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).

Find more information in the vignette and the documentation.

  • calculate total, between, within, and local segregation
  • decompose differences in total segregation over time
  • estimate standard errors and confidence intervals via bootstrapping
  • every method returns a tidy data.table for easy post-processing and plotting
  • it’s fast, because it uses the data.table package internally

Most of the procedures implemented in this package are described in more detail in this working paper.

Usage

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
#> 1:    M 0.426
#> 2:    H 0.419

Standard errors in all functions can be estimated via boostrapping. This will also apply bias-correction to the estimates:

mutual_total(schools00, "race", "school", weight = "n",
             se = TRUE, CI = 0.90, n_bootstrap = 500)
#> 500 bootstrap iterations on 877739 observations
#>    stat   est       se          CI    bias
#> 1:    M 0.422 0.000788 0.421,0.423 0.00362
#> 2:    H 0.415 0.000719 0.414,0.416 0.00357

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
#> 1:    M 0.0992
#> 2:    H 0.0977

# within states
mutual_total(schools00, "race", "school", within = "state", weight = "n")
#>    stat   est
#> 1:    M 0.326
#> 2:    H 0.321

Local segregation (ls) is a decomposition by units or groups (here racial groups). This function also support standard error and CI estimation. The sum of the proportion-weighted local segregation scores equals M:

local <- mutual_local(schools00, group = "school", unit = "race", weight = "n",
             se = TRUE, CI = 0.90, n_bootstrap = 500, wide = TRUE)
#> 500 bootstrap iterations on 877739 observations
local[, c("race", "ls", "p", "ls_CI")]
#>      race    ls       p       ls_CI
#> 1:  asian 0.591 0.02255 0.581,0.600
#> 2:  black 0.876 0.19015 0.872,0.879
#> 3:   hisp 0.771 0.15171 0.767,0.775
#> 4:  white 0.183 0.62808 0.182,0.184
#> 5: native 1.351 0.00751   1.32,1.38
sum(local$p * local$ls)
#> [1] 0.422

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
#> 1:             M1  0.42554
#> 2:             M2  0.41339
#> 3:           diff -0.01215
#> 4:      additions -0.00341
#> 5:       removals -0.01141
#> 6: group_marginal  0.01787
#> 7:  unit_marginal -0.01171
#> 8:     structural -0.00349

Find more information in the vignette.

How to install

To install the package from CRAN, use

install.packages("segregation")

To install the development version, use

devtools::install_github("elbersb/segregation")

Papers using the Mutual information index

(list incomplete)

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.

Elbers, B. (2019). A Method for Studying Difference in Segregation Levels Across Time and Space. SocArXiv Working Paper. https://osf.io/preprints/socarxiv/ya7zs/

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