A Solution to the Ecological Inference Problem ：Reconstructing Individual Behavior from Aggregate Data

Publication subTitle ：Reconstructing Individual Behavior from Aggregate Data

Author： King Gary  

Publisher： Princeton University Press‎

Publication year： 2013

E-ISBN: 9781400849208

P-ISBN(Paperback): 9780691012407

Subject： D09 in the history of politics, political history

Keyword： 政治学史、政治思想史

Language： ENG

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Description

This book provides 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? 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.

King begins with a qualitative overview, readable even by those without a statistical background. He then unifies the apparently diverse findings in the methodological literature, so that only one aggregation problem remains to be solved. He then presents his solution, as well as empirical evaluations of the solution that include over 16,000 comparisons of his estimates from real aggregate data to the known individual-level answer. The method works in practice.

King's solution to the ecologi

Chapter

Contents

Contents

List of Figures

List of Figures

List of Tables

List of Tables

Preface

Preface

Part I: Introduction

Part I: Introduction

1 Qualitative Overview

1 Qualitative Overview

1.1 The Necessity of Ecological Inferences

1.1 The Necessity of Ecological Inferences

1.2 The Problem

1.2 The Problem

1.3 The Solution

1.3 The Solution

1.4 The Evidence

1.4 The Evidence

1.5 The Method

1.5 The Method

2 Formal Statement of the Problem

2 Formal Statement of the Problem

Part II: Catalog of Problems to Fix

Part II: Catalog of Problems to Fix

3 Aggregation Problems

3 Aggregation Problems

3.1 Goodman's Regression: A Definition

3.1 Goodman's Regression: A Definition

3.2 The Indeterminacy Problem

3.2 The Indeterminacy Problem

3.3 The Grouping Problem

3.3 The Grouping Problem

3.4 Equivalence of the Grouping and Indeterminacy Problems

3.4 Equivalence of the Grouping and Indeterminacy Problems

3.5 A Concluding Definition

3.5 A Concluding Definition

4 Non-Aggregation Problems

4 Non-Aggregation Problems

4.1 Goodman Regression Model Problems

4.1 Goodman Regression Model Problems

4.2 Applying Goodman's Regression in 2 x 3 Tables

4.2 Applying Goodman's Regression in 2 x 3 Tables

4.3 Double Regression Problems

4.3 Double Regression Problems

4.4 Concluding Remarks

4.4 Concluding Remarks

Part III: The Proposed Solution

Part III: The Proposed Solution

5 The Data: Generalizing the Method of Bounds

5 The Data: Generalizing the Method of Bounds

5.1 Homogeneous Precincts: No Uncertainty

5.1 Homogeneous Precincts: No Uncertainty

5.2 Heterogeneous Precincts: Upper and Lower Bounds

5.2 Heterogeneous Precincts: Upper and Lower Bounds

5.2.1 Precinct-Level Quantities of Interest

5.2.1 Precinct-Level Quantities of Interest

5.2.2 District-Level Quantities of Interest

5.2.2 District-Level Quantities of Interest

5.3 An Easy Visual Method for Computing Bounds

5.3 An Easy Visual Method for Computing Bounds

6 The Model

6 The Model

6.1 The Basic Model

6.1 The Basic Model

6.2 Model Interpretation

6.2 Model Interpretation

6.2.1 Observable Implications of Model Parameters

6.2.1 Observable Implications of Model Parameters

6.2.2 Parameterizing the Truncated Bivariate Normal

6.2.2 Parameterizing the Truncated Bivariate Normal

6.2.3 Computing 2p Parameters from Only p bservations

6.2.3 Computing 2p Parameters from Only p bservations

6.2.4 Connections to the Statistics of Medical and Seismic Imaging

6.2.4 Connections to the Statistics of Medical and Seismic Imaging

6.2.5 Would a Model of Individual-Level Choices Help?

6.2.5 Would a Model of Individual-Level Choices Help?

7 Preliminary Estimation

7 Preliminary Estimation

7.1 A Visual Introduction

7.1 A Visual Introduction

7.2 The Likelihood Function

7.2 The Likelihood Function

7.3 Parameterizations

7.3 Parameterizations

7.4 Optional Priors

7.4 Optional Priors

7.5 Summarizing Information about Estimated Parameters

7.5 Summarizing Information about Estimated Parameters

8 Calculating Quantities of Interest

8 Calculating Quantities of Interest

8.1 Simulation is Easier than Analytical Derivation

8.1 Simulation is Easier than Analytical Derivation

8.1.1 Definitions and Examples

8.1.1 Definitions and Examples

8.1.2 Simulation for Ecological Inference

8.1.2 Simulation for Ecological Inference

8.2 Precinct-Level Quantities

8.2 Precinct-Level Quantities

8.3 District-Level Quantities

8.3 District-Level Quantities

8.4 Quantities of Interest from Larger Tables

8.4 Quantities of Interest from Larger Tables

8.4.1 A Multiple Imputation Approach

8.4.1 A Multiple Imputation Approach

8.4.2 An Approach Related to Double Regression

