Gravity-based accessibility measures — gravity • accessibility

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
)

Arguments

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 from_id, to_id and any others specified in travel_cost.
land_use_data: A data frame. The distribution of opportunities within the study area cells. Must contain the columns id and any others specified in opportunity.
opportunity: A string. The name of the column in land_use_data with the number of opportunities/resources/services to be considered when calculating accessibility levels.
travel_cost: A string. The name of the column in travel_matrix with the travel cost between origins and destinations.
decay_function: A fuction that converts travel cost into an impedance factor used to weight opportunities. This function should take a numeric vector and also return a numeric vector as output, with the same length as the input. For convenience, the package currently includes the following functions: decay_binary(), decay_exponential(), decay_power() and decay_stepped(). See the documentation of each decay function for more details.
group_by: A character vector. When not character(0) (the default), indicates the travel_matrix columns that should be used to group the accessibility estimates by. For example, if travel_matrix includes a departure time column, that specifies the departure time of each entry in the data frame, passing "departure_time" to this parameter results in accessibility estimates grouped by origin and by departure time.
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 logical. When calculating grouped accessibility estimates (i.e. when by_col is not NULL), some combinations of groups and origins may be missing. For example, if a single trip can depart from origin A at 7:15am and reach destination B within 55 minutes, but no trips departing from A at 7:30am can be completed at all, this second combination will not be included in the output. When TRUE (the default), the function identifies which combinations would be left out and fills their respective accessibility values with 0, which incurs in a performance penalty.

Value

A data frame containing the accessibility estimates for each origin/destination (depending if active is TRUE or FALSE) in the travel matrix.

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"))

df_linear <- gravity(
  travel_matrix,
  land_use_data,
  decay_function = decay_linear(cutoff = 50),
  opportunity = "schools",
  travel_cost = "travel_time"
)
head(df_linear)
#>                 id schools
#>             <char>   <num>
#> 1: 89a88cdb57bffff   9.260
#> 2: 89a88cdb597ffff  18.748
#> 3: 89a88cdb5b3ffff  20.900
#> 4: 89a88cdb5cfffff  13.660
#> 5: 89a88cd909bffff  18.980
#> 6: 89a88cd90b7ffff  24.780

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)
#>                 id      schools
#>             <char>        <num>
#> 1: 89a88cdb57bffff 2.705781e-06
#> 2: 89a88cdb597ffff 1.249277e-01
#> 3: 89a88cdb5b3ffff 8.269861e-03
#> 4: 89a88cdb5cfffff 3.023943e-03
#> 5: 89a88cd909bffff 3.059679e-02
#> 6: 89a88cd90b7ffff 8.581966e-02