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precise reason why such methods are not as
accurate as alternative modelling methods
discussed below.
Hence, this methodology (while offering a
useful overview of potential catchment area
revenue) is unreliable due to the inadequate
treatment of spatial interactions and the
inadequate treatment of competitor impacts (for
more details, see Benoit and Clarke 1997). The
alternative is to build models of interactions or
flows.
Let us label any residential zone such as a postal
sector or enumeration district (i) and any facility
location such as a centre or supermaket (j). Then
the number of people travelling between i and j
can be labelled Sij, and modelled using a spatial
interaction approach:
that destination vis-à-vis all other competing
destinations.
The model works on the assumption that, in
general, when choosing between centres that are
equally accessible, shoppers will show a preference
for the more attractive centre (which can be
measured by size or other attributes such as car-
parking availability, price, etc.). When centres are
equally attractive, shoppers will show a preference
for the more accessible centre. Note, however, that
these preferences are not deterministic. Thus,
when choosing between equally accessible centres,
shoppers will not always choose the most
attractive. The models are therefore able to
represent the stochastic nature of consumer
behaviour. Neighbouring households would not
be expected to behave in exactly the same way,
even though their characteristics are similar.
Equally, particular individuals and households will
not always use the same retail centres.
These models can be disaggregated in a number
of ways. First, recognition of different types of
consumer such as car owners and non-car owners
is important in most real-world applications.
Second, as mentioned above, the destination
attractiveness term can be disaggregated to
include all sorts of centre or store attributes
(Pacione 1974; Spencer 1978; Timmermans 1981;
Wilson 1983). Third, various forms of the
distance deterrence terms may be used and
different transport modes introduced. Wilson
(1983) provides a useful summary of the degree
to which retail models can be disaggregated,
while other authors have looked at new
formulations of spatial interaction models that
incorporate additional behavioural variables.
Fotheringham (1986) has argued that the models
need to be modified to allow stores in close
proximity to other stores to have greater
attractiveness to consumers. These competing-
destination models measure relative accessibility
of stores to one another to measure the degree
to which stores located close to each other have
a locational advantage over isolated outlets. This
may be particularly important in comparison
shopping.
where
S ij is the flow of people or money from residential
area i to supermarket j;
O i is a measure of demand in area i;
W j is a measure of the attractiveness of
supermarket j;
c ij is a measure of the cost of travel or distance
between i and j;
A i is a balancing factor that takes account of the
competition and ensures that all demand is
allocated to centres in the region.
Formally, it is written as:
The model allocates flows of expenditure between
origin and destination zones on the basis of two
main hypotheses:
1
Flows between an origin and destination will
be proportional to the relative attractiveness
of that destination vis-à-vis all other
competing destinations.
2
Flows between an origin and destination will
be proportional to the relative accessibility of
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