A solution to the ecological inference problem: reconstructing individual behavior from aggregate data
This book provides a solution to the ecological inference problem, which has plagued users of statistical methods for over 75 years: How can researchers reliably infer individual-level behavior from aggregate (ecological) data? In political science, this question arises when individual-level surveys...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ [u.a.]
Princeton Univ. Press
1997
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book provides a solution to the ecological inference problem, which has plagued users of statistical methods for over 75 years: How can researchers reliably infer individual-level behavior from aggregate (ecological) data? In political science, this question arises when individual-level surveys are unavailable (for instance, local or comparative electoral politics), unreliable (racial politics), insufficient (political geography), or infeasible (political history). This ecological inference problem also confronts researchers in numerous areas of major significance in public policy, and other academic disciplines, ranging from epidemiology and marketing to sociology and quantitative history. Although many have attempted to make such cross-level inferences, scholars agree that all existing methods yield very inaccurate conclusions about the world. In this volume, Gary King lays out a unique - and reliable - solution to this venerable problem. |
| Beschreibung: | XXII, 342 S. graph. Darst. |
| ISBN: | 0691012415 0691012407 |
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| 520 | 3 | |a This book provides a solution to the ecological inference problem, which has plagued users of statistical methods for over 75 years: How can researchers reliably infer individual-level behavior from aggregate (ecological) data? In political science, this question arises when individual-level surveys are unavailable (for instance, local or comparative electoral politics), unreliable (racial politics), insufficient (political geography), or infeasible (political history). This ecological inference problem also confronts researchers in numerous areas of major significance in public policy, and other academic disciplines, ranging from epidemiology and marketing to sociology and quantitative history. Although many have attempted to make such cross-level inferences, scholars agree that all existing methods yield very inaccurate conclusions about the world. In this volume, Gary King lays out a unique - and reliable - solution to this venerable problem. | |
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| 650 | 4 | |a Science politique - Méthodes statistiques | |
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Datensatz im Suchindex
| _version_ | 1804125998845788160 |
|---|---|
| adam_text | Contents
List of Figures xi
List of Tables xiii
Preface xv
Part I: Introduction 1
1 Qualitative Overview 3
1.1 The Necessity of Ecological Inferences 7
1.2 The Problem 12
1.3 The Solution 17
1.4 The Evidence 22
1.5 The Method 26
2 Formal Statement of the Problem 28
Part II: Catalog of Problems to Fix 35
3 Aggregation Problems 37
3.1 Goodman s Regression: A Definition 37
3.2 The Indeterminacy Problem 39
3.3 The Grouping Problem 46
3.4 Equivalence of the Grouping and
Indeterminacy Problems 53
3.5 A Concluding Definition 54
4 Non Aggregation Problems 56
4.1 Goodman Regression Model Problems 56
4.2 Applying Goodman s Regression in 2 x 3 Tables 68
4.3 Double Regression Problems 71
4.4 Concluding Remarks 73
Part III: The Proposed Solution 75
5 The Data: Generalizing the Method of Bounds 77
5.1 Homogeneous Precincts: No Uncertainty 78
viii Contents
5.2 Heterogeneous Precincts: Upper and Lower Bounds 79
5.2.1 Precinct Level Quantities of Interest 79
5.2.2 District Level Quantities of Interest 83
5.3 An Easy Visual Method for Computing Bounds 85
6 The Model 91
6.1 The Basic Model 92
