Skip to contents

School segregation indices for large-scale assessment data

Source: R/segregation.R
segregation_index.Rd

Computes the family of segregation indices used in educational stratification research – measuring how unevenly student groups are distributed across schools (or any nesting unit) – with survey-weighted counts, plausible-value pooling for achievement-based groups, and a choice of variance estimator: replicate weights or a clustered bootstrap with finite-sample bias correction.

Usage

segregation_index(
  data,
  unit,
  group = NULL,
  achievement = NULL,
  cutoff = NULL,
  indices = c("D", "S", "isolation", "Hutchens", "H", "M"),
  minority = NULL,
  weight = NULL,
  repweights = NULL,
  rep_method = c("BRR", "JK2", "JK1"),
  fay = 0.5,
  design = NULL,
  variance = c("replicate", "bootstrap", "none"),
  n_boot = 200L,
  debias = TRUE,
  boot_cluster = NULL,
  boot_seed = NULL,
  level = 0.95
)

Arguments

data

A data frame of student-level records.

unit

Name of the school / nesting-unit identifier column.

group

Name of a categorical group-membership column. Mutually exclusive with achievement/cutoff.

achievement

Character vector of plausible-value column names, used with cutoff to define an achievement-based (academic) group.

cutoff

Numeric threshold; students with achievement < cutoff form the "below" group.

indices

Which indices to return. Any of "D" (dissimilarity), "S" (Gorard's segregation index), "isolation" (minority isolation), "Hutchens" (square-root index), "H" (Theil's information / entropy index) and "M" (mutual information). H and M support more than two groups; D, S, isolation and Hutchens compare the minority group to the rest.

minority

Which group level is the minority for the binary indices. Defaults to the least frequent (weighted) level.

weight

Name of the final student weight column. If NULL, equal weights are used (with a message).

repweights

Optional character vector of replicate-weight columns (used when variance = "replicate").

rep_method, fay

Replication design and Fay factor; see rep_factor().

design

Optional lsa_design() bundling weight, repweights, rep_method and fay; when supplied it overrides those arguments.

variance

Variance estimator: "replicate" (default when repweights are supplied), "bootstrap" (default otherwise), or "none" (point estimates only).

n_boot

Number of bootstrap resamples (default 200).

debias

Logical; apply bootstrap bias correction under variance = "bootstrap" (default TRUE).

boot_cluster

Name of the column defining the stage-one bootstrap clusters (the primary sampling units); defaults to unit.

boot_seed

Optional integer seed for reproducible bootstrap draws (the global RNG state is restored on exit).

level

Confidence level for the stored interval (default 0.95).

Value

An object of class "segregation" / "lsastrat_estimate" (see lsastrat_estimate for methods): a coefficients data frame (one row per index) plus metadata.

Details

Two ways to define the group:

  • Social segregation: pass a categorical group column (e.g. an immigrant-background flag, or a disadvantaged/advantaged ESCS split).

  • Academic segregation: pass achievement (a vector of plausible-value columns) together with cutoff; students scoring below the cutoff form the minority group, and the index is pooled across plausible values.

Variance and bias

The entropy and dissimilarity indices (M, H, D, Gorard's S, Hutchens) are positively biased in finite samples, and large-scale assessments – with tens of students sampled per school across many schools – are the worst case. With variance = "bootstrap" a two-stage clustered bootstrap is used: stage one resamples whole clusters (the design level, giving a design-correct sampling variance) and stage two resamples students within each drawn cluster (the within-school fluctuation that drives the finite-sample bias). The bootstrap bias estimate is then subtracted when debias = TRUE (Elbers, 2023). With variance = "replicate" the supplied replicate weights give the sampling variance but no bias correction is applied; the point estimates are then the (upward-biased) plug-in values, so bootstrap variance is recommended when bias is a concern.

References

Gorard, S. & Taylor, C. (2002). What is segregation? Sociology, 36(4). Hutchens, R. (2004). One measure of segregation. International Economic Review, 45(2). Mora, R. & Ruiz-Castillo, J. (2011). Entropy-based segregation indices. Sociological Methodology, 41(1). Elbers, B. (2023). A method for studying differences in segregation. Sociological Methods & Research (R package segregation).

Examples

data(pisa_mini)
# social segregation by immigrant background, bootstrap bias-corrected
segregation_index(pisa_mini, unit = "school_id", group = "IMMIG",
                  weight = "W_FSTUWT", variance = "bootstrap",
                  n_boot = 99, boot_seed = 1)
#> Segregation indices (social segregation)
#>   unit: school_id  |  128 units  |  3 group(s)  |  minority: first_gen
#>   Variance: clustered bootstrap (B=99, cluster=school_id), bias-corrected
#> 
#> 
#>           Estimate Std.Error     t  df       p
#> D            0.578     0.037 15.45 Inf 7.8e-54
#> S            0.554     0.040 13.83 Inf 1.7e-43
#> isolation    0.097     0.027  3.55 Inf 3.8e-04
#> Hutchens     0.362     0.036  9.97 Inf 2.2e-23
#> H            0.095     0.017  5.50 Inf 3.9e-08
#> M            0.074     0.016  4.59 Inf 4.3e-06