Concentration Index

Calculates the Concentration Index (CI) of a given accessibility distribution. This measures estimates the extent to which accessibility inequalities are systematically associated with individuals' socioeconomic levels. CI values can theoretically vary between -1 and +1 (when all accessibility is concentrated in the most or in the least disadvantaged person, respectively). Negative values indicate that inequalities favor the poor, while positive values indicate a pro-rich bias. The function supports calculating the standard relative CI and the corrected CI, as proposed by Erreygers (2009) .

concentration_index(
  accessibility_data,
  sociodemographic_data,
  opportunity,
  population,
  income,
  type,
  group_by = character(0)
)

Arguments

accessibility_data

A data frame. The accessibility levels whose inequality should be calculated. Must contain the columns id and any others specified in opportunity.

sociodemographic_data

A data frame. The distribution of sociodemographic characteristics of the population in the study area cells. Must contain the columns id and any others specified in population and income.

opportunity

A string. The name of the column in accessibility_data with the accessibility levels to be considerend when calculating inequality levels.

population

A string. The name of the column in sociodemographic_data with the number of people in each cell. Used to weigh accessibility levels when calculating inequality.

income

A string. The name of the column in sociodemographic_data with the income variable that should be used to sort the population from the least to the most privileged. Please note that this variable should describe income per capita (e.g. mean income per capita, household income per capita, etc), instead of the total amount of income in each cell. Also note that, while income is generally used to rank population groups, any variable that can be used to describe one's socioeconomic status, such as education level, can be passed to this argument, as long as it can be numerically ordered (in which higher values denote higher socioeconomic status).

type

A string. Which type of Concentration Index to calculate. Current available options are "standard" and "corrected".

group_by

A character vector. When not character(0) (the default), indicates the accessibility_data columns that should be used to group the inequality estimates by. For example, if accessibility_data includes a scenario column that identifies distinct scenarios that each accessibility estimates refer to (e.g. before and after a transport policy intervention), passing "scenario" to this parameter results in inequality estimates grouped by scenario.

Value

A data frame containing the inequality estimates for the study area.

References

Erreygers G (2009). “Correcting the Concentration Index.” Journal of Health Economics, 28(2), 504--515. ISSN 0167-6296, doi:10.1016/j.jhealeco.2008.02.003 .

See also

Other inequality: gini_index(), palma_ratio(), theil_t()

Examples

data_dir <- system.file("extdata", package = "accessibility")
travel_matrix <- readRDS(file.path(data_dir, "travel_matrix.rds"))
land_use_data <- readRDS(file.path(data_dir, "land_use_data.rds"))

access <- cumulative_cutoff(
  travel_matrix,
  land_use_data,
  cutoff = 30,
  opportunity = "jobs",
  travel_cost = "travel_time"
)

ci <- concentration_index(
  access,
  sociodemographic_data = land_use_data,
  opportunity = "jobs",
  population = "population",
  income = "income_per_capita",
  type = "corrected"
)
ci
#>    concentration_index
#>                  <num>
#> 1:           0.3346494