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
)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.
A data frame. The distribution of opportunities within
the study area cells. Must contain the columns id and any others
specified in 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.
A string. The name of the column in travel_matrix
with the travel cost between origins and destinations.
A string. The name of the column in land_use_data with the
number of people in each origin that will be considered potential
competitors.
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.
A numeric. A parameter used to modulate the effect of demand
by population. When less than 1, opportunities are allocated more rapidly
to smaller centers relative to larger ones; values higher than 1 achieve
the opposite effect.
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.
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.
A logical. Whether to return spatial availability
results aggregated by origin-destination pair (TRUE) or by origin
(FALSE, the default). When TRUE, the output also includes the demand,
impedance and combined balancing factors used to calculate spatial
availability. Please note that the argument fill_missing_ids
does not affect the output when detailed_results is TRUE.
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
#> id jobs
#> <char> <num>
#> 1: A 66833.466
#> 2: B 133203.363
#> 3: C 9963.171
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
#> from_id to_id demand_bal_fac impedance_bal_fac combined_bal_fac
#> <char> <char> <num> <num> <num>
#> 1: A 1 0.23809524 0.8174384949 5.990064e-01
#> 2: A 2 0.23809524 0.1823951823 6.922691e-02
#> 3: A 3 0.23809524 0.0002033856 1.013219e-03
#> 4: B 1 0.71428571 0.1823951823 4.009692e-01
#> 5: B 2 0.71428571 0.8174384949 9.307605e-01
#> 6: B 3 0.71428571 0.0002033856 3.039656e-03
#> 7: C 1 0.04761905 0.0001663229 2.437577e-05
#> 8: C 2 0.04761905 0.0001663229 1.262535e-05
#> 9: C 3 0.04761905 0.9995932288 9.959471e-01
#> jobs
#> <num>
#> 1: 59900.642536
#> 2: 6922.691048
#> 3: 10.132187
#> 4: 40096.919886
#> 5: 93076.046417
#> 6: 30.396561
#> 7: 2.437577
#> 8: 1.262535
#> 9: 9959.471253