Getting started

Source: vignettes/getting-started.Rmd

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:

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  9.112911  0.2250393 28.81470 22.307320 11.54901 11.813675 28.61906
#> 2 12.126782 27.5932440 16.87612 26.552688 21.31737  9.444521 14.61809
#> 3 22.473089 11.9313407 17.60196  2.898803 26.26707  0.020982 24.01361
#>            h        i        j
#> 1 20.3611736 27.79044 21.24925
#> 2  0.9615546 11.37095 16.07453
#> 3 18.0320749 22.05473 14.04698

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 0.95155325
#> b 2.89084430
#> c 0.06906368
#> d 2.77743905
#> e 0.70064761
#> f 2.17895087
#> g 0.12489150
#> h 1.42512068
#> i 0.32975980
#> j 0.22943634

References