Title: | Transport Accessibility Measures |
---|---|
Description: | A set of fast and convenient functions to help conducting accessibility analyses. Given a pre-computed travel cost matrix and a land use dataset (containing the location of jobs, healthcare and population, for example), the package allows one to calculate accessibility levels and accessibility poverty and inequality. The package covers the majority of the most commonly used accessibility measures (such as cumulative opportunities, gravity-based and floating catchment areas methods), as well as the most frequently used inequality and poverty metrics (such as the Palma ratio, the concentration and Theil indices and the FGT family of measures). |
Authors: | Rafael H. M. Pereira [aut] , Daniel Herszenhut [aut, cre] , Joey Reid [ctb], Ipea - Institute for Applied Economic Research [cph, fnd] |
Maintainer: | Daniel Herszenhut <[email protected]> |
License: | MIT + file LICENSE |
Version: | 1.4.0.9000 |
Built: | 2024-10-15 05:37:37 UTC |
Source: | https://github.com/ipeaGIT/accessibility |
Calculates the balancing cost measure, which is defined as the travel cost required to reach as many opportunities as the number of people in a given origin. Originally proposed by Barboza et al. (2021), under the name "balancing time".
This function is generic over any kind of numeric travel cost, such as distance, time and money.
balancing_cost( travel_matrix, land_use_data, opportunity, travel_cost, demand, cost_increment = 1, group_by = character(0), fill_missing_ids = TRUE )
balancing_cost( travel_matrix, land_use_data, opportunity, travel_cost, demand, cost_increment = 1, group_by = character(0), fill_missing_ids = TRUE )
travel_matrix |
A data frame. The travel matrix describing the costs
(i.e. travel time, distance, monetary cost, etc.) between the origins and
destinations in the study area. Must contain the columns |
land_use_data |
A data frame. The distribution of opportunities within
the study area cells. Must contain the columns |
opportunity |
A string. The name of the column in |
travel_cost |
A string. The name of the column in |
demand |
A string. The name of the column in |
cost_increment |
A number. The cost increment that should be used when defining the travel cost distribution from which the potential balancing costs will be picked. For example, an increment of 1 tends to suitable for travel time distributions, meaning that the function will first check if any origins reach their balancing cost with a travel time of 0 minutes, then 1 minute, 2 minutes, 3, 4, ..., etc. A increment of 1 might be too big for a distribution of monetary costs, on the other hand, which could possibly benefit from a smaller increment of 0.05, for example, resulting in the function looking for balancing costs first at a cost of 0, then 0.05, 0.10, ..., etc. Defaults to 1. |
group_by |
A |
fill_missing_ids |
A |
A data frame containing the accessibility estimates for each
origin/destination (depending if active
is TRUE
or FALSE
) in the
travel matrix.
A data frame containing the accessibility estimates for each origin
in the travel matrix. Origins marked with a NA
balancing cost never reach
as many opportunities as there is people residing in them, given the
specified travel matrix.
Barboza MH, Carneiro MS, Falavigna C, Luz G, Orrico R (2021). “Balancing Time: Using a New Accessibility Measure in Rio de Janeiro.” Journal of Transport Geography, 90, 102924. ISSN 09666923, doi:10.1016/j.jtrangeo.2020.102924.
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")) bc <- balancing_cost( travel_matrix, land_use_data, opportunity = "jobs", travel_cost = "travel_time", demand = "population" ) head(bc)
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")) bc <- balancing_cost( travel_matrix, land_use_data, opportunity = "jobs", travel_cost = "travel_time", demand = "population" ) head(bc)
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) )
concentration_index( accessibility_data, sociodemographic_data, opportunity, population, income, type, group_by = character(0) )
accessibility_data |
A data frame. The accessibility levels whose
inequality should be calculated. Must contain the columns |
sociodemographic_data |
A data frame. The distribution of
sociodemographic characteristics of the population in the study area cells.
Must contain the columns |
opportunity |
A string. The name of the column in |
population |
A string. The name of the column in |
income |
A string. The name of the column in |
type |
A string. Which type of Concentration Index to calculate. Current
available options are |
group_by |
A |
A data frame containing the inequality estimates for the study area.
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.
