{"product_id":"a-solution-to-the-ecological-inference-problem-9780691012407","title":"A Solution to the Ecological Inference Problem","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides a solution to the ecological inference problem, which has plagued users of statistical methods for over seventy-five years: How can researchers reliably infer individual-level behavior from aggregate (ecological) data? This work begins with a qualitative overview, readable even by those without a statistical background.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"For decades, market researchers and statisticians have lamented their inability to deduce individual behavior from data on groups. But Gary King ...has come up with a formula that finally cracks this nut.\"--Business Week\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList 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  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  9.2.1 Using External Information 169  9.2.2 Unconditional Estimation: Xi 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  9.3.1 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  10.3.2 County Level 209  10.3.3 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  13.1.1 Data 235  13.1.2 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  14.1.1 The Problem with the Problem 250  14.1.2 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.1 Homogeneous Precincts 301  B.2 Heterogeneous Precincts 302  B.3 Heterogeneous Precincts 303  C Conditional Posterior Distribution 304  C.1 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","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403675279703,"sku":"9780691012407","price":49.6,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/a-solution-to-the-ecological-inference-problem-9780691012407","provider":"Book Curl","version":"1.0","type":"link"}