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EB

EB

ONLINE

Cham : Springer International Publishing, 2017

1 online zdroj

ISBN 978-3-319-41304-4 (e-kniha)

ISBN 978-3-319-41302-0 (print)

The Springer Series on Demographic Methods and Population Analysis, ISSN 1389-6784 ; 42

This book is open access under a CC BY-NC 2.5 license.

This book introduces new methods for measuring and analyzing residential segregation.  It begins by placing all popular segregation indices in the “difference of group means” framework wherein index scores can be obtained as simple differences of group means on individual-level residential attainments scored from area racial composition.  Drawing on the insight that in this framework index scores are additively determined by individual residential attainments, the book shows that the level of segregation in a given city can be equated to the effect of group membership (e.g., race) on individual residential attainments.  This unifies separate research traditions in the field by joining the analysis of segregation at the aggregate level with the analysis of residential attainments for individuals.  Next it shows how segregation analysis can be extended by using multivariate attainment models to assess the impact of group membership (i.e., the level of segregation for a city) while including controls for other relevant individual characteristics (e.g., income, education, language, nativity, etc.).  It then illustrates how one can use these models to quantitatively assess the extent to which segregation traces to impacts of group membership on residential attainments versus other factors such as group differences in income.  The book then shows how micro-level attainment models can be used to study macro-level variation in segregation; specifically, by estimating multi-level models of individual residential attainments to assess how the effect of group membership (i.e., segregation index scores) vary with city characteristics.  Finally, the book introduces refined versions of popular indices that are free of the vexing problem of upward bias..

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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