Other inequality:
gini_index()
,
palma_ratio()
,
theil_t()
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
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
Calculates the minimum travel cost to the closest N number of opportunities.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
cost_to_closest( travel_matrix, land_use_data, opportunity, travel_cost, n = 1, group_by = character(0), active = TRUE, fill_missing_ids = TRUE )
cost_to_closest( travel_matrix, land_use_data, opportunity, travel_cost, n = 1, group_by = character(0), active = TRUE, fill_missing_ids = TRUE )
travel_matrix |
A data frame. The travel matrix describing the costs
(i.e. travel time, distance, monetary cost, etc.) between the origins and
destinations in the study area. Must contain the columns |
land_use_data |
A data frame. The distribution of opportunities within
the study area cells. Must contain the columns |
opportunity |
A string. The name of the column in |
travel_cost |
A string. The name of the column in |
n |
A |
group_by |
A |
active |
A logical. Whether to calculate active accessibility (the of opportunities that can be reached from a given origin, the default) or passive accessibility (by how many people each destination can be reached). |
fill_missing_ids |
A |
A data frame containing the accessibility estimates for each
origin/destination (depending if active
is TRUE
or FALSE
) in the
travel matrix.
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")) df <- cost_to_closest( travel_matrix, land_use_data, n = 1, opportunity = "schools", travel_cost = "travel_time" ) head(df) df <- cost_to_closest( travel_matrix, land_use_data, n = c(1, 2), opportunity = "schools", travel_cost = "travel_time" ) head(df)
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")) df <- cost_to_closest( travel_matrix, land_use_data, n = 1, opportunity = "schools", travel_cost = "travel_time" ) head(df) df <- cost_to_closest( travel_matrix, land_use_data, n = c(1, 2), opportunity = "schools", travel_cost = "travel_time" ) head(df)
Calculates the number of opportunities accessible under a given specified travel cost cutoff.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
cumulative_cutoff( travel_matrix, land_use_data, opportunity, travel_cost, cutoff, group_by = character(0), active = TRUE, fill_missing_ids = TRUE )
cumulative_cutoff( travel_matrix, land_use_data, opportunity, travel_cost, cutoff, group_by = character(0), active = TRUE, fill_missing_ids = TRUE )
travel_matrix |
A data frame. The travel matrix describing the costs
(i.e. travel time, distance, monetary cost, etc.) between the origins and
destinations in the study area. Must contain the columns |
land_use_data |
A data frame. The distribution of opportunities within
the study area cells. Must contain the columns |
opportunity |
A string. The name of the column in |
travel_cost |
A |
cutoff |
Either a |
group_by |
A |
active |
A logical. Whether to calculate active accessibility (the of opportunities that can be reached from a given origin, the default) or passive accessibility (by how many people each destination can be reached). |
fill_missing_ids |
A |
A data frame containing the accessibility estimates for each
origin/destination (depending if active
is TRUE
or FALSE
) in the
travel matrix.
Other cumulative access:
cumulative_interval()
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")) # active accessibility: number of schools accessible from each origin df <- cumulative_cutoff( travel_matrix = travel_matrix, land_use_data = land_use_data, cutoff = 30, opportunity = "schools", travel_cost = "travel_time" ) head(df) df <- cumulative_cutoff( travel_matrix = travel_matrix, land_use_data = land_use_data, cutoff = c(30, 60), opportunity = "schools", travel_cost = "travel_time" ) head(df) # passive accessibility: number of people that can reach each destination df <- cumulative_cutoff( travel_matrix = travel_matrix, land_use_data = land_use_data, cutoff = 30, opportunity = "population", travel_cost = "travel_time", active = FALSE ) head(df) # using multiple travel costs pareto_frontier <- readRDS(file.path(data_dir, "pareto_frontier.rds")) df <- cumulative_cutoff( pareto_frontier, land_use_data = land_use_data, opportunity = "jobs", travel_cost = c("travel_time", "monetary_cost"), cutoff = list(c(20, 30), c(0, 5, 10)) ) head(df)
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")) # active accessibility: number of schools accessible from each origin df <- cumulative_cutoff( travel_matrix = travel_matrix, land_use_data = land_use_data, cutoff = 30, opportunity = "schools", travel_cost = "travel_time" ) head(df) df <- cumulative_cutoff( travel_matrix = travel_matrix, land_use_data = land_use_data, cutoff = c(30, 60), opportunity = "schools", travel_cost = "travel_time" ) head(df) # passive accessibility: number of people that can reach each destination df <- cumulative_cutoff( travel_matrix = travel_matrix, land_use_data = land_use_data, cutoff = 30, opportunity = "population", travel_cost = "travel_time", active = FALSE ) head(df) # using multiple travel costs pareto_frontier <- readRDS(file.path(data_dir, "pareto_frontier.rds")) df <- cumulative_cutoff( pareto_frontier, land_use_data = land_use_data, opportunity = "jobs", travel_cost = c("travel_time", "monetary_cost"), cutoff = list(c(20, 30), c(0, 5, 10)) ) head(df)
Calculates the average or median number of opportunities that can be reached considering multiple maximum travel cost thresholds within a given travel cost interval specified by the user. The time interval cumulative accessibility measures was originally proposed by Tomasiello et al. (2023).
