New methods for measuring and analyzing segregation

목차 (Table of Contents)

• CONTENTS
• 1 Introduction and Goals = 1
• References = 10
• 2 Alternative Formulas for Selected Indices = 11
• References = 16
• 3 Overview of the "Difference of Means" Framework = 19
• 3.1 Index Formulas : The Current State of Affairs = 19
• 3.2 The Difference of Means Formulation - The General Approach = 22
• 3.3 Additional Preliminary Remarks on Implementation = 24
• References = 25
• 4 Difference of Means Formulations for Selected Indices = 27
• 4.1 Scoring Residential Outcomes (y) for the Delta or Dissimilarity Index (D) = 27
• 4.2 Scoring Residential Outcomes (y) for the Gini Index (G) = 31
• 4.3 The Delta or Dissimilarity Index (D) as a Crude Version of G = 32
• 4.4 Scoring Residential Outcomes (y) for the Separation Index (S) = 33
• 4.5 A Side Comment on the Separation Index (S) and Uneven Distribution = 36
• 4.6 Scoring Residential Outcomes (y) for the Theil Index (H) = 39
• 4.7 Scoring Residential Outcomes (y) for the Hutchens Square Root Index (R) = 40
• References = 43
• 5 Index Differences in Registering Area Group Proportions = 45
• 5.1 Segregation as Group Differences in Individual Residential Attainments = 46
• 5.2 Implications for Sensitivity to Separation and Polarization = 52
• References = 56
• 6 Empirical Relationships Among Indices = 57
• 6.1 When Do Indices Agree? When Can They Disagree? = 61
• 6.2 Why Does Relative Group Size Matter? = 71
• References = 75
• 7 Distinctions Between Displacement and Separation = 77
• 7.1 The Increasing Practical Importance of the Distinction Between Displacement and Separation = 79
• 7.2 Prototypical Segregation and Concentrated Versus Dispersed Displacement = 81
• 7.2.1 Prototypical Segregation = 82
• 7.3 Clarifying the Logical Potential for D-S Concordance and Discordance - Analysis of Exchanges = 86
• 7.3.1 Overview of D-S Differences in Responding to Integration-Promoting Exchanges = 88
• 7.3.2 Examples of D-S Differences in Responding to Integration-Promoting Exchanges = 90
• 7.3.3 Implications of Analysis of Example Exchanges = 95
• 7.4 Clarifying the Potential for D-S Concordance and Discordance - Analytic Models = 97
• 7.4.1 Examples of Calculating Values of S$$His_{Min}$$ Given Values of D and P = 100
• 7.4.2 Examining D, S$$His_{Max}$$, and S$$His_{Min}$$ over Varying Combinations of D and P = 105
• 7.4.3 Implications of Findings from Analytic Models for S$$His_{Max}$$ and S$$His_{Min}$$ = 108
• 7.5 Is Separation a Distinct Dimension of Segregation? = 108
• References = 115
• 8 Further Comments on Differences Between Displacement and Separation = 117
• 8.1 Revisiting the Empirical Relationships of Displacement (D) and Separation (S) = 118
• 8.2 Scenarios for How D and S Discrepancies Can Arise = 122
• 8.3 A Practical Issue When Comparing D and S - Size of Spatial Units = 127
• 8.3.1 A Case Study of White-Black Segregation Cullman County Alabama = 130
• 8.3.2 A Case Study of White-Minority Segregation in Palacios TX = 132
• 8.3.3 Reiterating the Importance of Using "Right-Sized" Spatial Units = 133
• 8.3.4 More Practical Guidance for Using S = 135
• 8.4 A Simple Index of Polarization = 136
• References = 137
• 9 Unifying Micro-level and Macro-level Analyses of Segregation = 139
• 9.1 New Ways to Work with Detailed Summary File Tabulations = 141
• 9.2 Some Preliminaries = 142
• 9.3 Substantive Findings = 146
• 9.4 Opportunities to Perform Standardization and Components Analysis = 148
• 9.5 Comparison with Previous Approaches to "Taking Account" of Non-racial Social Characteristics = 150
• 9.6 Aggregate-Level Controls for Micro-level Determinants of Residential Outcomes = 152
• 9.7 New Interpretations of Index Scores Based on Bivariate Regression Analysis = 156
• 9.8 Multivariate Segregation Attainment Analysis (SAA) = 161
• 9.9 Unifying Aggregate Segregation Studies and Studies of Individual-Level Residential Attainment = 170
• 9.10 New Possibilities for Investigating Segregation Using Restricted Data = 172
• 9.11 An Example Analysis Using Restricted Microdata = 174
• References = 178
• 10 New Options for Investigating Macro-level Variation in Segregation = 181
• 10.1 New Specifications for Conducting Comparative and／or Trend Analyses of Segregation = 181
• References = 189
• 11 Aspatial and Spatial Applications of Indices of Uneven Distribution = 191
• References = 193
