In the previous sections of this chapter, results from the migration matrix have been used to analyse the patterns of UK migration between 2001/02 and 2010/11. In order to reduce the burden of information being presented when moves from origins to destinations are analysed, the city region framework has been used to group 406 LADs
into 47 functional regions. Given that in each year between 35 and 37 per cent of total LAD-LAD migrants are excluded when only moves across a boundary of one of the city region component parts are considered, this section assesses if the patterns seen at LAD scale hold when the city region framework is used. This analysis is carried out using a doubly constrained spatial interaction model (SIM, which has been implemented using the IMAGE system) and a set of modelled migration flows are presented as a validation tool from which it is possible to analyse how different the frictional effect of distance is when using the LAD and city region geographies.
The basic principle of the SIM in the context of migration is that three variables dictate the magnitude of each modelled flow: the sizes of the origin and destination populations both influence the volume of migration from/to that area and migration is inversely proportional to the distance between origin and destination where “migrants tend to minimise the uncertainty about a move by favouring closer destinations over more distant ones” (Fotheringham and O'Kelly 1989, p.9). This preference for shorter distance migration over longer distance migration is termed distance decay (and given the Greek symbol beta, ). The phenomenon is reported by Ravenstein (1885) as one of the laws of migration and confirmed in a large number of contemporary studies (Kalogirou 2005; Dennett and Wilson 2013; Fotheringham and Rogerson 1993;
Singleton et al. 2012).
Using a doubly constrained SIM (as originally specified by Wilson, 1970; 1971), modelled results at LAD and city region scale have been produced, with the constraints being the marginal origin or destination total for each LAD/city region component part.
By producing modelled results at LAD and city region scale, it is possible to assess the effect that choosing a classification which groups LADs has on results as “the routine is predictive rather than explanatory…and merely seeks to allocate a known number of outflows and inflows to links between these origins and destinations” (Fotheringham and O'Kelly 1989, p.3). Effectively, using the SIM provides a consistent way of modelling flows within the 406x406 LAD matrix and 47x47 city region matrix, so the results are comparable. Similarity between the results at two spatial scales would suggest that aggregating LADs to city regions still retains the underlying spatial structure of the data. As described by Daras et al. (2013), the doubly constrained SIM takes the form:
(6.1) where is the number of migrations between zone and zone ; is the total number of out-migrations originating from zone ; is the total number of in-migrations terminating in zone ; and are balancing factors that ensure out-migration and in-migration constraints are satisfied (here the marginal totals of the matrix) while represents the distance term where is the distance decay parameter. Such a doubly constrained SIM is implemented in a recent study by Dennett and Wilson (2013) who use it within a multilevel framework to model subnational international flows in Europe between 2002 and 2007. They choose the doubly constrained model as it makes “use of the maximum amount of available data” (p.1504) given that the marginal in and out-migration totals are available to them (as they are for the LAD and city region tables used in this chapter).
Table 6.5: SIM beta values and mean migration distance for predicted model of LAD and city region flows, 2001/02 to 2010/11
Table 6.5 shows two outputs: the distance decay parameters (beta values) and the mean migration distances for the two spatial interaction models (one at LAD and one at city region scale). Figure 6.13a visualises the beta values and Figure 6.13b visualises the mean migration distance across the time series. The beta value represents the frictional effect of distance, with a higher value meaning that distance has greater effect on the
likelihood of migration. The mean migration distance reports the average distance that all migrants in the system have moved and in both LAD and city region model is the average distance for all moves between area centroids. The mean migration distance is used to calibrate the final SIM output for both LAD and city region, as the mean distance for each SIM is the same as the observed mean distance in the two matrices.
There is considerable consistency in the trend across the decade for the beta value and mean migration distance at both LAD and city region scale. The LAD beta value is higher than the city region beta, which would be expected as there are 406 LADs, compared with 47 city region component areas meaning that distance is more of a hindrance where there are more options for shorter distance migration. For the same reason, mean migration distance is higher for the city region model than the LAD model, showing that the frictional effect of distance is greater on flows between areas that are much larger and involve longer distance movements. Despite these differences, the overall trend through the time series is one of increase for beta values and decrease in mean migration distance at both spatial scales. This suggests that between 2001/02 and 2010/11 the frictional effect of distance increases, which means that people are, overall, moving shorter distances. Both the LAD and city region SIM show a distinct peak of beta values for 2006/07, alongside a dip in mean migration distance.
a: SIM beta vales for LAD and city region areas
b: SIM mean migration distances for LAD and city region areas
Figure 6.13: SIM beta values and mean migration distances for LADs and city regions, 2001/02 to 22010/11
As a validation tool, that the trends seen at LAD and city region are similar is reassuring, as it suggests that using a city region framework to represent the data is a
suitable solution that maintains the structure of the migration patterns that are occurring at LAD scale. From the results presented in this section, it is possible to conclude that the similarity in the pattern of beta value and mean migration distance in the two models between 2001/02 and 2010/11 lends strength to the decision to use a city region framework to examine results produced at LAD scale.