SPATIAL INTERACTION MODELS – Richard Harris, Peter Sleight, Richard Webber

How the following retail question might be answered within a GI analytical environment? Suppose a consumer lives at location i (to be found at coordinate xi, yi) then what is the likelihood that they will visit a particular retail store at some other location j (at coordinate xi, yi)?

To answer this question, two ideas seem intuitive. First, that the attraction of the store to the consumer depends on what the store has to offer. This we shall quantify as the store’s mass (Mj), for reasons that will become clear. Second, that the consumer would prefer to travel a shorter distance to visit a store than a longer one and so the attraction of the store is related to the distance between locations i and j. These two assumptions allow the following spatial interaction model to be formed:

BIS GIS Formula 1

Where Fj(i) is the “force” of attraction that the store at j exerts on the consumer at i, increasing with the store’s “mass” but decreasing with the distance between i and j (the symbol α means proportional to). The power function, c, controls the distance. The higher its value, the less attractive the store is to a consumer at a fat distance relative to a consumer closer to the store. If c is given the value two and a constant g is introduced then previous equation can become:

BIS GIS Formula 2

The new equation is now analogous to a simple gravity equation expressing the force acting on an object i that is due to a body of mass Mj at distance dij from i.

So far only a single customer has been considered. S/he would have to have deep pockets to ensure the long-term success of the store! The total attraction of the store for n customers could be found by calculating and summing together the attraction for each individual consumer in turn:

BIS GIS Formula 3

However, it is expected that consumers living in a particular type of neighbourhood may have a different demand for the store compared to consumers living in another neighbourhood type. If the type of neighbourhood is denoted as k then neighbourhood differences in demand can be incorporated by giving each type a separate value of g and c. If there are nk consumers in neighbourhoods of type k then the total attraction of the store to them is:

BIS GIS Formula 4

But, given different numbers of consumers per neighbourhood type, then a better basis to compare neighbourhoods is with regards to the average attraction:

BIS GIS Formula 5

The last equation is less complicated than it may first appear! Remember, it only formalizes the assumptions made: that consumers are more likely to travel to a store with larger “mass”; that consumers are unlikely to travel to a store that is too far away; that demand for the store varies by neighbourhood type; and so too does the distance decay function (it is known, for example, that poorer neighbourhoods tend to do more of their shopping locally than richer neighbourhoods).

A measure of mass could be the size of the store or the number of specialist product lines it sells, while a survey could be used to measure differences in demand by neighbourhood.

Distance is more ambiguous. The shortest, straight-line distance between any i and j is easy to calculate given knowledge of their x and y locations (dMIN) but is an unrealistic measure if that shortest path cannot actually be traversed. Travelling from one to the opposite corner of a block in a city built to a grid plan often requires travelling east/west then north/south (or vice versa) where the diagonal path is blocked by buildings. In this circumstance the “Manhattan distance” could be a more realistic measure of the length travelled (dMAN). Moreover, often hat is meant by distance is really accessibility, in which case the “distance” between i and j is a function of the road and other transport networks, their length and the speed of travel along them – a speed that will likely change with the time of day and with the season. It may also be that consumers travel to the store not from home but from their workplace.

BIS GIS Formula 6

Issues of how to quantify the components of Fjk equation are neither trivial nor insurmountable but require further assumptions (simplifications of reality) to be made. Having done so, the equation could be used to estimate the attractiveness of a series of stores and that information used to calculate potential profitability, or to identify over or under performing stores. It could be used to identify potential locations for new stores on the basis of the local neighbourhood profiles provided by a geodemographic classification and it could also be used to estimate the impact on existing stores of a new store opening. For example, if a store is opened at the centre of a neighbourhood type that has above-average likelihood of residents visiting that particular chain then it is unlikely that those residents will travel further distances to visit existing stores. If the average spend of residents of the particular neighbourhood type is known and an estimate of how many of the local population travel to existing stores can be provided, then the impact of the new store on the existing network can be modelled.

Whether the simplifying assumptions of the model are realistic or nor depends a great deal on the context. There may be external influence (externalities) that lead consumers to prefer one shopping centre over another. Consumers may not act as rationally as the model assumes. The impact of competitor stores and their marketing strategies will almost certainly be relevant. All these additional factors suggest that our simple interaction model has potential for considerable development.



As the name implies, geodemographics is the coupling of information recording location (the geo) with other demographic, attribute data. This coupling defines a geographical dataset and, since GIS are systems to capture, store, transform, analyse, and display geographical data, it should not be surprising that GIS and geodemographics can be stablemates.

Geodemographic mapping is aligned to vector GIS which have their origins in cartography. Under the vector model, neighbourhoods are usually represented as two-dimensional areas – as polygons. Mapping geodemographic data usually requires a boundary file to be obtained to represent the neighbourhood and to which the attribute information is joined. Other GIS functions such as an overlay, aggregation or a point-in-polygon analysis may be required. The result may reveal apparent geodemographic patterns in a sample dataset. However, there is a risk that the patterns are due to chance and so the significance of any result should be tested. Maps can lie!

The process of collecting, managing and analysing neighbourhood information can be time consuming and difficult. Recognizing this situation and the market opportunity is presents, a number of GI software and data vendors have begun offering more joined-up solutions, making the process of acquiring, handling and visualizing neighbourhood data easies. Such systems can be extremely useful for all sorts of geographical enquiry and the cost of purchase is reducing.

GIS have their critics (limited spatial analysis, 3D visualization and temporal modelling are some of the complaints) but are nevertheless widely used to solve real-world problems and “to improve many of our day-to-day working and living arrangements”. There are examples of GIS applications in: the utilities; telecommunications; transportation management; emergency management; land administration; urban planning; the military; public libraries; health care; politics; monitoring land cover and land use; landscape conservation; agriculture; environmental assessment and even rebuilding a country!

Yet this “gallery of applications” also hints at why GIS could be a “nearly” technology for marketers. GIS are powerful and flexible, perhaps too much so, offering more functionality but, consequently, requiring more expert knowledge of how to use the software than a “typical” geodemographic user may actually require. In this light and again spotting a market niche, geodemographic vendors have developed their own analysis and visualization systems.



  • GIS are software used to capture, store, transform, analyse and display geographical data.
  • A geographic dataset contains both attribute and location information. The act of georeferencing adds geography to data.
  • A common georeferenced permits tables of data to be related and jointly manipulated.
  • The vector model commonly represents real-world objects as points, lines or polygons that are defined by a single or series of point coordinates.
  • A raster can be understood as a grid with associated attribute values.
  • GIS functions connected with geodemographic types of investigation include aggregation, overlay and point-in-polygon analysis,
  • There is a risk of attributing importance to apparent spatial patterns in geographical information when the patterns actually are of little or no significance. A related problem is that maps can “lie”.
  • Despite their many proven applications, GIS have been described as a “nearly technology” in marketing.

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