6.2 Model Interpretation 94
6.2.1 Observable Implications of Model Parameters 96
6.2.2 Parameterizing the Truncated Bivariate Normal 102
6.2.3 Computing 2p Parameters from Only p Observations 106
6.2.4 Connections to the Statistics of Medical and Seismic
Imaging 112
6.2.5 Would a Model of Individual Level Choices Help? 119
7 Preliminary Estimation 123
7.1 A Visual Introduction 124
7.2 The Likelihood Function 132
7.3 Parameterizations 135
7.4 Optional Priors 138
7.5 Summarizing Information about Estimated Parameters 139
8 Calculating Quantities of Interest 141
8.1 Simulation Is Easier than Analytical Derivation 141
8.1.1 Definitions and Examples 142
8.1.2 Simulation for Ecological Inference 144
8.2 Precinct Level Quantities 145
8.3 District Level Quantities 149
8.4 Quantities of Interest from Larger Tables 151
8.4.1 A Multiple Imputation Approach 151
8.4.2 An Approach Related to Double Regression 153
8.5 Other Quantities of Interest 156
9 Model Extensions 158
9.1 What Can Go Wrong? 158
9.1.1 Aggregation Bias 159
9.1.2 Incorrect Distributional Assumptions 161
9.1.3 Spatial Dependence 164
9.2 Avoiding Aggregation Bias 168
9.2.2 Using External Information 169
Contents ix
9.2.2 Unconditional Estimation: X, as a Covariate 174
9.2.3 Tradeoffs and Priors for the Extended Model 179
9.2.4 Ex Post Diagnostics 183
9.3 Avoiding Distributional Problems 184
9.3.2 Parametric Approaches 185
9.3.2 A Nonparametric Approach 191
Part IV: Verification 197
10 A Typical Application Described in Detail: Voter
Registration by Race 199
10.1 The Data 199
10.2 Likelihood Estimation 200
10.3 Computing Quantities of Interest 207
10.3.1 Aggregate 207
20.3.2 County Level 209
20.3.3 Other Quantities of Interest 215
11 Robustness to Aggregation Bias: Poverty Status by Sex 217
11.1 Data and Notation 217
11.2 Verifying the Existence of Aggregation Bias 218
11.3 Fitting the Data 220
11.4 Empirical Results 222
12 Estimation without Information: Black Registration in
Kentucky 226
12.1 The Data 226
12.2 Data Problems 227
12.3 Fitting the Data 228
12.4 Empirical Results 232
13 Classic Ecological Inferences 235
13.1 Voter Transitions 235
13.2.2 Data 235
23.2.2 Estimates 238
13.2 Black Literacy in 1910 241
Part V: Generalizations and Concluding Suggestions 247
14 Non Ecological Aggregation Problems 249
14.1 The Geographer s Modifiable Areal Unit Problem 249
x Contents
24.2.1 The Problem with the Problem 250
24.2.2 Ecological Inference as a Solution to the Modifiable
Areal Unit Problem 252
14.2 The Statistical Problem of Combining Survey and
Aggregate Data 255
14.3 The Econometric Problem of Aggregating
Continuous Variables 258
14.4 Concluding Remarks on Related Aggregation
Research 262
15 Ecological Inference in Larger Tables 263
15.1 An Intuitive Approach 264
15.2 Notation for a General Approach 267
15.3 Generalized Bounds 269
15.4 The Statistical Model 271
15.5 Distributional Implications 273
15.6 Calculating the Quantities of Interest 276
15.7 Concluding Suggestions 276
16 A Concluding Checklist 277
Part VI: Appendices 293
A Proof That All Discrepancies Are Equivalent 295
B Parameter Bounds 301
B.I Homogeneous Precincts 301
B.2 Heterogeneous Precincts: /3 s and 6 s 302
B.3 Heterogeneous Precincts: A, s 303
C Conditional Posterior Distribution 304
C.I Using Bayes Theorem 305
C.2 Using Properties of Normal Distributions 306
D The Likelihood Function 307
E The Details of Nonparametric Estimation 309
F Computational Issues 311
Glossary of Symbols 313
References 317
Index 337
Figures
1.1 Model Verification: Voter Turnout among African
Americans in Louisiana Precincts 23
1.2 Non Minority Turnout in New Jersey Cities and Towns 25
3.1 How a Correlation between the Parameters and X,
Induces Bias 41
4.1 Scatter Plot of Precincts in Marion County, Indiana:
Voter Turnout for the U.S. Senate by Fraction Black, 1990 60
4.2 Evaluating Population Based Weights 64
4.3 Typically Massive Heteroskedasticity in Voting Data 66