This function is generic over any kind of numeric travel cost, such as distance, time and money.
cumulative_interval( travel_matrix, land_use_data, opportunity, travel_cost, interval, interval_increment = 1, summary_function = stats::median, group_by = character(0), active = TRUE )
cumulative_interval( travel_matrix, land_use_data, opportunity, travel_cost, interval, interval_increment = 1, summary_function = stats::median, group_by = character(0), active = TRUE )
travel_matrix |
A data frame. The travel matrix describing the costs
(i.e. travel time, distance, monetary cost, etc.) between the origins and
destinations in the study area. Must contain the columns |
land_use_data |
A data frame. The distribution of opportunities within
the study area cells. Must contain the columns |
opportunity |
A string. The name of the column in |
travel_cost |
A string. The name of the column in |
interval |
A |
interval_increment |
A |
summary_function |
A function. This function is used to summarize a
distribution of accessibility estimates within a travel cost interval as a
single value. Can be any function that takes an arbitrary number of
numeric values as as input and returns a single number as output. Defaults
to |
group_by |
A |
active |
A logical. Whether to calculate active accessibility (the of opportunities that can be reached from a given origin, the default) or passive accessibility (by how many people each destination can be reached). |
A data frame containing the accessibility estimates for each
origin/destination (depending if active
is TRUE
or FALSE
) in the
travel matrix.
Tomasiello DB, Herszenhut D, Oliveira JLA, Braga CKV, Pereira RHM (2023). “A Time Interval Metric for Cumulative Opportunity Accessibility.” Applied Geography, 157, 103007. ISSN 0143-6228, doi:10.1016/j.apgeog.2023.103007.
Other cumulative access:
cumulative_cutoff()
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")) df <- cumulative_interval( travel_matrix = travel_matrix, land_use_data = land_use_data, interval = c(20, 30), opportunity = "schools", travel_cost = "travel_time" ) head(df) df <- cumulative_interval( travel_matrix = travel_matrix, land_use_data = land_use_data, interval = c(40, 80), opportunity = "jobs", travel_cost = "travel_time" ) head(df)
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")) df <- cumulative_interval( travel_matrix = travel_matrix, land_use_data = land_use_data, interval = c(20, 30), opportunity = "schools", travel_cost = "travel_time" ) head(df) df <- cumulative_interval( travel_matrix = travel_matrix, land_use_data = land_use_data, interval = c(40, 80), opportunity = "jobs", travel_cost = "travel_time" ) head(df)
Returns a binary weighting function (frequently used to calculate cumulative opportunities measures) to be used inside accessibility calculating functions.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
decay_binary(cutoff)
decay_binary(cutoff)
cutoff |
A |
A function
that takes a generic travel cost vector (numeric
) as
an input and returns a list
of weight vectors (a list of numeric
vectors, named after the arguments passed to the decay function).
Other decay functions:
decay_exponential()
,
decay_linear()
,
decay_logistic()
,
decay_power()
,
decay_stepped()
weighting_function <- decay_binary(cutoff = 30) weighting_function(c(20, 35)) weighting_function <- decay_binary(cutoff = c(30, 45)) weighting_function(c(20, 35))
weighting_function <- decay_binary(cutoff = 30) weighting_function(c(20, 35)) weighting_function <- decay_binary(cutoff = c(30, 45)) weighting_function(c(20, 35))
Returns a negative exponential weighting function to be used inside accessibility calculating functions.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
decay_exponential(decay_value)
decay_exponential(decay_value)
decay_value |
A |
A function
that takes a generic travel cost vector (numeric
) as
an input and returns a list
of weight vectors (a list of numeric
vectors, named after the arguments passed to the decay function).
