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Cham : Springer International Publishing AG, 2017

1 online resource (348 pages)

ISBN 9783319413044 (electronic bk.)

ISBN 9783319413020

The Springer Series on Demographic Methods and Population Analysis Ser. ; v.42

Print version: Fossett, Mark New Methods for Measuring and Analyzing Segregation Cham : Springer International Publishing AG,c2017 ISBN 9783319413020

001894808

express

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 SMin Given // Values of D and P 100 // 7.4.2 Examining D, SMax> and SMin over Varying Combinations of D and P 105 // 7.4.3 Implications of Findings from Analytic // Models for SMax and SMin 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 // 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 // xvi Contents // 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 ? = 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 ? = 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 ? = 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 ? = 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 ? = 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

(Au-PeEL)EBL6367949

(MiAaPQ)EBC6367949

(OCoLC)1021280094