5.1 A Data Summary Convenient for Statistical Modeling 81
5.2 Image Plots of Upper and Lower Bounds on $ 86
5.3 Image Plots of Upper and Lower Bounds on fif 87
5.4 Image Plots of Width of Bounds 88
5.5 A Scattercross Graph of Voter Turnout by Fraction
Hispanic 89
6.1 Features of the Data Generated by Each Parameter 100
6.2 Truncated Bivariate Normal Distributions 105
6.3 A Tomography Plot 114
6.4 Truncated Bivariate Normal Surface Plot 116
7.1 Verifying Individual Level Distributional Assumptions
with Aggregate Data 126
7.2 Observable Implications for Sample Parameter Values 127
7.3 Likelihood Contour Plots 137
8.1 Posterior Distributions of Precinct Parameters I3b, 148
8.2 Support of the Joint Distribution of 0* and )3f with
Bounds Specified for Drawing A* 155
9.1 The Worst of Aggregation Bias: Same Truth, Different
Observable Implications 160
9.2 The Worst of Distributional Violations: Different True
Parameters, Same Observable Implications 163
9.3 Conclusive Evidence of Aggregation Bias from
Aggregate Data 176
9.4 Profile Likelihood 178
9.5 Controlling for Aggregation Bias 179
9.6 Extended Model Tradeoffs 180
9.7 A Tomography Plot with Evidence of Multiple Modes 187
9.8 Building a Nonparametric Density Estimate 194
9.9 Nonparametric Density Estimate for a Difficult Case 195
xii Figures
10.1 A Scattercross Graph for Southern Counties, 1968 201
10.2 Tomography Plot of Southern Race Data with
Maximum Likelihood Contours 204
10.3 Scatter Plot with Maximum Likelihood Results
Superimposed 206
10.4 Posterior Distribution of the Aggregate Quantities of
Interest 208
10.5 Comparing Estimates to the Truth at the County Level 210
10.6 27,500 Simulations of /3f 212
10.7 Verifying Uncertainty Estimates 213
10.8 275 Lines Fit to 275 Points 214
11.1 South Carolina Tomography Plot 221
11.2 Posterior Distributions of the State Wide Fraction in
Poverty by Sex in South Carolina 222
11.3 Fractions in Poverty for 3,187 South Carolina Block
Groups 223
11.4 Percentiles at Which True Values Fall 224
12.1 A Scattercross Graph of Fraction Black by Fraction
Registered 227
12.2 Tomography Plot with Parametric Contours and a
Nonparametric Surface Plot 229
12.3 Posterior Distributions of the State Wide Fraction of
Blacks and Whites Registered 231
12.4 Fractions Registered at the County Level 232
12.5 80% Posterior Confidence Intervals by True Values 233
13.1 Fulton County Voter Transitions 236
13.2 Aggregation Bias in Fulton County Data 238
13.3 Fulton County Tomography Plot 239
13.4 Comparing Voter Transition Rate Estimates with the
Truth in Fulton County 241
13.5 Alternative Fits to Literacy by Race Data 242
13.6 Black Literacy Tomography Plot and True Points 243
13.7 Comparing Estimates to the County Level Truth in
Literacy by Race Data 244
Tables
1.1 The Ecological Inference Problem at the District Level 13
1.2 The Ecological Inference Problem at the Precinct Level 14
1.3 Sample Ecological Inferences 16
2.1 Basic Notation for Precinct i 29
2.2 Alternative Notation for Precinct i 31
2.3 Simplified Notation for Precinct i 31
4.1 Comparing Goodman Model Parameters to the
Parameters of Interest in the 2x3 Table 70
9.1 Consequences of Spatial Autocorrelation: Monte Carlo
Evidence 168
9.2 Consequences of Distributional Misspecification: Monte
Carlo Evidence 189
10.1 Maximum Likelihood Estimates 202
10.2 Reparameterized Maximum Likelihood Estimates 203
10.3 Verifying Estimates of jt 207
11.1 Evidence of Aggregation Bias in South Carolina 219
11.2 Goodman Model Estimates: Poverty by Sex 220
12.1 Evidence of Aggregation Bias in Kentucky 228
12.2 80% Confidence Intervals for t/ and 4 230
15.1 Example of a Larger Table 265
15.2 Notation for a Large Table 268
|
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| indexdate | 2024-07-09T18:10:28Z |
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| isbn | 0691012415 0691012407 |
| language | English |
