An R package to calculate and decompose entropy-based, multigroup segregation indices, with a focus on the Mutual Information Index (M) and Theil’s Information Index (H).
- calculate total, between, within, and local segregation
- decompose differences in total segregation over time
- estimate standard errors via bootstrapping
- every method returns a tidy data frame for easy post-processing and plotting
- it’s fast, because it uses the
The package provides an easy way to calculate segregation measures, based on the Mutual Information Index (M) and Theil’s Entropy Index (H).
library(segregation) # example dataset with fake data provided by the package mutual_total(schools00, "race", "school", weight = "n") #> stat est #> M 0.426 #> H 0.419
Standard errors in all functions can be estimated via boostrapping:
mutual_total(schools00, "race", "school", weight = "n", se = TRUE) #> stat est se #> M 0.429 0.000935 #> H 0.422 0.000985
Decompose segregation into a between-state and a within-state term (the sum of these equals total segregation):
# between states mutual_total(schools00, "race", "state", weight = "n") #> stat est #> M 0.0992 #> H 0.0977 # within states mutual_total(schools00, "race", "school", within = "state", weight = "n") #> stat est #> M 0.326 #> H 0.321
Local segregation (
ls) is a decomposition by units (here racial
groups). The sum of the proportion-weighted local segregation scores
(local <- mutual_local(schools00, group = "school", unit = "race", weight = "n", se = TRUE, wide = TRUE)) #> race ls ls_se p p_se #> asian 0.667 0.006736 0.02261 0.000124 #> black 0.885 0.002595 0.19005 0.000465 #> hisp 0.782 0.002582 0.15179 0.000317 #> white 0.184 0.000725 0.62810 0.000687 #> native 1.528 0.022868 0.00745 0.000135 sum(local$p * local$ls) #>  0.429
Decompose the difference in M between 2000 and 2005, using iterative proportional fitting (IPF) and the Shapley decomposition, as suggested by Karmel and Maclachlan (1988) and Deutsch et al. (2006):
mutual_difference(schools00, schools05, group = "race", unit = "school", weight = "n", method = "shapley") #> stat est #> M1 0.42554 #> M2 0.41339 #> diff -0.01215 #> additions -0.00341 #> removals -0.01141 #> group_marginal 0.01623 #> unit_marginal -0.01674 #> structural 0.00318
Find more information in the documentation.
How to install
To install the package from CRAN, use
To install the development version, use
Papers using the Mutual information index
DiPrete, T. A., Eller, C. C., Bol, T., & van de Werfhorst, H. G. (2017). School-to-Work Linkages in the United States, Germany, and France. American Journal of Sociology, 122(6), 1869-1938. https://doi.org/10.1086/691327
Forster, A. G., & Bol, T. (2017). Vocational education and employment over the life course using a new measure of occupational specificity. Social Science Research, 70, 176-197. https://doi.org/10.1016/j.ssresearch.2017.11.004
Van Puyenbroeck, T., De Bruyne, K., & Sels, L. (2012). More than ‘Mutual Information’: Educational and sectoral gender segregation and their interaction on the Flemish labor market. Labour Economics, 19(1), 1-8. https://doi.org/10.1016/j.labeco.2011.05.002
Mora, R., & Ruiz-Castillo, J. (2003). 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. https://doi.org/10.1023/A:1026198429377
References on entropy-based segregation indices
Deutsch, J., Flückiger, Y. & Silber, J. (2009). Analyzing Changes in Occupational Segregation: The Case of Switzerland (1970–2000), in: Yves Flückiger, Sean F. Reardon, Jacques Silber (eds.) Occupational and Residential Segregation (Research on Economic Inequality, Volume 17), 171–202.
Theil, H. (1971). Principles of Econometrics. New York: Wiley.
Frankel, D. M., & Volij, O. (2011). Measuring school segregation. Journal of Economic Theory, 146(1), 1-38. https://doi.org/10.1016/j.jet.2010.10.008
Mora, R., & Ruiz-Castillo, J. (2009). The Invariance Properties of the Mutual Information Index of Multigroup Segregation, in: Yves Flückiger, Sean F. Reardon, Jacques Silber (eds.) Occupational and Residential Segregation (Research on Economic Inequality, Volume 17), 33-53.
Mora, R., & Ruiz-Castillo, J. (2011). Entropy-based Segregation Indices. Sociological Methodology, 41(1), 159–194. https://doi.org/10.1111/j.1467-9531.2011.01237.x
Karmel, T. & Maclachlan, M. (1988). Occupational Sex Segregation — Increasing or Decreasing? Economic Record 64: 187-195. https://doi.org/10.1111/j.1475-4932.1988.tb02057.x
Watts, M. The Use and Abuse of Entropy Based Segregation Indices. Working Paper. URL: http://www.ecineq.org/ecineq_lux15/FILESx2015/CR2/p217.pdf