Other decay functions:
decay_binary()
,
decay_linear()
,
decay_logistic()
,
decay_power()
,
decay_stepped()
weighting_function <- decay_exponential(decay_value = 0.1) weighting_function(c(20, 30)) weighting_function <- decay_exponential(decay_value = c(0.1, 0.2)) weighting_function(c(20, 30))
weighting_function <- decay_exponential(decay_value = 0.1) weighting_function(c(20, 30)) weighting_function <- decay_exponential(decay_value = c(0.1, 0.2)) weighting_function(c(20, 30))
Returns a linear weighting function to be used inside accessibility calculating functions.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
decay_linear(cutoff)
decay_linear(cutoff)
cutoff |
A |
A function
that takes a generic travel cost vector (numeric
) as
an input and returns a list
of weight vectors (a list of numeric
vectors, named after the arguments passed to the decay function).
Other decay functions:
decay_binary()
,
decay_exponential()
,
decay_logistic()
,
decay_power()
,
decay_stepped()
weighting_function <- decay_linear(cutoff = 30) weighting_function(c(20, 35)) weighting_function <- decay_linear(cutoff = c(30, 45)) weighting_function(c(20, 35))
weighting_function <- decay_linear(cutoff = 30) weighting_function(c(20, 35)) weighting_function <- decay_linear(cutoff = c(30, 45)) weighting_function(c(20, 35))
Returns a logistic weighting function (in which the weights follow the distribution of a reversed cumulative logistic curve) to be used inside accessibility calculating functions. The logistic curve is parameterized with the cutoff that sets its inflection point and the standard deviation that sets its steepness.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
decay_logistic(cutoff, sd)
decay_logistic(cutoff, sd)
cutoff |
A |
sd |
A |
When using a function created with decay_logistic()
, the output is
named after the combination of cutoffs ("c"
) and standard deviations
("sd"
) - e.g. given the cutoffs c(30, 40)
and the standard deviations
c(10, 20)
, the first element of the output will be named "c30;sd10"
and
the second will be named "c40;sd20"
. This function uses the adjusted
logistic decay curve proposed by
Bauer and Groneberg (2016), in which the
condition f(0) = 1 is met (i.e. the weight of an opportunity whose cost to
reach is 0 is 1).
A function
that takes a generic travel cost vector (numeric
) as
input and returns a vector of weights (numeric
).
Bauer J, Groneberg DA (2016). “Measuring Spatial Accessibility of Health Care Providers – Introduction of a Variable Distance Decay Function within the Floating Catchment Area (FCA) Method.” PLOS ONE, 11(7), e0159148. ISSN 1932-6203, doi:10.1371/journal.pone.0159148.
Other decay functions:
decay_binary()
,
decay_exponential()
,
decay_linear()
,
decay_power()
,
decay_stepped()
weighting_function <- decay_logistic(cutoff = 30, sd = 5) weighting_function(c(0, 30, 45, 60)) weighting_function <- decay_logistic(cutoff = c(30, 45), sd = c(5, 10)) weighting_function(c(0, 30, 45, 60))
weighting_function <- decay_logistic(cutoff = 30, sd = 5) weighting_function(c(0, 30, 45, 60)) weighting_function <- decay_logistic(cutoff = c(30, 45), sd = c(5, 10)) weighting_function(c(0, 30, 45, 60))
Returns an inverse power weighting function to be used inside accessibility calculating functions.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
decay_power(decay_value)
decay_power(decay_value)
decay_value |
A |
A function
that takes a generic travel cost vector (numeric
) as
an input and returns a list
of weight vectors (a list of numeric
vectors, named after the arguments passed to the decay function).
