TABLE OF CONTENTS Multidimensional statistical methods, which are appropriate for the analysis of a set of structured information over several geographic levels, require a certain formalism that we address in this section before presenting the methods themselves. We start with a formalism from geographical questioning, to which is then associated a statistical formalism of different relations that we need to consider.
" The notion of scale is connected to the notion of measure of space or time. Going from one scale to another means changing units of measure" [PAV 94]. Thus defined, this notion refers to an infinite number of map zonings in regular and homogenous grids, constituting the "unit of measure" for the observation of space (see Figure 2.1a). This notion of scale concerns all those perceive space as a continuum such as physicists, ecologists, etc. In social sciences and especially in geography, the notion of scale mostly refers to a set of predefined levels often forming irregular and non-homogenous partitions of space and leaving very little room for the choice of order of magnitude of the grids (see Figure 2.1b). Such partitions can have coherent functioning logic for the event studied, or can be only mandatory passages for the collection of certain information.
At all events, grids often show significant size and form heterogenity. These map zonings are called into question because they introduce strong biases on observed spatial relations and...
