Modelling Migration with Poisson Regression

Most statistical analysis is based on the assumption that error is normally distributed, but many data sets are based on discrete data (the number of migrants from one place to another must be a whole number). Recent developments in statistics have often involved generalising methods so that they can be properly applied to non-normal data. For example, Nelder and Wedderburn (1972) developed the theory of generalised linear modelling, where the dependent or response variable can take a variety of different probability distributions linked in one of several possible ways to a linear predictor, based on a combination of independent or explanatory variables. Several common statistical techniques are special cases of the generalised linear models, including the usual form of regression analysis, Ordinary Least Squares regression, and binomial logit modelling. Another important special case is Poisson regression, which has a Poisson-distributed dependent variable, linked logarithmically to a linear combination of independent variables. Poisson regression may be an appropriate method when the dependent variable is constrained to be a non-negative integer, usually a count of the number of events in certain categories. It assumes that each event is independent of the others, though the probability of an event may be linked to available explanatory variables. This chapter illustrates how Poisson regression can be carried out using the Stata package, proceeding to discuss various problems and issues which may arise in the use of the method. The number of migrants from area i to area j must be a non-negative integer and is likely to vary according to zone population, distance and economic variables. The availability of high-quality migration data through the WICID facility permits detailed analysis at levels from the region to the output areas. A vast range of possible explanatory variables can also be derived from the 2001 Census data. Model results are discussed in terms of the significant explanatory variables, the overall goodness of fit and the big residuals. Comparisons are drawn with other analytic techniques such as OLS regression. The relationship to Wilson’s entropy maximising methods is described, and variants on the method are explained. These include negative binomial regression and zero-censored and zero-truncated models.

Estimating Spatially Consistent Interaction Flows Across Three Censuses

A significant problem facing geographical researchers who wish to compare migration and commuting flows over time is that the boundaries of the geographical areas, between which flows are recorded, often change. This chapter describes an innovative method for re-estimating the migration and commuting data collected in the 1981 and 1991 Censuses for the geographical units used in the 2001 Census. The estimated interaction data are provided as origin-destination flow matrices for wards in England and Wales and pseudo-postcode sectors in Scotland. Altogether, there were about 10,000 zones in 1981, 1991 and 2001, providing huge but sparsely populated matrices of 10,000 by 10,000 cells. Because of the changing boundaries during inter-censal periods, virtually no work has attempted to compare local level migration and commuting flows in the two decades, 1981-91 and 1991-2001. The re-estimated spatially consistent interaction flows described here allow such comparisons to be made and we use migration change in England and commuting change in Liverpool to demonstrate the value of these new data.

Analysing Structures of Interregional Migration in England

In this chapter, we explore the age and ethnic structures of interregional migration in England, as measured by the 1991 and 2001 Censuses. In doing so, we first analyse the main effect and two-way interaction components of migration flow tables cross-classified by (1) origin, destination and age and (2) origin, destination and ethnicity. Second, we test the significance of three-way interaction terms over time by comparing various unsaturated log-linear model fits. The aim is to identify the key structures in the migration flow tables and how they have changed over time. This is important for understanding the mechanisms underlying the more general patterns of migration. These analyses could also be used to inform the estimation or projection of migration flows. Our findings are that, despite a large increase in the levels of interregional migration, migration structures in England have remained fairly stable over time. The main changes have to do with the increases in the relative levels of ethnic migration over time, which has been unequal across space.

Temporal and Spatial Consistency

One of the major problems challenging time series research based on stock and flow data is the inconsistency that occurs over time due to changes in variable definition, data classification and spatial boundary configuration. The census of population is a prime example of a source whose data are fraught with these problems, resulting in even the simplest comparison between the 2001 Census and its predecessor in 1991 being difficult. The first part of this chapter introduces the subject of inconsistencies between related data sets, with general reference to census interaction data. Various types of inconsistency are described. A number of approaches to dealing with inconsistency are then outlined, with examples of how these have been used in practice. The handling of journey to work data of persons who work from home is then used as an illustrative example of the problems posed by inconsistencies in base populations. Home-workers have been treated in different ways in successive UK censuses, a factor which can cause difficulties not only for researchers interested in such working practices, but also for those interested in other aspects of commuting. The latter set of problems are perhaps more pernicious, as users are less likely to be aware of the biases introduced into data sets that are being compared. In the second half of this chapter, we make use of a time series data set of migration interaction data that does have temporal consistency to explore how migration propensities and patterns in England and Wales have changed since 1999 and in particular since the year prior to the 2001 Census. The data used are those that are produced by the Office of National Statistics based on comparisons of NHS patient records from one year to the next and adjusted using data on NHS patients re-registering in different health authorities. The analysis of these data suggests that the massive exodus of individuals from major metropolitan across the country that has been identified in previous studies is continuing apace, particularly from London whose net losses doubled in absolute terms between 1999 and 2004 before reducing marginally in 2005 and 2006. Whilst this pattern of counterurbanisation is evident for all-age flows, it conceals significant variations for certain age groups, not least those aged between 16 and 24, whose migration propensities are high and whose net redistribution is closely connected with the location of universities. The time series analyses are preceded by a comparison of patient register data with corresponding data from the 2001 Census. This suggests strong correlation between the indicators selected and strengthens the argument that patient register data in more recent years provide reliable evidence for researchers and policy makers on how propensities and patterns change over time.

