Calculates expected values when true segregation is zero

When sample sizes are small, one group has a small proportion, or when there are many units, segregation indices are typically upwardly biased, even when true segregation is zero. This function simulates tables with zero segregation, given the marginals of the dataset, and calculates segregation. If the expected values are large, the interpretation of index scores might have to be adjusted.

Usage

dissimilarity_expected(
  data,
  group,
  unit,
  weight = NULL,
  fixed_margins = TRUE,
  n_bootstrap = 100
)

Arguments

data

A data frame.

group

A categorical variable or a vector of variables contained in data. Defines the first dimension over which segregation is computed.

unit

A categorical variable or a vector of variables contained in data. Defines the second dimension over which segregation is computed.

weight

Numeric. (Default NULL)

fixed_margins

Should the margins be fixed or simulated? (Default TRUE)

n_bootstrap

Number of bootstrap iterations. (Default 100)

Value

A data.table with one row, corresponding to the expected value of the D index when true segregation is zero.

Examples

# build a smaller table, with 100 students distributed across
# 10 schools, where one racial group has 10% of the students
small <- data.frame(
    school = c(1:10, 1:10),
    race = c(rep("r1", 10), rep("r2", 10)),
    n = c(rep(1, 10), rep(9, 10))
)
dissimilarity_expected(small, "race", "school", weight = "n")
#>         stat       est         se
#> 1: D under 0 0.3777778 0.09862504
# with an increase in sample size (n=1000), the values improve
small$n <- small$n * 10
dissimilarity_expected(small, "race", "school", weight = "n")
#>         stat       est         se
#> 1: D under 0 0.1201111 0.03093485