Modelling Migration in England and Wales at the Ward Level and the Problem of Estimating Inter-Ward Distances

Seraphim Alvanides, Paul Boyle, Oliver Duke-Williams, Stan Openshaw and Ian Turton
School of Geography, University of Leeds, Leeds LS2 9JT, United Kingdom

A considerable research effort has been devoted to modelling aggregate migration within England and Wales, both to understand the factors which influence the complex pattern of flows and to identify broad trends in the redistribution of population. Two major problems with these models are addressed here.

Firstly, the vast majority of this migration modelling literature has considered flows between large areal units, such as districts, counties or regions, and this ignores the majority of migration which occurs within these areas over short distances. Detailed ward-level migration flow data were available from the 1981 Census, but they were difficult to access, only disaggregated migrants by sex, and were hard to handle, because of the size of some of the matrices involved. Consequently, few researchers took the opportunity to model these flows, despite the fact that important migration processes may have been masked by the scales at which the modelling work was undertaken. The ward-level data which became available from the 1991 Census have been made much simpler to access through the SMSTAB package developed at Leeds and these data are disaggregated by both age and sex. The opportunity to model migration at this detailed scale of analysis is enticing, but the problem then becomes one of dealing with very large data sets using complex modelling routines; the matrix of total inter-ward flows is 99302, for example. In this study, advances in parallel programming and the data-handling capability of the T3D based in Edinburgh have allowed a series of Spatial Interaction Models to be fitted for the inter-ward flows within England and Wales.

Secondly, most migration modelling strategies include origin and destination mass terms and some measure of distance, or cost, between these places as key explanatory variables. The distance between each pair of areal units is usually the most important explanatory variable and decisions about how to measure it, and the form of the distance decay curve, are crucial to model performance. Straight-line distances between each area’s population-weighted centroid are usually employed, but this is unrealistic as it under-estimates the distance moved between places separated by physical barriers, such as river estuaries or high ground. It also ignores the problem that crossing densely populated urban settlements may be much more time-consuming than crossing less densely populated areas, giving the appearance that these distances are further. Deriving a more realistic estimate of the 99302 inter-ward distances is a daunting prospect although a variety of, more or less, practical alternatives exist. For this exercise a set of increasingly complex alternatives were investigated. First, a network was generated by creating arcs between each of the contiguous ward centroids and using Arc-Info the shortest distance between each pair of wards was calculated. This solves the estuary problem and provides a second distance matrix to compare with the standard Euclidean distance matrix. Using a topological surface ward heights were estimated and the gradient between each pair of wards could be calculated. Weights were then added to the network to represent the underlying topography. Similarly, the ward population densities were used to weight arcs which were within large urban settlements. Combined, these measures allow a more realistic interpretation of the inter-ward ‘distances’ to be derived.

The results from the various models which include these different distance estimates are compared and the ‘unusual’ patterns of population redistribution within England and Wales are highlighted.