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| spelling | King, Gary 1958- Verfasser (DE-588)135604311 aut A solution to the ecological inference problem reconstructing individual behavior from aggregate data Gary King Princeton, NJ [u.a.] Princeton Univ. Press 1997 XXII, 342 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier This book provides a solution to the ecological inference problem, which has plagued users of statistical methods for over 75 years: How can researchers reliably infer individual-level behavior from aggregate (ecological) data? In political science, this question arises when individual-level surveys are unavailable (for instance, local or comparative electoral politics), unreliable (racial politics), insufficient (political geography), or infeasible (political history). This ecological inference problem also confronts researchers in numerous areas of major significance in public policy, and other academic disciplines, ranging from epidemiology and marketing to sociology and quantitative history. Although many have attempted to make such cross-level inferences, scholars agree that all existing methods yield very inaccurate conclusions about the world. In this volume, Gary King lays out a unique - and reliable - solution to this venerable problem. Aggregatie gtt Inferencia Inférence (Logique) Politieke wetenschappen gtt Science politique - Méthodes statistiques Inference Political statistics Interferenz (DE-588)4197629-0 gnd rswk-swf Interferenz Ökologie (DE-588)4261387-5 gnd rswk-swf Umweltschutz (DE-588)4061644-7 gnd rswk-swf (DE-588)4056995-0 Statistik gnd-content Umweltschutz (DE-588)4061644-7 s Interferenz (DE-588)4197629-0 s DE-604 Interferenz Ökologie (DE-588)4261387-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007723147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | King, Gary 1958- A solution to the ecological inference problem reconstructing individual behavior from aggregate data Aggregatie gtt Inferencia Inférence (Logique) Politieke wetenschappen gtt Science politique - Méthodes statistiques Inference Political statistics Interferenz (DE-588)4197629-0 gnd Interferenz Ökologie (DE-588)4261387-5 gnd Umweltschutz (DE-588)4061644-7 gnd |
| subject_GND | (DE-588)4197629-0 (DE-588)4261387-5 (DE-588)4061644-7 (DE-588)4056995-0 |
| title | A solution to the ecological inference problem reconstructing individual behavior from aggregate data |
| title_auth | A solution to the ecological inference problem reconstructing individual behavior from aggregate data |
| title_exact_search | A solution to the ecological inference problem reconstructing individual behavior from aggregate data |
| title_full | A solution to the ecological inference problem reconstructing individual behavior from aggregate data Gary King |
| title_fullStr | A solution to the ecological inference problem reconstructing individual behavior from aggregate data Gary King |
| title_full_unstemmed | A solution to the ecological inference problem reconstructing individual behavior from aggregate data Gary King |
| title_short | A solution to the ecological inference problem |
| title_sort | a solution to the ecological inference problem reconstructing individual behavior from aggregate data |
| title_sub | reconstructing individual behavior from aggregate data |
| topic | Aggregatie gtt Inferencia Inférence (Logique) Politieke wetenschappen gtt Science politique - Méthodes statistiques Inference Political statistics Interferenz (DE-588)4197629-0 gnd Interferenz Ökologie (DE-588)4261387-5 gnd Umweltschutz (DE-588)4061644-7 gnd |
| topic_facet | Aggregatie Inferencia Inférence (Logique) Politieke wetenschappen Science politique - Méthodes statistiques Inference Political statistics Interferenz Interferenz Ökologie Umweltschutz Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007723147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kinggary asolutiontotheecologicalinferenceproblemreconstructingindividualbehaviorfromaggregatedata |