-new Developments in Multidimensional Geographical Data and Policy Analysis

This paper aims at providing a survey of recently developed multidimensional methods in the field of spatial data and policy analysis. After a brief methodological introduction, various multidimensional techniques for data analysis are discussed. Much emphasis is placed on the treatment of soft (ordinal or qualitative) data. Next, several multidimensional methods for policy analysis (multi-objective programming, multicriteria analysis) are discussed. Here again much attention is paid to the treatment of soft information. *) Introduction Phenomena and problems in modern, societies are characterized by complexity, variation and interwoven relationships. This also holds true for spatial patterns and processes. Quantitative geography aims at providing theories and methods which describe such spatial structures and developments in a mathematical and/or statistical way in order to analyse in an operational way the dispersion and coherence of phenomena in regional and urban systems. The picture of spatial systems is in general rather complicated, and hardly any phenomenon in such systems can adequately be described or represented by means of a simple attribute such as a single scalar variable. Normally, such phenomena have a whole set of attributes (aspects, criteria, features) which give a represenstative mapping of these phenomena. Such a multidimensional representation of phenomena in spatial systems requires adjusted operational methods for an appropriate regional and urban data analysis as well as for a satisfactory policy analysis. During the* seventies a wide variety of multidimensional methods has been developed which are extremely useful for data and decision analysis. Many of them are able to provide ah operational framework for the analysis of spatial behaviour and for planning and decision problems . In the present paper the value of multidimensional methods will be set out by providing a selected survey of these methods and of their potential or actual applications. Multidimensional Analysis x The pluriformity of spatial patterns and of changes therein reqqires very of ten a multidimensional analytical framework. This ist a prequisite for arriving at an operational and comprehensive insight into complex phenomena such as residential location decisions, evaluationof intangibles, the existence of interregional inequalities, decline in environmental quality, spatial interaction and attractiveness, and so forth. In formal terms, a multidimensional approach implies that a certain variable x is characterized by a vector profile v with clements Vi (i = 1,. . . , ! ) . Several parts of this paper are based on Nijkamp (1979).