8.4.2 An Approach Related to Double Regression

8.5 Other Quantities of Interest

8.5 Other Quantities of Interest

9 Model Extensions

9 Model Extensions

9.1 What can go Wrong?

9.1 What can go Wrong?

9.1.1 Aggregation Bias

9.1.1 Aggregation Bias

9.1.2 Incorrect Distributional Assumptions

9.1.2 Incorrect Distributional Assumptions

9.1.3 Spatial Dependence

9.1.3 Spatial Dependence

9.2 Avoiding Aggregation Bias

9.2 Avoiding Aggregation Bias

9.2.1 Using External Information

9.2.1 Using External Information

9.2.2 Unconditional Estimation: X as a Covariate

9.2.2 Unconditional Estimation: X as a Covariate

9.2.3 Tradeoffs and Priors for the Extended Model

9.2.3 Tradeoffs and Priors for the Extended Model

9.2.4 Ex Post Diagnostics

9.2.4 Ex Post Diagnostics

9.3 Avoiding Distributional Problems

9.3 Avoiding Distributional Problems

9.3.1 Parametric Approaches

9.3.1 Parametric Approaches

9.3.2 a Nonparametric Approach

9.3.2 a Nonparametric Approach

Part IV: Verification

Part IV: Verification

10 A Typical Application Described in Detail: Voter Registration by Race

10 A Typical Application Described in Detail: Voter Registration by Race

10.1 The Data

10.1 The Data

10.2 Likelihood Estimation

10.2 Likelihood Estimation

10.3 Computing Quantities of Interest

10.3 Computing Quantities of Interest

10.3.1 Aggregate

10.3.1 Aggregate

10.3.2 County Level

10.3.2 County Level

10.3.3 Other Quantities of Interest

10.3.3 Other Quantities of Interest

11 Robustness to Aggregation Bias: Poverty Status by Sex

11 Robustness to Aggregation Bias: Poverty Status by Sex

11.1 Data and Notation

11.1 Data and Notation

11.2 Verifying the Existence of Aggregation Bias

11.2 Verifying the Existence of Aggregation Bias

11.3 Fitting the Data

11.3 Fitting the Data

11.4 Empirical Results

11.4 Empirical Results

12 Estimation Without Information: Black Registration in Kentucky

12 Estimation Without Information: Black Registration in Kentucky

12.1 The Data

12.1 The Data

12.2 Data Problems

12.2 Data Problems

12.3 Fitting the Data

12.3 Fitting the Data

12.4 Empirical Results

12.4 Empirical Results

13 Classic Ecological Inferences

13 Classic Ecological Inferences

13.1 Voter Transitions

13.1 Voter Transitions

13.1.1 Data

13.1.1 Data

13.1.2 Estimates

13.1.2 Estimates

13.2 Black Literacy in 1910

13.2 Black Literacy in 1910

Part V: Generalizations and Concluding Suggestions

Part V: Generalizations and Concluding Suggestions

14 Non-Ecological Aggregation Problems

14 Non-Ecological Aggregation Problems

14.1 The Geographer's Modifiable Areal Unit Problem

14.1 The Geographer's Modifiable Areal Unit Problem

14.1.1 The Problem with the Problem

14.1.1 The Problem with the Problem

14.1.2 Ecological Inference as a Solution to the Modifiable Areal Unit Problem

14.1.2 Ecological Inference as a Solution to the Modifiable Areal Unit Problem

14.2 The Statistical Problem of Combining Survey and Aggregate Data

14.2 The Statistical Problem of Combining Survey and Aggregate Data

14.3 the Econometric Problem of Aggregating Continuous Variables

14.3 the Econometric Problem of Aggregating Continuous Variables

14.4 Concluding Remarks on Related Aggregation Research

14.4 Concluding Remarks on Related Aggregation Research

15 Ecological Inference in Larger Tables

15 Ecological Inference in Larger Tables

15.1 An Intuitive Approach

15.1 An Intuitive Approach

15.2 Notation for a General Approach

15.2 Notation for a General Approach

15.3 Generalized Bounds

15.3 Generalized Bounds

15.4 The Statistical Model

15.4 The Statistical Model

15.5 Distributional Implications

15.5 Distributional Implications

15.6 Calculating the Quantities of Interest

15.6 Calculating the Quantities of Interest

15.7 Concluding Suggestions

15.7 Concluding Suggestions

16 A Concluding Checklist

16 A Concluding Checklist

Part VI: Appendices

Part VI: Appendices

A Proof That All Discrepancies Are Equivalent

A Proof That All Discrepancies Are Equivalent

B Parameter Bounds

B Parameter Bounds

B.1 Homogeneous Precincts

B.1 Homogeneous Precincts

B.2 Heterogeneous Precincts: β's and θ's

B.2 Heterogeneous Precincts: β's and θ's

B.3 Heterogeneous Precincts: λi's

B.3 Heterogeneous Precincts: λi's

C Conditional Posterior Distribution

C Conditional Posterior Distribution

C.1 Using Bayes Theorem

C.1 Using Bayes Theorem

C.2 Using Properties of Normal Distributions

C.2 Using Properties of Normal Distributions

D The Likelihood Function

D The Likelihood Function

E The Details of Nonparametric Estimation

E The Details of Nonparametric Estimation

F Computational Issues

F Computational Issues

Glossary of Symbols

Glossary of Symbols

References

References

Index

Index

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