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Shapley decomposition of inequality of educational opportunity

Source: R/ieop_decompose.R
ieop_decompose.Rd

Attributes the relative inequality of educational opportunity (the circumstance \(R^2\) from ieop()) to each individual circumstance using Shapley values: each circumstance's contribution is its average marginal increase in \(R^2\) over all orderings of the circumstance set. The contributions are additive and sum to the total relative IOp, so they answer "how much of the inequality of opportunity is due to migration vs parental education vs books?". Estimates are pooled across plausible values and, when replicate weights are supplied, carry design-based standard errors.

Usage

ieop_decompose(
  data,
  achievement,
  circumstances,
  weight = NULL,
  repweights = NULL,
  rep_method = c("BRR", "JK2", "JK1"),
  fay = 0.5,
  design = NULL,
  level = 0.95
)

Arguments

data

A data frame of student-level records.

achievement

Character vector of achievement plausible-value columns.

circumstances

Character vector of circumstance columns; each entry (a variable, including all of its dummy levels) is one Shapley "player".

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.

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.

level

Confidence level for the stored interval (default 0.95).

Value

An object of class "ieop_decompose" / "lsastrat_estimate" with one row per circumstance (the Shapley contribution to relative IOp).

Details

Because the Shapley value requires fitting a regression for every subset of circumstances (\(2^k\)), the number of circumstances is capped at 8.

References

Shorrocks, A. F. (2013). Decomposition procedures for distributional analysis: a unified framework based on the Shapley value. Journal of Economic Inequality, 11, 99-126.

Examples

data(pisa_mini)
ieop_decompose(pisa_mini, paste0("PV", 1:10, "MATH"),
               circumstances = c("IMMIG", "parental_edu", "books"),
               weight = "W_FSTUWT", repweights = paste0("W_FSTURWT", 1:64))
#> Inequality of opportunity: Shapley decomposition
#>   10 plausible value(s)  |  n = 2048  |  3 circumstance(s)
#>   Variance: BRR, 64 replicate weights (+ PV imputation); t reference
#> 
#> 
#>              Estimate Std.Error    t    df       p
#> IMMIG           0.009     0.005 2.01 425.3 4.5e-02
#> parental_edu    0.106     0.013 7.86 263.8 9.8e-14
#> books           0.094     0.013 7.44 178.5 4.1e-12
#> 
#> Shapley contributions to relative IOp (R^2); they sum to the total