Other decay functions:
decay_binary()
,
decay_exponential()
,
decay_linear()
,
decay_logistic()
,
decay_stepped()
weighting_function <- decay_power(decay_value = 0.1) weighting_function(c(20, 35)) weighting_function <- decay_power(decay_value = c(0.1, 0.2)) weighting_function(c(20, 35))
weighting_function <- decay_power(decay_value = 0.1) weighting_function(c(20, 35)) weighting_function <- decay_power(decay_value = c(0.1, 0.2)) weighting_function(c(20, 35))
Returns a stepped weighting function to be used inside accessibility calculating functions.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
decay_stepped(steps, weights)
decay_stepped(steps, weights)
steps |
A |
weights |
A |
When both steps
and weights
parameters are given list
s, their
content are matched element-wise to define each stepped weighting function
i.e. the first element of steps
is matched to the first element of
weights
, the second element of steps
is matched to the second of
weights
, etc. When using a function created with decay_stepped()
, the
output is named after the combination of steps ("s"
) and weights ("w"
)
e.g. given the steps c(10, 20, 30)
and the weights c(0.66, 0.33, 0)
,
the output will be named "s(10,20,30);w(0.66,0.33,0)"
.
A function
that takes a generic travel cost vector (numeric
) as
an input and returns a vector of weights (numeric
).
Other decay functions:
decay_binary()
,
decay_exponential()
,
decay_linear()
,
decay_logistic()
,
decay_power()
weighting_function <- decay_stepped( c(10, 20, 30, 40), weights = c(0.75, 0.5, 0.25, 0) ) weighting_function(c(5, 25, 35, 45)) weighting_function <- decay_stepped( list(c(10, 20, 30, 40), c(10, 20, 30, 40)), weights = list(c(0.75, 0.5, 0.25, 0), c(0.8, 0.6, 0.4, 0.2)) ) weighting_function(c(5, 25, 35, 45)) # intervals are open on the right, so the values change exactly at each step weighting_function(c(0, 10, 20, 30, 40))
weighting_function <- decay_stepped( c(10, 20, 30, 40), weights = c(0.75, 0.5, 0.25, 0) ) weighting_function(c(5, 25, 35, 45)) weighting_function <- decay_stepped( list(c(10, 20, 30, 40), c(10, 20, 30, 40)), weights = list(c(0.75, 0.5, 0.25, 0), c(0.8, 0.6, 0.4, 0.2)) ) weighting_function(c(5, 25, 35, 45)) # intervals are open on the right, so the values change exactly at each step weighting_function(c(0, 10, 20, 30, 40))
Calculates the FGT metrics, a family of poverty measures originally proposed
by Foster et al. (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
parameter used to calculate them (either 0, 1 or 2) and which also changes
their interpretation. Please see the details section for more information on
the interpretation of the measures.
fgt_poverty( accessibility_data, sociodemographic_data, opportunity, population, poverty_line, group_by = character(0) )
fgt_poverty( accessibility_data, sociodemographic_data, opportunity, population, poverty_line, group_by = character(0) )
accessibility_data |
A data frame. The accessibility levels whose
poverty levels should be calculated. Must contain the columns |
sociodemographic_data |
A data frame. The distribution of
sociodemographic characteristics of the population in the study area cells.
Must contain the columns |
opportunity |
A string. The name of the column in |
population |
A string. The name of the column in |
poverty_line |
A |
group_by |
A |
A data frame containing the three poverty estimates (FGT0, FGT1 and FGT2) for the study area.
The interpretation of each FGT measure depends on the parameter
used to calculate it:
with (FGT0) the measure captures the extent of poverty
as a simple headcount - i.e. the proportion of people below the poverty line;
with (FGT1) the measure, also know as the "poverty gap
index", captures the severity of poverty as the average percentage distance
between the poverty line and the accessibility of individuals below the
poverty line;
with (FGT2) the measure simultaneously captures the
extent and the severity of poverty by calculating the number of people
below the poverty line weighted by the size of the accessibility shortfall
relative to the poverty line.
FGT values range from 0 to 1. A value of 0 indicates that every individual is above the poverty line. When every individual is below the poverty line, however, FGT0 value is 1 and FGT1 and FGT2 values approach 1.
Foster J, Greer J, Thorbecke E (1984). “A Class of Decomposable Poverty Measures.” Econometrica, 52(3), 761–766. ISSN 0012-9682, doi:10.2307/1913475, 1913475.
