Getting started

Floating Catchment Area (FCA) methods to Calculate Spatial Accessibility.

Perform various floating catchment area methods to calculate a spatial accessibility index (SPAI) for demand point data. The distance matrix used for weighting is normalized in a preprocessing step using common functions (gaussian, gravity, exponential or logistic).

Installation

You can install the released version of fca from CRAN with:

install.packages("fca")

And the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("egrueebler/fca")

Example

This is a basic example which shows you how to calculate a SPAI for demand point data using FCA methods.

Create an example population, supply and distances:

# Population df with column for size
pop <- data.frame(
  orig_id = letters[1:10],
  size = c(100, 200, 50, 100, 500, 50, 100, 100, 50, 500)
)

# Supply df with column for capacity
sup <- data.frame(
  dest_id = as.character(1:3),
  capacity = c(1000, 200, 500)
)

# Distance matrix with travel times from 0 to 30
D <- matrix(
  runif(30, min = 0, max = 30),
  ncol = 10, nrow = 3, byrow = TRUE,
  dimnames = list(c(1:3), c(letters[1:10]))
)
D
#>             a         b        c         d         e         f         g
#> 1  3.59270070  4.900790 25.44487 12.994056 10.806397  6.594363 22.680487
#> 2  0.08718463  8.725655 23.22225  1.745991  3.797449 16.122522 25.157177
#> 3 28.84891297 12.221267 26.59572  1.975859  9.082860  9.563194  4.882521
#>           h         i        j
#> 1 18.116346  2.714827 5.509787
#> 2  4.277505 20.472026 3.782054
#> 3  4.033152 10.727065 6.679484

Normalize distance matrix with gaussian function, apply a threshold of 20 minutes (to compute beta for the function) and formatting input data as named vectors for the FCA method (match IDs of distance weight matrix with demand and supply data).

library(fca)

# Normalize distances
W <- dist_normalize(
  D,
  d_max = 20,
  imp_function = "gaussian", function_d_max = 0.01
)

# Ensure order of ids
pop <- pop[order(pop$orig_id), ]
sup <- sup[order(sup$dest_id), ]

# Named vectors
(p <- setNames(pop$size, as.character(pop$orig_id)))
#>   a   b   c   d   e   f   g   h   i   j 
#> 100 200  50 100 500  50 100 100  50 500
(s <- setNames(sup$capacity, as.character(sup$dest_id)))
#>    1    2    3 
#> 1000  200  500

Apply FCA method on formatted input, get SPAI for each origin location (p):

(spai <- spai_3sfca(p, s, W))
#>          step3
#> a 1.4434067823
#> b 1.4201284966
#> c 0.0009055064
#> d 0.9072056678
#> e 0.4734788174
#> f 1.3473104178
#> g 1.2270887497
#> h 0.8100786945
#> i 2.3227682812
#> j 1.1138153846