# 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          h
    #> 1  1.165296 23.940221  4.420221 24.338810 29.40716 10.99555 15.99315 22.0770353
    #> 2 22.250196  5.106196 18.901658 23.243694 28.74460 29.89078 21.85673 13.1939604
    #> 3 20.711940  7.165924 22.205717  4.813175 27.29280 25.16371 13.64475  0.3557868
    #>           i        j
    #> 1  8.846327 5.491492
    #> 2 27.544878 9.992862
    #> 3 17.380077 7.127191

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 2.9771456866
    #> b 1.0897984651
    #> c 2.3821799172
    #> d 1.2009856195
    #> e 0.0002327127
    #> f 0.7575795086
    #> g 0.1732212020
    #> h 1.4077847838
    #> i 1.1566673716
    #> j 1.3823777631

## References

- Grüebler E. (2021). Geospatial Analysis of Access to Healthcare: Child Development Needs and Available Care in the Canton of Zurich.
- Bauer, J., & Groneberg, D. A. (2016). Measuring Spatial Accessibility of Health Care Providers – Introduction of a Variable Distance Decay Function within the Floating Catchment Area (FCA) Method.
- Joerg, R., Lenz, N., Wetz, S., & Widmer, M. (2019). Ein Modell zur Analyse der Versorgungsdichte. Herleitung eines Index zur räumlichen Zugänglichkeit mithilfe von GIS und Fallstudie zur ambulanten Grundversorgung in der Schweiz.