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" ) poverty <- fgt_poverty( access, opportunity = "jobs", sociodemographic_data = land_use_data, population = "population", poverty_line = 95368 ) poverty
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" ) poverty <- fgt_poverty( access, opportunity = "jobs", sociodemographic_data = land_use_data, population = "population", poverty_line = 95368 ) poverty
Calculates accessibility accounting for the competition of resources using a measure from the floating catchment area (FCA) family. Please see the details for the available FCA measures.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
floating_catchment_area( travel_matrix, land_use_data, opportunity, travel_cost, demand, method, decay_function, group_by = character(0), fill_missing_ids = TRUE )
floating_catchment_area( travel_matrix, land_use_data, opportunity, travel_cost, demand, method, decay_function, group_by = character(0), fill_missing_ids = TRUE )
travel_matrix |
A data frame. The travel matrix describing the costs
(i.e. travel time, distance, monetary cost, etc.) between the origins and
destinations in the study area. Must contain the columns |
land_use_data |
A data frame. The distribution of opportunities within
the study area cells. Must contain the columns |
opportunity |
A string. The name of the column in |
travel_cost |
A string. The name of the column in |
demand |
A string. The name of the column in |
method |
A string. Which floating catchment area measure to use.
Current available options are |
decay_function |
A |
group_by |
A |
fill_missing_ids |
A |
A data frame containing the accessibility estimates for each
origin/destination (depending if active
is TRUE
or FALSE
) in the
travel matrix.
The package currently includes two built-in FCA measures:
2SFCA - the 2-Step Floating Catchment Area measure was the first accessibility metric in the FCA family. It was originally proposed by Luo and Wang (2003).
BFCA - the Balanced Floating Catchment Area measure calculates accessibility accounting for competition effects while simultaneously correcting for issues of inflation of demand and service levels that are present in other FCA measures. It was originally proposed by Paez et al. (2019) and named in Pereira et al. (2021).
Luo W, Wang F (2003).
“Measures of Spatial Accessibility to Health Care in a GIS Environment: Synthesis and a Case Study in the Chicago Region.”
Environment and Planning B: Planning and Design, 30(6), 865–884.
ISSN 0265-8135, 1472-3417, doi:10.1068/b29120.
Paez A, Higgins CD, Vivona SF (2019).
“Demand and Level of Service Inflation in Floating Catchment Area (FCA) Methods.”
PLOS ONE, 14(6), e0218773.
ISSN 1932-6203, doi:10.1371/journal.pone.0218773.
Pereira RHM, Braga CKV, Servo LM, Serra B, Amaral P, Gouveia N, Paez A (2021).
“Geographic Access to COVID-19 Healthcare in Brazil Using a Balanced Float Catchment Area Approach.”
Social Science & Medicine, 273, 113773.
ISSN 0277-9536, doi:10.1016/j.socscimed.2021.113773.
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")) # 2SFCA with a step decay function df <- floating_catchment_area( travel_matrix, land_use_data, method = "2sfca", decay_function = decay_binary(cutoff = 50), opportunity = "jobs", travel_cost = "travel_time", demand = "population" ) head(df) # BFCA with an exponential decay function df <- floating_catchment_area( travel_matrix, land_use_data, method = "bfca", decay_function = decay_exponential(decay_value = 0.5), opportunity = "jobs", travel_cost = "travel_time", demand = "population" ) head(df)
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")) # 2SFCA with a step decay function df <- floating_catchment_area( travel_matrix, land_use_data, method = "2sfca", decay_function = decay_binary(cutoff = 50), opportunity = "jobs", travel_cost = "travel_time", demand = "population" ) head(df) # BFCA with an exponential decay function df <- floating_catchment_area( travel_matrix, land_use_data, method = "bfca", decay_function = decay_exponential(decay_value = 0.5), opportunity = "jobs", travel_cost = "travel_time", demand = "population" ) head(df)
Calculates the Gini Index of a given accessibility distribution.
gini_index( accessibility_data, sociodemographic_data, opportunity, population, group_by = character(0) )
gini_index( accessibility_data, sociodemographic_data, opportunity, population, group_by = character(0) )
accessibility_data |
A data frame. The accessibility levels whose
inequality should be calculated. Must contain the columns |
sociodemographic_data |
A data frame. The distribution of
sociodemographic characteristics of the population in the study area cells.
Must contain the columns |
opportunity |
A string. The name of the column in |
population |
A string. The name of the column in |
group_by |
A |
A data frame containing the inequality estimates for the study area.
