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)A numeric vector. The cost value that serves as the
inflection point of the cumulative logistic curve.
A numeric vector with same length as cutoff. The standard
deviation of the logistic curve. Values near 0 result in weighting curves
that approximate binary decay, while higher values tend to linearize the
decay.
A function that takes a generic travel cost vector (numeric) as
input and returns a vector of weights (numeric).
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).
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))
#> $`c30;sd5`
#> [1] 1.000000e+00 5.000094e-01 4.314804e-03 1.877853e-05
#>
weighting_function <- decay_logistic(cutoff = c(30, 45), sd = c(5, 10))
weighting_function(c(0, 30, 45, 60))
#> $`c30;sd5`
#> [1] 1.000000e+00 5.000094e-01 4.314804e-03 1.877853e-05
#>
#> $`c45;sd10`
#> [1] 1.00000000 0.93850470 0.50014263 0.06178056
#>