Analysing Interaction Data

Large and complex interaction data sets present researchers with analytical challenges and this chapter attempts to identify and illustrate a number of ways to analyse origin-destination flows. Given the impossible task of providing a comprehensive review in such a limited space, certain analytical measures, modelling methods and visualisation techniques have been selected for inclusion, following an introduction to the notation commonly employed to represent interaction variables. Various Census and NHS patient register data sets are used to exemplify interaction measures, beginning with simple net balances and inflow/outflow ratios and moving onto indices of connectivity, inequality and distance moved. The multiplicative component framework is introduced as a particularly useful analytical approach. More sophisticated methods of modelling interaction data using statistical or mathematical calibration techniques are reviewed, examples of log-linear regression and spatial interaction model structure are highlighted in the context of historical calibration and a brief discussion of the use models for future projection is included. Maps that show patterns of geographical movement function as effective illustrative and research tools. Computerized mapping of geographical movement has evolved since the 1970s and 1980s and, in this chapter, we introduce a new method of mapping flows using vectors and illustrate this approach with micro data on pupils travelling to school. The chapter aims to provide a broad introduction to analysis methods for interaction data, many of which are subsequently applied in later chapters of the book.

Defining Labour Market Areas by Analysing Commuting Data

This chapter draws on research undertaken in revising a set of functional regions known as Travel-to-Work Areas (TTWAs) which are the only official statistical areas in the UK defined by academics. The objective of the research is to define the maximum possible number of separate TTWAs that satisfy appropriate statistical criteria that ensure the areas meet guiding principles for labour market area boundary definition. Thus, the research is an example of a functional regionalisation which is highly constrained by the purpose to which the resulting boundaries will be put. The chapter briefly reviews previous TTWA definition methods, setting this in the context of the very limited academic research on regionalisation methods. The production of the 2001 Census commuting data provided opportunities for defining new labour market areas and the chapter explains how the TTWA research has responded with several key innovations. The empirical component of the chapter then illustrates the effect of these innovations by presenting a new visualisation of the workings of the definition method and also some analysis of the sensitivity of the results to changes in the method. Finally, there is a very brief look at some possible ways in which this field of research could be extended.

Internal Migration Propensities and Patterns of London's Ethnic Groups

The ethnic dimension of internal migration in Britain below the district scale has been understudied despite its importance for understanding local and community development. Data from the 2001 Census shows that migration propensities by ethnic group and age for London migrants differ considerably from national migration propensities, especially when migrants within London are distinguished from those arriving in or leaving the capital. Whilst disaggregating ward net migration on this basis reveals processes of deconcentration within London, dispersal from outer wards to the rest of the country and net in-migration to inner wards from outside London and from overseas, patterns of net movement vary by ethnicity and age, influenced by the geographical pattern of ethnic population residential location. Evidence from an analysis of net migration, population concentration and deprivation by quintile group suggests that migrants from most of the non-white ethnic groups are tending to move within London to areas containing lower proportions of those in the same ethnic group. White migrants, on the other hand, are moving towards areas with higher white population concentrations. Finally, there is a tendency for all ethnic groups to move away from more deprived wards towards less deprived areas within London, particularly Indians aged over 25.

New Migrant Databank Concept and Development

Few parts of the UK remain unaffected by the surge in migration from central and eastern Europe that has been evident since the expansion of the European Union in 2004. However, the statistical instruments available to measure the multi-dimensional impact of international migration remain inadequate. The lack of empirical evidence to support research and analysis of migrant populations is an issue that affects a broad range of organisations at international, national, regional and local level. The problem is particularly acute in a selected set of local areas, where migrant populations have had a significant demographic, economic and social impacts. This chapter reports on work examining the changing profile and dynamics of the UK’s ethnic populations. The estimation and projection of ethnic group populations for local areas requires accurate intelligence on the inflow and outflow of international migrants. In the absence of a definitive source of data that can provide these statistics, the New Migrant Databank (NMD) has been developed which combines alternative sources of international migration data into a common statistical framework for presentation and analysis. The alternative sources of international migration data are summarised and a number of analytical examples are provided to illustrate how the NMD can provide a much improved picture of patterns and trends at a local level and the basis for improved intelligence on local estimates of both short-term and long-term migration. A number of developments are suggested, both to focus future research and to extend the content and value of the NMD as a common source of intelligence on UK immigration and emigration.

Interaction Data

As we saw in Chapter 1, interaction data sets have been derived from a number of sources, including censuses, other surveys and from a range of administrative sources. These typically have the characteristic that the data form large, sparsely populated matrices. Where the matrices do have non-zero values, those numbers are often small. This is highly significant when confidentiality is concerned – small numbers in aggregate data are generally seen as representing an increased risk of disclosure of data. This chapter looks at confidentiality issues with particular regard to interaction data. Different types of disclosure are considered, together with the reasons why interaction data are thought to pose particular disclosure problems. Methods of disclosure control are outlined, and then two particular methods are studied: those used in the 1991 and the 2001 UK Censuses. The methods used and the extent of their effects are described, and suggestions for how best to use the affected data sets are given.

Commuting to School

The education sector in England and Wales is becoming increasingly data rich, with the regular collection of the Pupil Level Annual School Census (PLASC) and school preference information, together with the compilation of school performance league tables. However, it is also a rapidly changing environment both in terms of demographic demand as well as policy responses from Government. The latest policy documents require that local education authorities provide fair and equitable admissions policies for all, while at the same time limiting the number of surplus school places. Moreover, funding has to be targeted appropriately in the face of significant changes in the complexion and number of state educated school pupils. Therefore, it is crucial for education planners to be able to interpret the large quantities of data collected each year into valuable intelligence to support planning and decision making. This chapter explores the use of classic spatial interaction models with journey to school data for the purpose of school network planning for the city of Leeds. The limitations associated with the application of spatial interaction models in the education sector will be discussed, and modifications to the computational form will be explored using a genetic algorithm. Spatial interaction models representing pupils from different socio-demographic backgrounds will be calibrated and incorporated into an overarching logic model called the Spatial Education Model (SEM). Finally, the SEM will be used to forecast pupil numbers attending schools in the study area up to the year 2013.