Calculates detailed within-category segregation scores for M and H

Calculates the segregation between group and unit within each category defined by within.

Usage

mutual_within(
  data,
  group,
  unit,
  within,
  weight = NULL,
  se = FALSE,
  CI = 0.95,
  n_bootstrap = 100,
  base = exp(1),
  wide = FALSE
)

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.
within: A categorical variable or a vector of variables contained in data that defines the within-segregation categories.
weight: Numeric. (Default NULL)
se: If TRUE, the segregation estimates are bootstrapped to provide standard errors and to apply bias correction. The bias that is reported has already been applied to the estimates (i.e. the reported estimates are "debiased") (Default FALSE)
CI: If se = TRUE, compute the confidence (CI*100) in addition to the bootstrap standard error. This is based on percentiles of the bootstrap distribution, and a valid interpretation relies on a larger number of bootstrap iterations. (Default 0.95)
n_bootstrap: Number of bootstrap iterations. (Default 100)
base: Base of the logarithm that is used in the calculation. Defaults to the natural logarithm.
wide: Returns a wide dataframe instead of a long dataframe. (Default FALSE)

Value

Returns a data.table with four rows for each category defined by within. The column est contains four statistics that are provided for each unit:

M is the within-category M, and p is the proportion of the category. Multiplying M and p gives the contribution of each within-category towards the total M.

H is the within-category H, and ent_ratio provides the entropy ratio, defined as EW/E, where EW is the within-category entropy, and E is the overall entropy. Multiplying H, p, and ent_ratio gives the contribution of each within-category towards the total H. If se is set to TRUE, an additional column se contains the associated bootstrapped standard errors, an additional column CI contains the estimate confidence interval as a list column, an additional column bias contains the estimated bias, and the column est contains the bias-corrected estimates. If wide is set to TRUE, returns instead a wide dataframe, with one row for each within category, and the associated statistics in separate columns.

References

Henri Theil. 1971. Principles of Econometrics. New York: Wiley.

Ricardo Mora and Javier Ruiz-Castillo. 2011. "Entropy-based Segregation Indices". Sociological Methodology 41(1): 159–194.

Examples

if (FALSE) {
(within <- mutual_within(schools00, "race", "school",
    within = "state",
    weight = "n", wide = TRUE
))
# the M for state "A" is .409
# manual calculation
schools_A <- schools00[schools00$state == "A", ]
mutual_total(schools_A, "race", "school", weight = "n") # M => .409

# to recover the within M and H from the output, multiply
# p * M and p * ent_ratio * H, respectively
sum(within$p * within$M) # => .326
sum(within$p * within$ent_ratio * within$H) # => .321
# compare with:
mutual_total(schools00, "race", "school", within = "state", weight = "n")
}