Zhazira Amirgaliyeva
Kazakh National University named after al-Farabi
About evolution of the retail gravity model
Shopping takes an important role in our daily routine and organisation of the
retail sector has significance for every household. The characteristics of
shopping can also help to investigate changes in the social and economical
behaviour of households and technological innovations. Over a short period of
time, the interaction of such changes, namely changes in customer mobility and
expenditure, technology and regulation caused fundamental change in land use
planning within retail arrangements, one main example of such structural
change is the replacement of the traditional neighbourhood stores by larger
multi-purpose shopping centres.
Progression of technology in communication and transportation services made
consumers available to shop on a world scale, passing through international
boundaries and different time zones, however, despite the fact that purchase of
wide-range of goods is available through an online service, traditional timespace interactions in shopping remain stable.
In a framework of this publication, we consider historical background of a wellknown gravity model approach for modelling such traditional shopping
interactions between consumers and retail centres.
Modelling of shopping activities is significant for studying the retail and
consumer spatial interactions along with making expectations about the
business enlargement over a period of time in a considered geographical area. A
good example for the development of such model is a gravity model formulated
basically based on an idea of gravity related to Newtons law of universal
gravitation in physics which states that intercommunication of people from two
sites is proportional to their size and inverse to the distance between them. This
concept of costumer gravity was originally utilized by Reilly in 1929 and
Converse in 1929. Afterwards, the gravity model has developed and became
fundamental for various issues in spatial interaction modelling (for instance,
shopping trips, population ows, trac movements). Figure 1 demonstrates the
development of the retail gravity model that “occupies a central cog in the
evolution of spatial science and is at the edifice in the generation of ideas
borrowed from physics and their application to consumer behaviour".
Figure 1: Graphical representation of the gravity model evolution in the
framework of consumer behaviour
A brief information on historical background of the gravity model evolution
will be introduced below according to Robert Baker's research given in his book
named "Dynamic trip modelling from shopping centres to the Internet".
Development of the gravity model is essentially associated with quantitative
revolution in the history of geographical science in the 1960s and 1970s, which
characterised with the growth of quantitative methods and the change of
approach from regional geography into a spatial science behind geographical
research. For instance, significant analysis of consumer behaviour by
implementation of the utility and probability principles into the gravity model
were introduced by Huf in 1963, which states that consumer's comprehension of
the utility of a retail centre has considerable consequence in the choice of
alternative centres regarding travelling effect and expense.
Huf also pointed out some main deficiencies of the gravity model such as there
was insufficient hypothetical work which could elucidate occurrence of a
consistent pattern in shopping behaviour. In 1959 Scheider verified this
perception while studying gravity basis for intervening opportunities model of
Stouer which states that “the probability of a trip located at a destination in a
region is proportional to the number of destination opportunities contained in
that region", hence proximity of destinations always has an advantage in
journey formation.
It was imperative to ascertain the level of justification of the experimental data
to obtain a method of gravity model. In urban spatial connections, the impact of
remoteness has been a substantive determining factor, but the underlying
proceedings of consistent behaviour pattern were not clarified enough. At the
end of 1960s, Wilson attempted to eliminate complexities in constructing
gravity models using maximising entropy concept from a complex information
systems theory, hence the replacement of Newtonian equivalent with measure
of disorder (entropy) become the key of gravity interaction. Originally the
actual model of Wilson was designed for “the interaction between the journeyto-work of a number of workers in a residential zone to the number of jobs in an
employment zone". Likewise, the study of possible maximum expenses between
resident
sites
and
shopping
centres
was
conducted.
The model of Wilson contributed to the theoretical foundation of gravity
interaction, which has been utilized for an extensive variety of research on
modelling dynamic trips. Though the spatial behaviour of consumers was
insufficiently answered, yet the method was adequate at experimental level.
Many researchers as well as Gordon had developed his paper on this issue; he
claimed that the random formation of the gravity model does not deny
reasonable practice of an individual, but accepts unfeasibility accounting for
varied qualities of individual preferences. In 1978 Curry and Sheppard raised
the doubt about entropy maximisation method claiming that due to incomplete
information the method employ unreasonable biased statements. Sheppard
approved that two evident constraints on interconnection features in space,
information and cost, are not clearly and empirically de ned in Wilson's
derivation, so in his perception entropy was not a solution for explaining the
reasons of regularities occurrence. He contends “that the orientation of research
should be the search for the theory of individual behaviour that can be
aggregated into patterns of group interaction, consistent with the gravity
hypothesis".
In following studies, Wilson interceded in favour of entropy maximising
approach for modelling spacial interactivities claiming that its methods can be
adopted to satisfy various constraints in modelling complex behaviour, which
assist to understand the terms of the model. In support, Sheppard admits that
although the gravity model is inadequate in some sense it keeps giving
convincing experimental specifications.
From Baker's research we know that afterwards there were many other attempts
to construct the function of gravity interaction, however in the 1980s and 1990s
its value criticised as “the complexity of the real world has proved the
calibration process problematical and the specification of gravity models
fraught with difficulty".
Each decade put series of different impact on gravity model. For instance, the
end of 1970s and the beginning of 1980s was the time when a tendency in
mathematical modelling of spatial behaviour developed, and potential theory
was the source of the gravity model theory. Nevertheless, such introduction of
potential functions was not a novelty as preceding works on gravity model was
integrated with the concept of potential functions. As example, economic
potential function, market and sales potentials, population potential have been
practised by Gordon, Wilson and Huf respectively. In the 1970s Curry
following the studies conducted by Golledge and Burnett makes a formulation
of the potential theory of stochastic preferences in relation to Markov processes.
Spacial ordering is constructed from a theory of random walks, while potentials
are formulated in relation to probability. As prior mentioned, incomplete
information has been the obstacle to clarify; the consumer keeping in mind the
smallest possible loss chooses decision distribution that is unsystematic, so this
neglects a preference arrangement in defining consumer needs and
experimentally accounts for a minor proportion of shopping behaviour in a
retail site. Sheppard also claimed that if Stouffer's model of 'intervening
opportunities' developed in 1940 preserves existing conditions then a potential
function can always be found. Although the conception of potential is adequate
to spatial interaction, it does not assist to develop the model significantly, as a
physical analogy is not always apparent, which makes general acceptance of
such concepts problematical. Baker believes that “the e orts by Huf and Wilson
still remain the reference point for subsequent disaggregate choice modelling
and aggregate follow modelling, respectively".
In his research conducted in 1992 Brown argues that there have been many
works with attempts to synthesis of disaggregate and aggregate methodologies
to consumers behaviour and seek for a comprehensive model of such
interactions, as attempts to calibrate gravity models were problematic. Although
the gravity model has a rich research background and was successfully applied
for a number of essential theories of spatial interaction such as spatial
competition, rent bid and central place theories, the nature and direction of
gravity modelling was under mounting disillusionment after all due to
calibration issues.