Geoscience Reference
In-Depth Information
Simplest model that included a snow-related factor:
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8.4.3 B uilding a S Patial i interaction M odel
Spatial analysis is used as a tool to describe the flow of people, goods or services from one place to
another (Thomas and Hugget, 1980). One of the tools for this type of analysis is spatial interaction
models. These can be used in transport planning, land-use planning, retail decision support and
other similar applications. Commuting and travel behaviour by individuals is particularly relevant
and is a popular application of spatial interaction modelling (see O'Kelly et al., 2012; Openshaw
and Turton, 1994; Salas-Olmedo and Nogués, 2012; Wilson, 1969), in which conventional spatial
interaction models include entropy-based solutions for estimating the flow ( T (Tij), ) between origin
( i ) and destination ( j ) (O'Kelly, 2010; Openshaw, 1976) and an entropy-based model has been
developed using GP (Diplock and Openshaw, 1996). Problems are often represented as a matrix
categorised by the predictor used in each study (e.g. number, cost or distance of trips), spatial
reference point (e.g. town or parish) and a set of independent variables (e.g. demographics, eth-
nicity, class) which can thereafter be modelled using traditional statistical techniques or novel
data-driven ones such as GP.
The following spatial interaction model was originally presented in the irst edition of this topic
(Diplock, 2000). It is a useful case study because not only does it show how GP can be used to build
spatial interaction models but also because it is able to demonstrate some of the features of GP that
were typical in the late 1990s. The example is a study of journey-to-work data in which the number
of trips to work is predicted from data collected for Durham County as part of the UK Census in
1966. The GP source code and search algorithm used for the Durham journey-to-work analysis was
programmed almost entirely from scratch in Fortran (Diplock, 2000). Nowadays, command-line
programming is seldom necessary thanks to the availability of GP software. Indeed, we are now
in the age of powerful desktop computers and user-friendly packages such as GeneXproTools and
Eureqa , meaning that GP modelling requires comparatively little effort in terms of software coding
and parameterisation, and run times have been reduced to as little as 30 min, depending on the size
of the data set and the power of your computer.
Input data for the County Durham journey-to-work example comprised 5329 records pre-
sented in a 73 × 73 matrix. Two model types were developed and tested using different types
of journey flow data: (1) volume based and (2) probability based. The volume-based models
calculate predicted flows, that is, the number of workers moving between zones, which add up
to the total number of flows. The probability-based model takes the number of workers and flow
and calculates each flow as a percentage of the total and then predicts an output based on these
units, which add up to 1. In each case, the models were evolved to predict flow ( T (Tij), ), measured by
the number of journeys to work to and from the 73 census zones. Seven independent variables
were used to evolve the GP model, which are described in Table 8.8. The mathematical functions
used for model development and validation are shown in Table 8.9. The goodness-of-fit measure
selected for model evaluation was the sum-of-squares error (SoS). The probability model outputs
were subsequently converted back to volumes, for error calculation purposes so that both sets of
results could be compared.
The two preferred solutions are rather large and cumbersome, as can be seen in Equations 8.8
and 8.9. To help make the GP outputs simpler and easier to work with, they were simplified using
a piece of software capable of resolving and simplifying equations called Maple V (release 3), the
outputs of which are shown in Equations 8.10 and 8.11.
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