TABLE OF CONTENTS These different applications show the interest of the adaptation of multidimensional statistical methods to take into account the spatial data structure. Space is considered throughout all the relations that structure its different components. The formalization of these relations, proposed in this chapter, is based on proximity (neighborhood, affiliation), which is a very flexible and generic notion for many situations in the processing of space. This formalization can integrate and explain the links between entities of the same level or of different levels, nested or not. The description of spatial structures associated with the different levels, their comparison and the consideration of their variability constitute genuine multilevel analysis systems.
Several methods are developed and consider this specificity to confirm the spatial structure and to measure its effects. They are the answer to a real necessity of comparing statistical distributions and territorial and spatial structures, statistical heterogenity and discontinuity in space. Local analysis methods and multilevel methods appear complementary: they cover all the approaches that we have described. The local analysis methods presented here are appropriate when there are a priori assumptions or information on observation or individual pairs, which is the case with geographical information. They have the advantage of being easily implemented with traditional statistical tools, as long as we have ways to formalize the relations between the units that we attempt to develop or to integrate in the analysis by proximity or partition graphs. The multilevel model, on the other hand, uses specific resolution methods which...
