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Calculate Enhanced Two-Step Floating Catchment Area (E2SFCA) accessibility scores

Source: R/03-spax_e2sfca.R
spax_e2sfca.Rd

Implements the Enhanced Two-Step Floating Catchment Area (E2SFCA) method as proposed by Luo & Qi (2009). This method improves upon the original 2SFCA by incorporating distance decay effects and allowing for variable catchment sizes, providing more realistic measures of spatial accessibility to services.

Usage

spax_e2sfca(
  demand,
  supply,
  distance,
  decay_params = list(method = "gaussian", sigma = 30),
  demand_normalize = "identity",
  id_col = NULL,
  supply_cols = NULL,
  indicator_names = NULL,
  snap = FALSE
)

Arguments

demand

SpatRaster representing spatial distribution of demand

supply

vector, matrix, or data.frame containing supply capacity values

distance

SpatRaster stack of travel times/distances to facilities

decay_params

List of parameters for decay function:

  • method: "gaussian", "exponential", "power", or "binary"

  • sigma: decay parameter controlling the rate of distance decay

  • Additional parameters passed to custom decay functions

demand_normalize

Character specifying normalization method:

  • "identity": No normalization (original weights)

  • "standard": Weights sum to 1 (prevents demand inflation)

  • "semi": Normalize only when sum > 1 (prevents deflation)

id_col

Character; column name for facility IDs if supply is a data.frame

supply_cols

Character vector; names of supply columns if supply is a data.frame

indicator_names

Character vector; custom names for output accessibility layers

snap

Logical; if TRUE enable fast computation mode (default = FALSE)

Value

A spax object containing:

  • accessibility: SpatRaster of accessibility scores

  • type: Character string "E2SFCA"

  • parameters: List of model parameters used

  • facilities: data.frame of facility-level information

  • call: The original function call

Details

The E2SFCA method enhances the original 2SFCA by introducing:

Step 1: For each facility j: * Weight demand points by distance decay: Wd(dij) * Calculate supply-to-demand ratio Rj = Sj/sum(Pi * Wd(dij))

Step 2: For each demand location i: * Weight facility ratios by distance decay: Wr(dij) * Calculate accessibility score Ai = sum(Rj * Wr(dij))

Key improvements over original 2SFCA: 1. Distance decay within catchments 2. Differentiated travel behavior in demand vs. access phases 3. Smoother accessibility surfaces 4. More realistic representation of access barriers

The method supports various distance decay functions and normalization approaches to handle different accessibility scenarios and prevent demand overestimation in overlapping service areas.

References

Luo, W., & Qi, Y. (2009). An enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to primary care physicians. *Health & Place*, *15*(4), 1100-1107. https://doi.org/10.1016/j.healthplace.2009.06.002

See also

* [spax_2sfca()] for the original method without distance decay * [compute_access()] for more flexible accessibility calculations * [calc_decay()] for available decay functions

Examples

# Load example data
library(terra)
library(sf)

# Convert under-5 population density to proper format
pop_rast <- read_spax_example("u5pd.tif")
hos_iscr <- read_spax_example("hos_iscr.tif")

# Drop geometry for supply data
hc12_hos <- hc12_hos |> st_drop_geometry()

# Calculate accessibility with Gaussian decay
result <- spax_e2sfca(
  demand = pop_rast,
  supply = hc12_hos,
  distance = hos_iscr,
  decay_params = list(
    method = "gaussian",
    sigma = 30 # 30-minute characteristic distance
  ),
  demand_normalize = "semi", # Prevent demand inflation
  id_col = "id",
  supply_cols = "s_doc"
)

# Extract and plot accessibility surface
plot(result$accessibility, main = "Doctor Accessibility (E2SFCA)")


# Access facility-level information
head(result$facilities)
#>     id s_doc
#> 1 c172   522
#> 2 c173   321
#> 3 c174    67
#> 4 c175    81
#> 5 c176   175
#> 6 c177    77

# Compare different decay functions
result_exp <- spax_e2sfca(
  demand = pop_rast,
  supply = hc12_hos,
  distance = hos_iscr,
  decay_params = list(
    method = "exponential",
    sigma = 0.1
  ),
  demand_normalize = "semi",
  id_col = "id",
  supply_cols = "s_doc"
)

# Plot both for comparison
plot(c(result$accessibility, result_exp$accessibility),
  main = c("Gaussian Decay", "Exponential Decay")
)