Design of Homogenous Territorial Units. A Methodological Proposal and Applications

Abstract

The interest in geographical information technologies has grown considerably over the last three decades. Today, geographical information is no longer the exclusive domain of government and public administrations (in the areas of planning, demography and topography), thanks to the development of computer tools which have enabled firms and academic institutions to use this information. <br/><br/>Statistical information of this kind is usually published at a variety of territorial levels in order to provide information of interest to all potential users. When using this information, researches have two alternatives for defining the basic territorial units for use in the study: first, they may use geographical units designed following normative criteria (that is, officially established territorial units such as towns or provinces) or, second, they can apply analytical criteria in order to design geographical units directly related to the phenomena under examination. <br/><br/>Most empirical studies use geographical units based on normative criteria, for several reasons: these units are officially established, they have traditionally been used in other studies, their use makes comparison of results easier and there is less scope for criticism. However, studies using units of this type may have an "Achilles' heel": they may be very restrictive, or unsuited the problem considered. For example, if we are analysing phenomena such as the regional effects of monetary and fiscal policy, how will the results be affected if the aggregated areas^ in each region are heterogeneous? Can these results change if the areas are redefined in such a way that each region contains similar areas? <br/><br/>This situation could be improved by the use of regionalisation processes to design geographical units based on analytical criteria by aggregating small geographical units^, but without reaching the upper level, or alternatively by combining information obtained from different levels. In this context, the design of analytical geographical units should consider three fundamental aspects: <br/><br/>a. Geographical contiguity. The aggregation of areas into regions such that the areas assigned to a region are internally connected or contiguous. <br/><br/>b. Equality: In some cases, it is important that the regions designed are "equal" in terms of a particular variable (for example population, size, presence of infrastructures, etc). <br/><br/>In this thesis dissertation, the term "area" will be used to denote the smallest territorial unit. The aggregation of areas will form a "region" and the aggregation of regions will cover the whole considered territory. <br/><br/>Apart from aspects such as statistical secrets or other legislation on the treatment of statistical data, according to Wise et al. (1997), this kind of territorial units are designed in such a way as to be above minimum population or household thresholds, to reduce the effect of outliers when aggregating data or to reduce possible inaccuracies in the data, and to simplify information requirements for calculations and to facilitate its visualisation and interpretations in maps. <br/><br/>See, for example, Albert et al. (2003), who analyse the spatial distribution of economic activity using information with different levels of regional aggregation, NUTS III for Spain and France and NUTS II for other countries, with the objective of "using similar territorial units". López-Bazo et al. (1999) analyse inequalities and regional convergence at the European level in terms of GDP per capita using a database for 143 regions using NUTS II data for Belgium, Denmark, Germany, Greece, Spain, France, Italy, Netherlands and Portugal, and NUTS-I data for the United Kingdom, Ireland and Luxembourg so as to ensure the comparability of geographical units. <br/><br/>c. Interaction between areas: Some variables do not exactly define geographical characteristics that can be used to aggregate the different areas, but may describe some kind of interaction between them (for example, distance, time, number or trips between areas, etc). These variables can also be used as interaction variables using a dissimilarity measure between areas in terms of socio-economic characteristics. The objective in this kind of regionalisation process is to make the areas belonging to the same region as homogeneous as possible with regard to the attribute(s) specified. <br/><br/>Unfortunately, in most cases, the aggregation of territorial information is usually done using "ad-hoc" criteria, due to the lack of sufficiently flexible regionalisation methods. In fact, most of these methods have been developed to deal with very particular regionalisation problems, so when applied in other contexts the results may be highly restrictive or inappropriate for the problem under consideration. However, whatever territorial aggregation method is applied, there is an implicit risk, known in the literature as the "Modifiable Areal Unit Problem" (Openshaw, 1984): the sensitivity of the results to the aggregation of geographical data and its consequences on the analysis. <br/><br/>The main objective in this thesis dissertation is to implement a new automated regionalisation tool to design homogeneous geographical units directly related to the phenomena analysed which overcomes some of the disadvantages of the methodologies currently available. <br/><br/>Thus, the specific objectives are: <br/><br/>a. To formulate the regionalisation problem as a linear optimisation model able to take into account not only the areal characteristics but also their non-metric and contiguity relationships. <br/><br/>b. To propose a heuristic model able to solve bigger regionalisation problems, incorporating in its search procedure the characteristics of a regionalisation process. <br/><br/>c. To compare the homogeneity of the analytical regions designed by applying the regionalisation model proposed in this thesis with those obtained using another regionalisation method based on normative criteria. For this comparison, provincial time series of unemployment rates in Spain will be used. <br/><br/>This dissertation is organised as follows. Chapter 2 briefly summarises the literature on different regionalisation methods. Special emphasis will be placed on those methodologies which have made the greatest impact on the specialist literature and on those that have been tested satisfactorily in real problems. <br/><br/>In chapter 3 the regionalisation problem is formulated as a linear optimisation model in which the problem of obtaining r homogeneous regions is based on the minimisation of the total heterogeneity, measured as the sum of the dissimilarity relationships between areas belonging to the same region. The proposed model has the following characteristics: <br/><br/>a. It is an automated regionalisation model that is able to design a given number of homogeneous geographical units from aggregated small areas subject to contiguity requirements. <br/><br/>b. The aggregation process takes into account not only the characteristics of each area but also the relationships between them (symmetric and not necessarily metric). <br/><br/>c. By formulating the regionalisation problem as a linear optimisation problem, we have the chance of finding the global optimum from among all feasible solutions. <br/><br/>d. More consistent solutions can be easily obtained by introducing additional constraints taking into account other specific requirements that are relevant for the regionalisation process.<br/> <br/>e. There is more freedom than in other methodologies regarding the shapes of the regions, which depend only on data characteristics and are not imposed by the methodology chosen. <br/><br/>f. With this model a region consists of two or more contiguous areas; this implies that no region can be formed by a single area. <br/>In order to apply this model in larger-scale regionalisation processes, Chapter 4 presents an algorithm called the RASS (Regionalisation Algorithm with Selective Search). The key advantage of this new algorithm is that the way it operates is based on the features of regionalisation processes themselves, where available information about the relationships between areas can play a crucial role in directing the search process more selective, more efficient and less random fashion. In fact, the RASS incorporates inside the linear optimisation model presented in chapter 3 in order to achieve local improvements in the objective function. These improvements can generate significant changes in regional configurations, changes that would be very difficult to obtain using other adapted iterative methods. <br/><br/>In Chapter 5 provincial time series of unemployment rates in Spain are used to compare the results obtained by applying two analytical regionalisation models, each one representing a different regionalisation strategy: a two-stage procedure based on cluster analysis and the RASS algorithm. The results will also be compared with normative regions available at two different scales: NUTS II and NUTS I. <br/><br/>Lastly, in Chapter 6 we present the most important conclusions and make proposals for further research lines.