Zoning and spatial units

Before any routing happens, a decision is made about what the origins and destinations are: individual addresses, postcode zones, municipalities, or grid cells. This decision introduces errors that no amount of routing precision can repair, and it is the most under reported source of difference between accessibility studies.

Aggregation error

Two ways to place the representative point of a zone. Grey triangles are the geometric centroids of Dutch PC4 areas; black dots are the weighted centres of the residential objects those areas contain.

When a zone is represented by a single point, every dwelling in it is treated as if it were at that point. Two distinct problems follow.

• Intrazonal impedance is undefined. The distance from a zone to itself is zero by construction, which is wrong, and it matters most for exactly the short trips where accessibility differences are sharpest, such as walking to a shop or cycling to school. Common fixes are a fraction of the zone's radius, or the mean distance between address pairs inside the zone.
• The representative point is a choice. A geometric centroid can fall in a lake, on an industrial estate, or outside the zone entirely for a horseshoe shaped municipality. A population weighted point derived from address or building data is almost always better, and is what we use. The Dutch PC4 travel time matrix in Applications places each zone at the weighted centre of its BAG residential objects, as in the figure above.

Aggregation error grows with zone size and with the heterogeneity inside the zone. It is largest in rural areas, where zones are big, which means it systematically distorts precisely the urban versus rural comparisons that accessibility studies are often commissioned to make.

The modifiable areal unit problem

Results depend on both the scale of the zoning and the way boundaries are drawn at that scale, the modifiable areal unit problem. Two zonings of the same country with the same number of zones can produce different rankings.

The practical response is not to solve it, since it cannot be solved, but to bound it: compute the indicator at two or more spatial resolutions and report whether the conclusion holds.

Choosing a unit

Unit	When appropriate	Cost
Addresses or buildings	Local studies, service distance analysis, anything where short distances matter	Highest, millions of origins
Grid cells (100 m, 500 m)	National and continental studies, comparability across countries	Moderate, regular, no MAUP boundary effects but still scale effects
Postcode zones (PC4, PC6)	Where results must join to administrative or commercial data	Moderate, irregular sizes
Municipalities or regions	Policy reporting at that level only	Low, heavy aggregation error

Note that origins and destinations need not use the same unit. A common and efficient pattern is fine grained origins, where people live, against exact destination locations, where facilities are. This keeps precision where it matters without a full address to address matrix.

Edge effects

Destinations just outside the study area are invisible to the model, so locations near the boundary score artificially low. This is a data extent problem rather than a zoning one, but it shows up the same way on the map. Mitigate it by extending the network and the destination set well beyond the study area, with a margin at least as large as the largest threshold or the effective range of the decay function. See Network data sources.

Related

• Connecting origins and destinations to the network
• Euclidean versus network distance
• Accessibility indicators