Integer matrix diagonalization
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Classification of Multivariate Objects Using Interval Quantile Classes
Journal of Classification
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In this paper a comparison of two concepts of neighbourhoods of spatial areas--physical and socio-economical--is presented. The former usually concerns their location on an administrative map and a possible community of borders, the latter--a similarity in terms of a composite social or economical phenomenon. The paper describes the classical theory of a neighbourhood and its matrix and shows how it can be used in multivariate data analysis. An efficient method of comparison of both types of neighbourhood matrices, using the Smith normal form, known from algebra, of an integer matrix, is proposed. We show also how the variance of disturbances as well as of spatial lag vectors and of effects and prediction correlation can be estimated. Our theoretical considerations are supplemented by a numerical example which looks at neighbourhoods of spatial areas included in a fairly small region of Poland, around Kalisz, in terms of their geographical location and the situation of their labour market and a relevant simulation study. These studies showed that the distance between both types of neighbourhood are often significant, even it is not always reflected in the correlation of effects and predictions when spatial econometrical models are applied.