Other inequality:
concentration_index()
,
palma_ratio()
,
theil_t()
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" ) gini <- gini_index( access, sociodemographic_data = land_use_data, opportunity = "jobs", population = "population" ) gini
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" ) gini <- gini_index( access, sociodemographic_data = land_use_data, opportunity = "jobs", population = "population" ) gini
Calculates gravity-based accessibility using a decay function specified by the user.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
gravity( travel_matrix, land_use_data, opportunity, travel_cost, decay_function, group_by = character(0), active = TRUE, fill_missing_ids = TRUE )
gravity( travel_matrix, land_use_data, opportunity, travel_cost, decay_function, group_by = character(0), active = TRUE, fill_missing_ids = TRUE )
travel_matrix |
A data frame. The travel matrix describing the costs
(i.e. travel time, distance, monetary cost, etc.) between the origins and
destinations in the study area. Must contain the columns |
land_use_data |
A data frame. The distribution of opportunities within
the study area cells. Must contain the columns |
opportunity |
A string. The name of the column in |
travel_cost |
A string. The name of the column in |
decay_function |
A |
group_by |
A |
active |
A logical. Whether to calculate active accessibility (the of opportunities that can be reached from a given origin, the default) or passive accessibility (by how many people each destination can be reached). |
fill_missing_ids |
A |
A data frame containing the accessibility estimates for each
origin/destination (depending if active
is TRUE
or FALSE
) in the
travel matrix.
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")) df_linear <- gravity( travel_matrix, land_use_data, decay_function = decay_linear(cutoff = 50), opportunity = "schools", travel_cost = "travel_time" ) head(df_linear) df_exp <- gravity( travel_matrix, land_use_data, decay_function = decay_exponential(decay_value = 0.5), opportunity = "schools", travel_cost = "travel_time" ) head(df_exp)
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")) df_linear <- gravity( travel_matrix, land_use_data, decay_function = decay_linear(cutoff = 50), opportunity = "schools", travel_cost = "travel_time" ) head(df_linear) df_exp <- gravity( travel_matrix, land_use_data, decay_function = decay_exponential(decay_value = 0.5), opportunity = "schools", travel_cost = "travel_time" ) head(df_exp)
Calculates the Palma Ratio of a given accessibility distribution. Originally defined as the income share of the richest 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 richest 10% divided by the average accessibility of the poorest 40%.
palma_ratio( accessibility_data, sociodemographic_data, opportunity, population, income, group_by = character(0) )
palma_ratio( accessibility_data, sociodemographic_data, opportunity, population, income, group_by = character(0) )
accessibility_data |
A data frame. The accessibility levels whose
inequality should be calculated. Must contain the columns |
sociodemographic_data |
A data frame. The distribution of
sociodemographic characteristics of the population in the study area cells.
Must contain the columns |
opportunity |
A string. The name of the column in |
population |
A string. The name of the column in |
income |
A string. The name of the column in |
group_by |
A |
A data frame containing the inequality estimates for the study area.
Other inequality:
concentration_index()
,
gini_index()
,
theil_t()
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" ) palma <- palma_ratio( access, sociodemographic_data = land_use_data, opportunity = "jobs", population = "population", income = "income_per_capita" ) palma
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" ) palma <- palma_ratio( access, sociodemographic_data = land_use_data, opportunity = "jobs", population = "population", income = "income_per_capita" ) palma
Calculates spatial availability, an accessibility measured proposed by Soukhov et al. (2023) that takes into account competition effects. The accessibility levels that result from using this measure are proportional both to the demand in each origin and to the travel cost it takes to reach the destinations.
This function is generic over any kind of numeric travel cost, such as distance, time and money.
spatial_availability( travel_matrix, land_use_data, opportunity, travel_cost, demand, decay_function, alpha = 1, group_by = character(0), fill_missing_ids = TRUE, detailed_results = FALSE )
spatial_availability( travel_matrix, land_use_data, opportunity, travel_cost, demand, decay_function, alpha = 1, group_by = character(0), fill_missing_ids = TRUE, detailed_results = FALSE )
travel_matrix |
A data frame. The travel matrix describing the costs
(i.e. travel time, distance, monetary cost, etc.) between the origins and
destinations in the study area. Must contain the columns |
land_use_data |
A data frame. The distribution of opportunities within
the study area cells. Must contain the columns |
opportunity |
A string. The name of the column in |
travel_cost |
A string. The name of the column in |
demand |
A string. The name of the column in |
decay_function |
A |
alpha |
A |
group_by |
A |
fill_missing_ids |
A |
detailed_results |
A |
A data frame containing the accessibility estimates for each
origin/destination (depending if active
is TRUE
or FALSE
) in the
travel matrix.
