| List of Figures | p. xi |
| List of Tables | p. xiii |
| Preface | p. xv |
| Introduction | p. 1 |
| Qualitative Overview | p. 3 |
| The Necessity of Ecological Inferences | p. 7 |
| The Problem | p. 12 |
| The Solution | p. 17 |
| The Evidence | p. 22 |
| The Method | p. 26 |
| Formal Statement of the Problem | p. 28 |
| Catalog Of Problems To Fix | p. 35 |
| Aggregation Problems | p. 37 |
| Goodman's Regression: A Definition | p. 37 |
| The Indeterminacy Problem | p. 39 |
| The Grouping Problem | p. 46 |
| Equivalence of the Grouping and Indeterminacy Problems | p. 53 |
| A Concluding Definition | p. 54 |
| Non-Aggregation Problems | p. 56 |
| Goodman Regression Model Problems | p. 56 |
| Applying Goodman's Regression in 2 x 3 Tables | p. 68 |
| Double Regression Problems | p. 71 |
| Concluding Remarks | p. 73 |
| The Proposed Solution | p. 75 |
| The Data: Generalizing the Method of Bounds | p. 77 |
| Homogeneous Precincts: No Uncertainty | p. 78 |
| Heterogeneous Precincts: Upper and Lower Bounds | p. 79 |
| Precinct-Level Quantities of Interest | p. 79 |
| District-Level Quantities of Interest | p. 83 |
| An Easy Visual Method for Computing Bounds | p. 85 |
| The Model | p. 91 |
| The Basic Model | p. 92 |
| Model Interpretation | p. 94 |
| Observable Implications of Model Parameters | p. 96 |
| Parameterizing the Truncated Bivariate Normal | p. 102 |
| Computing 2pParameters from Onlyp Observations | p. 106 |
| Connections to the Statistics of Medical and Seismic Imaging | p. 112 |
| Would a Model of Individual-Level Choices Help? | p. 119 |
| Preliminary Estimation | p. 123 |
| A Visual Introduction | p. 124 |
| The Likelihood Function | p. 132 |
| Parameterizations | p. 135 |
| Optional Priors | p. 138 |
| Summarizing Information about Estimated Parameters | p. 139 |
| Calculating Quantities of Interest | p. 141 |
| Simulation Is Easier than Analytical Derivation | p. 141 |
| Definitions and Examples | p. 142 |
| Simulation for Ecological Inference | p. 144 |
| Precinct-Level Quantities | p. 145 |
| District-Level Quantities | p. 149 |
| Quantities of Interest from Larger Tables | p. 151 |
| A Multiple Imputation Approach | p. 151 |
| An Approach Related to Double Regression | p. 153 |
| Other Quantities of Interest | p. 156 |
| Model Extensions | p. 158 |
| What Can Go Wrong? | p. 158 |
| Aggregation Bias | p. 159 |
| Incorrect Distributional Assumptions | p. 161 |
| Spatial Dependence | p. 164 |
| Avoiding Aggregation Bias | p. 168 |
| Using External Information | p. 169 |
| Unconditional Estimation:X i as a Covariate | p. 174 |
| Tradeoffs and Priors for the Extended Model | p. 179 |
| Ex Post Diagnostics | p. 183 |
| Avoiding Distributional Problems | p. 184 |
| Parametric Approaches | p. 185 |
| A Nonparametric Approach | p. 191 |
| Verification | p. 197 |
| A Typical Application Described in Detail: Voter Registration by Race | p. 199 |
| The Data | p. 199 |
| Likelihood Estimation | p. 200 |
| Computing Quantities of Interest | p. 207 |
| Aggregate | p. 207 |
| County Level | p. 209 |
| Other Quantities of Interest | p. 215 |
| Robustness to Aggregation Bias: Poverty Status by Sex | p. 217 |
| Data and Notation | p. 217 |
| Verifying the Existence of Aggregation Bias | p. 218 |
| Fitting the Data | p. 220 |
| Empirical Results | p. 222 |
| Estimation without Information: Black Registration in Kentucky | p. 226 |
| The Data | p. 226 |
| Data Problems | p. 227 |
| Fitting the Data | p. 228 |
| Empirical Results | p. 232 |
| Classic Ecological Inferences | p. 235 |
| Voter Transitions | p. 235 |
| Data | p. 235 |
| Estimates | p. 238 |
| Black Literacy in 1910 | p. 241 |
| Generalizations and Concluding Suggestions | p. 247 |
| Non-Ecological Aggregation Problems | p. 249 |
| The Geographer's Modifiable Areal Unit Problem | p. 249 |
| The Problem with the Problem | p. 250 |
| Ecological Inference as a Solution to the Modifiable Areal Unit Problem | p. 252 |
| The Statistical Problem of Combining Survey and Aggregate Data | p. 255 |
| The Econometric Problem of Aggregating Continuous Variables | p. 258 |
| |
| Table of Contents provided by Publisher. All Rights Reserved. |