• 12 Relevance of Individual-Level Residential Outcomes for Describing Segregation = 195
• 12.1 An Example Analysis of Segregation and Exposure to Neighborhood Poverty = 202
• 13 Relevance of Individual-Level Residential Outcomes for Segregation Theory = 207 (4)
• References = 209
• 14 Index Bias and Current Practices = 211
• 14.1 Overview of the Issue of Index Bias = 214
• 14.1.1 Effective Neighborhood Size (ENS) : A Further Complication = 218
• 14.1.2 The Practical Relevance of Variation in Effective Neighborhood Size = 220
• 14.1.3 Random Distribution Is a Valid, Useful, and Conceptually Desirable Reference Point = 221
• 14.2 Prevailing Practices for Avoiding Complications Associated with Index Bias = 222
• 14.2.1 Unwelcome Consequences of Prevailing Practices = 223
• 14.2.2 Efficacy of Prevailing Practices : Screening Cases on Minority Population Size = 227
• 14.2.3 Efficacy of Prevailing Practices : Weighting Cases by Minority Population Size = 229
• 14.2.4 An Aside on Weighting Cases by Minority Population Size = 230
• 14.2.5 Summing Up Comments on Prevailing Practices = 232
• 14.3 Limitations of Previous Approaches for Dealing Directly with Index Bias = 232
• 14.4 Summary = 234
• References = 235
• 15 New Options for Understanding and Dealing with Index Bias = 237
• 15.1 The Source of the Initial Insight = 239
• 15.2 Building on the Initial Insight = 242
• 15.3 A More Detailed Exposition of Bias in the Separation Index = 243
• 15.4 Situating This Result and Its Implications in the Difference of Means Framework = 246
• 15.4.1 Expected Distributions of p' and y' Under Random Assignment = 247
• 15.5 Reviewing a Simple Example in Detail = 247
• 15.5.1 Additional Reflections on Results Presented in Tables 15.1 and 15.2 = 253
• 15.6 Summary = 254
• References = 254
• 16 Comparing Behavior of Unbiased and Standard Versions of Popular Indices = 257
• 16.1 Documenting the Attractive Behavior of Unbiased Versions of Indices of Uneven Distribution = 263
• 16.1.1 Summary of Behavior of Unbiased Indices = 268
• 16.2 Documenting Additional Desirable Behavior of Unbiased Indices Based on the Difference of Means Formulation = 268
• 16.3 Conceptual and Practical Issues and Potential Impact on Research = 275
• References = 279
• 17 Final Comments = 281
• References = 284
• Appendices = 285
• Appendix A : Summary of Notation and Conventions = 285
• Pairwise Calculations = 285
• Reference and Comparison Groups (Groups 1 and 2) = 285
• City-Wide Terms for Pairwise Calculations = 286
• Area-Specific Terms for Pairwise Calculations = 286
• Terms for Individuals or Households = 286
• Selected Terms and Conventions Relevant for the Gini Index (G) = 287
• Selected Terms and Conventions Relevant for the Theil Entropy Index (H) = 287
• Selected Terms and Conventions Relevant for the Atkinson Index (A) = 287
• Appendix B : Formulating Indices of Uneven Distribution as Overall Averages of Individual-Level Residential Outcomes = 288
• Focusing Attention on Individual-Level Residential Outcomes = 289
• Summary of Difference of Means Formulations = 292
• Appendix C : Establishing the Scaling Functions y＝f (p) Needed to Cast the Gini Index (G) and the Dissimilarity Index (D) as Differences of Group Means on Scaled Pairwise Contact = 293
• The General Task = 294
• Introducing the Function y＝f (p) for the Gini Index (G) = 295
• Calculating G as a Difference of Means = 297
• Deriving G as a Difference of Means = 298
• A Brief Demonstration = 299
• Getting on with the Derivation = 300
• The Dissimilarity Index (D) - A Special Case of the Gini Index (G) = 308
• Alternative Graphical Explorations of Relative Rank Position = 315
• The Nature of the Y-P Relationship for G = 318
• Appendix D : Establishing the Scaling Function y＝f (p) Needed to Cast the Separation Index (S) as a Difference of Group Means on Scaled Pairwise Contact = 320
• Variance Analysis = 323
• Formulation as a Difference of Means = 326
• Appendix E : Establishing the Scaling Function y＝f (p) Needed to Cast the Theil Entropy Index (H) as a Difference of Group Means on Scaled Pairwise Contact = 327
• Adjusting the Range to 0-1 = 329
• A Loose End When p＝P = 329
• Appendix F : Establishing the Scaling Function y＝f (p) Needed to Cast the Hutchens' Square Root Index (R) as a Difference of Group Means on Scaled Pairwise Contact = 330
• Adjusting the Range to 0-1 = 332
• A Loose End When p＝P = 332
• An Observation = 333
• References = 333