Soukhov A, Páez A, Higgins CD, Mohamed M (2023). “Introducing Spatial Availability, a Singly-Constrained Measure of Competitive Accessibility.” PLOS ONE, 18(1), e0278468. ISSN 1932-6203, doi:10.1371/journal.pone.0278468.
# the example below is based on Soukhov et al. (2023) paper travel_matrix <- data.table::data.table( from_id = rep(c("A", "B", "C"), each = 3), to_id = as.character(rep(1:3, 3)), travel_time = c(15, 30, 100, 30, 15, 100, 100, 100, 15) ) land_use_data <- data.table::data.table( id = c("A", "B", "C", "1", "2", "3"), population = c(50000, 150000, 10000, 0, 0, 0), jobs = c(0, 0, 0, 100000, 100000, 10000) ) df <- spatial_availability( travel_matrix, land_use_data, opportunity = "jobs", travel_cost = "travel_time", demand = "population", decay_function = decay_exponential(decay_value = 0.1) ) df detailed_df <- spatial_availability( travel_matrix, land_use_data, opportunity = "jobs", travel_cost = "travel_time", demand = "population", decay_function = decay_exponential(decay_value = 0.1), detailed_results = TRUE ) detailed_df
# the example below is based on Soukhov et al. (2023) paper travel_matrix <- data.table::data.table( from_id = rep(c("A", "B", "C"), each = 3), to_id = as.character(rep(1:3, 3)), travel_time = c(15, 30, 100, 30, 15, 100, 100, 100, 15) ) land_use_data <- data.table::data.table( id = c("A", "B", "C", "1", "2", "3"), population = c(50000, 150000, 10000, 0, 0, 0), jobs = c(0, 0, 0, 100000, 100000, 10000) ) df <- spatial_availability( travel_matrix, land_use_data, opportunity = "jobs", travel_cost = "travel_time", demand = "population", decay_function = decay_exponential(decay_value = 0.1) ) df detailed_df <- spatial_availability( travel_matrix, land_use_data, opportunity = "jobs", travel_cost = "travel_time", demand = "population", decay_function = decay_exponential(decay_value = 0.1), detailed_results = TRUE ) detailed_df
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, the index can be decomposed into a between-groups inequaliy component and a within-groups component.
theil_t( accessibility_data, sociodemographic_data, opportunity, population, socioeconomic_groups = NULL, group_by = character(0) )
theil_t( accessibility_data, sociodemographic_data, opportunity, population, socioeconomic_groups = NULL, group_by = character(0) )
accessibility_data |
A data frame. The accessibility levels whose
inequality should be calculated. Must contain the columns |
sociodemographic_data |
A data frame. The distribution of
sociodemographic characteristics of the population in the study area cells.
Must contain the columns |
opportunity |
A string. The name of the column in |
population |
A string. The name of the column in |
socioeconomic_groups |
A string. The name of the column in
|
group_by |
A |
If socioeconomic_groups
is NULL
, a data frame containing the
total Theil T estimates for the study area. If not, 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.
Other inequality:
concentration_index()
,
gini_index()
,
palma_ratio()
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" ) ti <- theil_t( access, sociodemographic_data = land_use_data, opportunity = "jobs", population = "population" ) ti # to calculate inequality between and within income deciles, we pass # "income_decile" to socioeconomic_groups. # some cells, however, 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 access <- access[! access$id %in% na_decile_ids, ] sociodem_data <- land_use_data[! land_use_data$id %in% na_decile_ids, ] ti <- theil_t( access, sociodemographic_data = sociodem_data, opportunity = "jobs", population = "population", socioeconomic_groups = "income_decile" ) ti
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" ) ti <- theil_t( access, sociodemographic_data = land_use_data, opportunity = "jobs", population = "population" ) ti # to calculate inequality between and within income deciles, we pass # "income_decile" to socioeconomic_groups. # some cells, however, 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 access <- access[! access$id %in% na_decile_ids, ] sociodem_data <- land_use_data[! land_use_data$id %in% na_decile_ids, ] ti <- theil_t( access, sociodemographic_data = sociodem_data, opportunity = "jobs", population = "population", socioeconomic_groups = "income_decile" ) ti