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

mutual_expected(
  data,
  group,
  unit,
  weight = NULL,
  within = NULL,
  fixed_margins = TRUE,
  n_bootstrap = 100,
  base = exp(1)
)

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)

within

Apply algorithm within each group defined by this variable, and report the weighted average. (Default NULL)

fixed_margins

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

n_bootstrap

Number of bootstrap iterations. (Default 100)

base

Base of the logarithm that is used in the calculation. Defaults to the natural logarithm.

Value

A data.table with two rows, corresponding to the expected values of segregation when true segregation is zero.

Examples

if (FALSE) {
# the schools00 dataset has a large sample size, so expected segregation is close to zero
mutual_expected(schools00, "race", "school", weight = "n")

# but we can 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))
)
mutual_expected(small, "race", "school", weight = "n")
# with an increase in sample size (n=1000), the values improve
small$n <- small$n * 10
mutual_expected(small, "race", "school", weight = "n")
}