accessibility not only includes functions to calculate accessibility levels from travel time matrices and land use datasets, but also to calculate accessibility inequality and poverty from an accessibility distribution. This vignette briefly presents these functions.
We first need to calculate the accessibility levels that we are going
to use in this demonstration. To do so, we use the
cumulative_cutoff()
function and the sample data included
in the package.
library(accessibility)
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,
opportunity = "jobs",
travel_cost = "travel_time",
cutoff = 30
)
head(access)
#> id jobs
#> <char> <int>
#> 1: 89a881a5a2bffff 14561
#> 2: 89a881a5a2fffff 29452
#> 3: 89a881a5a67ffff 16647
#> 4: 89a881a5a6bffff 10700
#> 5: 89a881a5a6fffff 6669
#> 6: 89a881a5b03ffff 37029
The functions we’ll be demonstrating in this section take much of the same information as input, including:
palma_ratio()
calculates the Palma Ratio of a given
accessibility distribution. Originally defined as the income share of
the wealthiest 10% of a population divided by the income share of the
poorest 40%, this measure has been adapted in transport planning as the
average accessibility of the wealthiest 10% divided by the average
accessibility of the poorest 40%. Palma Ratio values higher than 1
indicate a scenario in which the wealthiest population has higher
accessibility levels than the poorest, whereas values lower than 1
indicate the opposite situation.
This function includes an additional income
parameter,
used to list the column in the sociodemographic dataset with the income
variable that should be used to classify the population in socioeconomic
groups. 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.
gini_index()
calculates the Gini Index of a given
accessibility distribution. Probably the most frequently used inequality
measure in transport planning, this index estimates how much a
distribution deviates from a hypothetical situation in which everyone
has the exact same accessibility conditions. Gini Index values range
from 0 to 1. A value of 0 indicates a scenario of perfect equality, in
which everyone has the same accessibility levels, whereas a value of 1
indicates a scenario of perfect inequality, in which the accessibility
levels in a study area are all concentrated into a single cell.
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 cell, respectively). Negative values indicate
that inequalities favor the poor, while positive values indicate a
pro-rich bias.
Just like palma_ratio()
, this function includes an
income
parameter to indicate which variable from the
sociodemographic dataset should be used to rank the population from the
least to the most privileged groups. Unlike the Palma Ratio function,
however, any variable that can be used to describe one’s socioeconomic
status, such as education level, for example, can be passed to this
argument, as long as it can be numerically ordered (in which higher
values denote higher socioeconomic status).
concentration_index()
also includes a type
parameter, used to indicate which Concentration Index to calculate. This
parameter currently supports two values, "standard"
and
"corrected"
, which respectively identify the standard
relative CI and the corrected CI, proposed by Erreygers (2009).
theil_t()
calculates the Theil T Index of a given
accessibility distribution. Values range from 0 (when all individuals
have exactly the same accessibility levels) to the natural log of
n, in which n is the number of individuals in the
accessibility dataset.
If the individuals can be classified into mutually exclusive and
completely exhaustive groups (i.e. into groups that do not overlap and
cover the entire population), the index can be decomposed into a
between- and a within-groups inequality component. The function includes
a socioeconomic_groups
parameter to indicate which variable
from the sociodemographic dataset should be used identify the
socioeconomic groups used to calculate these components.
Please note that the output theil_t()
varies based on
the value of socioeconomic_groups
. If NULL
(the default), the between- and within-groups components are not
calculated, and the function returns a data frame containing only the
total aggregate inequality for the returned area. If
socioeconomic_groups
is not NULL
, however, the
function returns a list containing three dataframes: one summarizing the
total inequality and the between- and within-groups components, one
listing the contribution of each group to the between-groups component
and another listing the contribution of each group to the within-groups
component. Both behaviors are shown below.
theil_without_groups <- theil_t(
access,
sociodemographic_data = land_use_data,
opportunity = "jobs",
population = "population"
)
theil_without_groups
#> theil_t
#> <num>
#> 1: 0.3616631
# some cells are classified as in the decile NA because their income per capita
# is NaN, as they don't have any population. we filter these cells from our
# accessibility data, otherwise the output would include NA values (note that
# subsetting the data like this doesn't affect the assumption that groups are
# completely exhaustive, because cells with NA income decile don't have any
# population)
na_decile_ids <- land_use_data[is.na(land_use_data$income_decile), ]$id
no_na_access <- access[! access$id %in% na_decile_ids, ]
sociodem_data <- land_use_data[! land_use_data$id %in% na_decile_ids, ]
theil_with_groups <- theil_t(
no_na_access,
sociodemographic_data = sociodem_data,
opportunity = "jobs",
population = "population",
socioeconomic_groups = "income_decile"
)
theil_with_groups
#> $summary
#> component value share_of_total
#> <char> <num> <num>
#> 1: between_group 0.1280753 0.3541287
#> 2: within_group 0.2335878 0.6458713
#> 3: total 0.3616631 1.0000000
#>
#> $within_group_component
#> income_decile value share_of_component
#> <fctr> <num> <num>
#> 1: 1 0.009181454 0.03930622
#> 2: 2 0.011413697 0.04886255
#> 3: 3 0.019320622 0.08271246
#> 4: 4 0.023606928 0.10106232
#> 5: 5 0.031470429 0.13472633
#> 6: 6 0.023539337 0.10077296
#> 7: 7 0.033329635 0.14268567
#> 8: 8 0.032585905 0.13950173
#> 9: 9 0.020299031 0.08690107
#> 10: 10 0.028840780 0.12346868
#>
#> $between_group_component
#> income_decile value
#> <fctr> <num>
#> 1: 1 -0.037573783
#> 2: 2 -0.036276865
#> 3: 3 -0.031829123
#> 4: 4 -0.021600054
#> 5: 5 -0.009938574
#> 6: 6 -0.004401762
#> 7: 7 0.025936879
#> 8: 8 0.042240708
#> 9: 9 0.075742415
#> 10: 10 0.125775443
fgt_poverty()
calculates the FGT metrics, a family of
poverty measures originally proposed by Foster,
Greer, and Thorbecke (1984) that capture the extent and severity
of poverty within an accessibility distribution. The FGT family is
composed of three measures that differ based on the α parameter used to calculate them
(either 0, 1 or 2) and which also changes their interpretation:
This function includes an additional poverty_line
parameter, used to define the poverty line below which individuals are
considered to be in accessibility poverty.