mutualinf: An R Package for Computing and Decomposing the Mutual Information Index of Segregation

In this article, we present the R package mutualinf for computing and decomposing the mutual information index of segregation by means of recursion and parallelization techniques. The mutual information index is the only multigroup index of segregation that satisfies strong decomposability properties, both for organizational units and groups. The mutualinf package contributes by (1) implementing the decomposition of the mutual information index into a “between” and a “within” term; (2) computing, in a single call, a chain of decompositions that involve one “between” term and several “within” terms; (3) providing the contributions of the variables that define the groups or the organizational units to the overall segregation; and (4) providing the demographic weights and local indexes employed in the computation of the “within” term. We illustrate the use of mutualinf using Chilean school enrollment data. With these data, we study socioeconomic and ethnic segregation in schools.

Rafael Fuentealba-Chaura (School of Computer Science) , Daniel Guinea-Martin (Department of Sociology) , Ricardo Mora (Department of Economics) , Julio Rojas-Mora (Department of Computer Science)

0.1 Supplementary materials

Supplementary materials are available in addition to this article. It can be downloaded at

G. Akerlof and R. E. Kranton. Identity economics how our identities shape our work, wages and well-being. Princeton University Press, 2010.
K. Crenshaw. Mapping the margins: Intersectionality, identity politics, and violence against women of color. Stan. L. Rev., 43: 1241, 1990.
M. Dowle and A. Srinivasan. Data.table: Extension of ‘data.frame‘. 2021. URL R package version 1.14.0.
O. D. Duncan and B. Duncan. A methodological analysis of segregation indexes. American Sociological Review, 20(2): 210, 1955.
B. Elbers. Segregation: Entropy-based segregation indices. 2021. URL R package version 0.5.0.
Y. Flückiger and J. Silber. The measurement of segregation in the labor force. Physica-Verlag Heidelberg, 1999.
D. M. Frankel and O. Volij. Measuring school segregation. Journal of Economic Theory, 146(1): 1–38, 2011.
D. Guinea-Martin and R. Mora. Computing decomposable multigroup indexes of segregation. Universidad Carlos III de Madrid. Departamento de Economía. 2021.
S. Kullback. Information theory and statistics. Wiley Publication in Mathematical Statistics, 1959.
D. S. Massey and N. A. Denton. The dimensions of residential segregation. Social Forces, 67(2): 281–315, 1988.
R. Mora and J. Ruiz-Castillo. Additively decomposable segregation indexes. The case of gender segregation by occupations and human capital levels in Spain. The Journal of Economic Inequality, 1(2): 147–179, 2003.
R. Mora and J. Ruiz-Castillo. Entropy-based segregation indices. Sociological Methodology, 41(1): 159–194, 2011.
S. F. Reardon and G. Firebaugh. Measures of multigroup segregation. Sociological Methodology, 32(1): 33–67, 2002.
H. Theil and A. J. Finizza. A note on the measurement of racial integration of schools by means of informational concepts. The Journal of Mathematical Sociology, 1(2): 187–193, 1971.
B. S. Zoloth. An investigation of alternative measures of school segregation. University of Wisconsin, 1974.



Text and figures are licensed under Creative Commons Attribution CC BY 4.0. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".


For attribution, please cite this work as

Fuentealba-Chaura, et al., "mutualinf: An R Package for Computing and Decomposing the Mutual Information Index of Segregation", The R Journal, 2023

BibTeX citation

  author = {Fuentealba-Chaura, Rafael and Guinea-Martin, Daniel and Mora, Ricardo and Rojas-Mora, Julio},
  title = {mutualinf: An R Package for Computing and Decomposing the Mutual Information Index of Segregation},
  journal = {The R Journal},
  year = {2023},
  note = {},
  doi = {10.32614/RJ-2023-047},
  volume = {15},
  issue = {2},
  issn = {2073-4859},
  pages = {77-88}