Bias and Covariates......Page 353
RESULTS......Page 355
EI Diagnostics......Page 358
DISCUSSION......Page 359
REFERENCES......Page 361
15.1 INTRODUCTION......Page 363
15.2 NOTATION AND PROBLEM FEATURES......Page 364
15.3 GOODMAN REGRESSION......Page 367
15.4 KING’S TBN METHOD......Page 368
15.5.1 Mattos and Veiga’s Version......Page 369
15.5.2 KRT’s Version......Page 371
15.6 MONTE CARLO EXPERIMENTS......Page 372
15.7.1 Differences between the EI models......Page 373
15.7.3 Potential Situations......Page 375
SIMULATING THE TBN DATA (FIRST PART)......Page 376
SIMULATING THE BBH DATA (SECOND PART)......Page 377
15.7.5 Evaluation and Comparison Indicators......Page 378
15.8.1 First Part......Page 379
15.8.2 Second Part......Page 384
15.8.3 Discussion......Page 387
15.9 CONCLUSION......Page 389
Conversion to Frequencies......Page 390
APPENDIX 2. SIMULATING FROM A BIVARIATE BBH DISTRIBUTION......Page 391
APPENDIX 3......Page 392
REFERENCES......Page 393
16.1 INTRODUCTION......Page 395
16.2.2 Nonlinear Optimization......Page 397
16.3 ASSESSING THE NUMERICAL ACCURACY OF STATISTICAL ESTIMATES......Page 398
16.3.2 Measuring Accuracy and Stability......Page 399
16.3.2.1 Using Data Perturbations for Sensitivity Analysis......Page 401
16.3.2.3 Some Practical Details of Applying the Perturbation Method......Page 402
16.4.1 Goodman’s Regression......Page 404
16.4.2 Achen and Shively’s Quadratic Model......Page 405
16.4.3 King’s EI......Page 406
16.4.5 Observations and Evaluations: Sensitivity and Correctness......Page 408
16.5 CONCLUSION......Page 417
REFERENCES......Page 418
Index......Page 421