|
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  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  | 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 | 148 |
|
8.2 | Support of the Joint Distribution of  and with Bounds Specified for Drawing  | 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 |
|
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 | 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 |
