Handbook of Market Area and Accessibility Models

Two-Step Floating Catchment Area (2SFCA) Analysis

Background

The Two-step Floating Catchment Area (2SFCA) Analysis was developed by Luo and Wang[1] in the context of health geography, more specifically: to measure the spatial accessibility of healthcare providers. The basic idea is to include both the capacity utilization of the providers (supply-to-demand ratio) and their accessibility from the demand locations. Furthermore, a catchment threshold is introduced, which is a maximum distance or travel time up to which supply locations and demand locations are considered.

Model formulation

The basic 2SFCA Analysis is calculated as follows [1]:

Step 1: \(R_j = \frac{S_j}{\sum_{k \in \{d_{kj} \leq d_0\}} P_k}\)

where \(R_j\) is the supply-to-demand ratio at location \(j\) which is within the catchment threshold, \(P_k\) is the population of origin \(k\) which is within the catchment threshold, \(S_j\) is the number of opportunities at location \(j\), \(d_{kj}\) is the distance or travel time between \(k\) and \(j\), and \(d_0\) is the catchment threshold.

Step 2: \(A_i^F = \sum_{j \in \{d_{ij} \leq d_0\}} R_j\)

where \(A_i^F\) is the accessibility at origin \(i\) and \(d_{ij}\) is the distance or travel time between \(i\) and \(j\).

Empirical application

A basic 2SFCA Analysis involves the following steps:

  1. Define a study area and divide it into \(I\) customer origins (e.g., municipalities, ZIP code areas, census tracts)
  2. Define a catchment threshold \(d_0\)
  3. Identify the relevant \(J\) supply locations within the study area
  4. Collect the size values \(S_j\) (e.g., opportunities) of all \(J\) supply locations and the local populations \(P_k\)
  5. Calculate travel costs \(d_{kj}\) and \(d_{ij}\) (up to \(d_0\)) and store them travel cost matrices
  6. Calculate \(R_j\) for all supply locations
  7. Sum \(R_j\) over all customer origins to calculate \(A_i^F\)

Further notes

The empirical application of the 2SFCA Analysis has the same requirements as a Huff Model analysis, including the calculation of travel costs for all \(I \times J\) combinations of customer origins and supply locations. For more information on the calculation of a travel cost matrix, see the corresponding Huff Model section.

The approach was extended by including distance decay functions from market area models instead of defining a distance threshold[2][3].

For a broader discussion of 2SFCA Analysis, including a comparison with other approaches to modeling accessibility, see the paper by Rauch et al.[4]

References

[1] Luo W, Wang F (2003) Measures of spatial accessibility to health care in a GIS environment: synthesis and a case study in the Chicago region. Environment and Planning B: Planning and Design 30: 865-884. 10.1068/b29120

[2] Luo J (2014) Integrating the Huff Model and Floating Catchment Area Methods to Analyze Spatial Access to Healthcare Services. Transactions in GIS 18(3): 436-448. 10.1111/tgis.12096

[3] Subal J, Paal P, Krisp JM (2021) Quantifying spatial accessibility of general practitioners by applying a modified huff three-step floating catchment area (MH3SFCA) method. International Journal of Health Geography 20: 9. 10.1186/s12942-021-00263-3

[4] Rauch S, Stangl S, Haas T, Rauh J, Heuschmann PU (2023) Spatial inequalities in preventive breast cancer care: A comparison of different accessibility approaches for prevention facilities in Bavaria, Germany. Journal of Transport & Health 29: 101567. 10.1016/j.jth.2023.101567