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On the Upward Bias of the Dissimilarity Index and Its Corrections

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  • Angelo Mazza
  • Antonio Punzo

Abstract

The dissimilarity index of Duncan and Duncan is widely used in a broad range of contexts to assess the overall extent of segregation in the allocation of two groups in two or more units. Its sensitivity to random allocation implies an upward bias with respect to the unknown amount of systematic segregation. In this article, following a multinomial framework based on the assumption that individuals allocate themselves independently and that unit sizes are not fixed, we provide (1) a mathematical proof of the nonnegativity of the bias, (2) an analytic way of obtaining the same results of a recent bootstrap-based bias correction but without using resampling, and (3) a new bias correction that outperforms, in terms of both bias and mean square error, those based on grouped jackknife, bootstrap, and double bootstrap.

Suggested Citation

  • Angelo Mazza & Antonio Punzo, 2015. "On the Upward Bias of the Dissimilarity Index and Its Corrections," Sociological Methods & Research, , vol. 44(1), pages 80-107, February.
    • Handle: RePEc:sae:somere:v:44:y:2015:i:1:p:80-107
    DOI: 10.1177/0049124114543242
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    References listed on IDEAS

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    1. Silber, Jacques G., 1989. "On the measurement of employment segregation," Economics Letters, Elsevier, vol. 30(3), pages 237-243, September.
    2. Rebecca Allen & Simon Burgess & Frank Windmeijer, 2009. "More Reliable Inference for Segregation Indices," The Centre for Market and Public Organisation 09/216, The Centre for Market and Public Organisation, University of Bristol, UK.
    3. T. Karmel & M. Maclachlan, 1988. "Occupational Sex Segregation —Increasing or Decreasing?," The Economic Record, The Economic Society of Australia, vol. 64(3), pages 187-195, September.
    4. Carrington, William J & Troske, Kenneth R, 1997. "On Measuring Segregation in Samples with Small Units," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 402-409, October.
    5. Karmel, T & Maclachlan, M, 1988. "Occupational Sex Segregation--Increasing or Decreasing?," The Economic Record, The Economic Society of Australia, vol. 64(186), pages 187-195, September.
    6. Michael R. Ransom, 2000. "Sampling Distributions of Segregation Indexes," Sociological Methods & Research, , vol. 28(4), pages 454-475, May.
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    Cited by:

    1. Federico Benassi & Francesca Bitonti & Angelo Mazza & Salvatore Strozza, 2023. "Sri Lankans’ residential segregation and spatial inequalities in Southern Italy: an empirical analysis using fine-scale data on regular lattice geographies," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(2), pages 1629-1648, April.
    2. Angelo Mazza, 2017. "Dealing With The Bias Of The Dissimilarity Index Of Segregation1," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 71(2), pages 11-20, April-Jun.
    3. Kelvyn Jones & David Manley & Ron Johnston & Dewi Owen, 2018. "Modelling residential segregation as unevenness and clustering: A multilevel modelling approach incorporating spatial dependence and tackling the MAUP," Environment and Planning B, , vol. 45(6), pages 1122-1141, November.
    4. Bertoli, Simone & Ozden, Caglar & Packard, Michael, 2021. "Segregation and internal mobility of Syrian refugees in Turkey: Evidence from mobile phone data," Journal of Development Economics, Elsevier, vol. 152(C).
    5. Coral Río & Olga Alonso-Villar, 2022. "On Measuring Segregation in a Multigroup Context: Standardized Versus Unstandardized Indices," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 163(2), pages 633-659, September.
    6. Anna Maria Altavilla & Angelo Mazza & Antonio Punzo, 2014. "A comparison of bias correction methods for the dissimilarity index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 68(3-4), pages 159-166, July-Dece.
    7. Angelo Mazza & Antonio Punzo, 2016. "Spatial attraction in migrants' settlement patterns in the city of Catania," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 35(5), pages 117-138.

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