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The statistical properties of the Mutual Information index of multigroup segregation

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Author Info
Ricardo Mora
Javier Ruiz-Castillo

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Abstract

This paper explores the statistical properties of an index of multigroup segregation based on the entropy concept, the Mutual Information (M ) index. In the context of school segregation by ethnic group, the paper establishes that (i) the M index is a monotonic transformation of the likelihood-ratio test for the independence of school and ethnic status, while (ii) the within-group term of the M index for any partition of the set of schools (or ethnic groups) is a monotonic transformation of the likelihood-ratio test for the independence of schools and ethnic groups within the partition in question. This last result is applied to study whether the level of segregation differs significantly within any number of cities, countries or time periods. It is also shown how statistical tests for pair wise comparisons of segregation levels between schools, school districts, ethnic groups, supergroups, cities, countries or time periods can be performed.

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we077443.

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Date of creation: Nov 2007
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Handle: RePEc:cte:werepe:we077443

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ricardo Mora & Javier Ruiz-Castillo, 2008. "A defense of an entropy based index of multigroup segregation," Economics Working Papers we074645, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  2. Robert Hutchens, 2004. "One Measure of Segregation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 555-578, 05. [Downloadable!] (restricted)
  3. Frankel, David M. & Volij, Oscar, 2007. "Measuring Segregation," Staff General Research Papers 12818, Iowa State University, Department of Economics. [Downloadable!]
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  4. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July. [Downloadable!] (restricted)
  5. Ricardo Mora & Javier Ruiz-Castillo, 2007. "The invariance properties of the Mutual Information index of multigroup segregation," Economics Working Papers we077544, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  6. Karmel, T & Maclachlan, M, 1988. "Occupational Sex Segregation--Increasing or Decreasing?," The Economic Record, The Economic Society of Australia, vol. 64(186), pages 187-95, September.
  7. Boisso, Dale & Hayes, Kathy & Hirschberg, Joseph & Silber, Jacques, 1994. "Occupational segregation in the multidimensional case : Decomposition and tests of significance," Journal of Econometrics, Elsevier, vol. 61(1), pages 161-171, March. [Downloadable!] (restricted)
  8. Chakravarty, Satya R. & Silber, Jacques, 2007. "A generalized index of employment segregation," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 185-195, March. [Downloadable!] (restricted)
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  1. Rebecca Allen & Simon Burgess & Frank Windmeijer, 2009. "More Reliable Inference for Segregation Indices," The Centre for Market and Public Organisation 09/216, Department of Economics, University of Bristol, UK. [Downloadable!]
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This page was last updated on 2009-11-26.

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