Introduction to unit Spatial Dependency

The question of the dependency is thus more complex to formulate in the case of predefined objects resulting from a spatial division. There are two distinct situations:

• The considered spatial features are resulting of the spatial distribution of properties of the phenomenon which one wishes to describe:
  • Example 1 (features produced by the distribution of landcover types; see Fig 2.2a): In this situation, the spatial dependency is absent by definition, the contiguous neighbours of each feature have different properties. These properties are categories expressed numerically at a nominal scale, for which only the identity or the difference has a meaning.
  • Example 2 (features produced by the distribution of the classes of soil quality for agriculture; see Fig 2.2b): Numerical properties of features express hierarchical position in the scale of aptitude, their contents are thus described as being of “ordinal” level. It is thus relevant to describe the way in which the level of soil quality varies according to the space.

Discontinuous spatial distributions for resulting features Resulting spatial features Resulting spatial features Fig 2.2a: Landcover categories (nominal scale) Fig 2.2b: Units of aptitude for agriculture (ordinal scale) Figure 2.2

• The considered spatial features are defined a priori and one wishes to describe the spatial distribution of their properties for another particular phenomenon:
  • Example 3 (the spatial distribution of the major economical sector for administrative features such as the "districts" of a study area; see Fig 2.3a): In this situation, the spatial dependency can exist for a phenomenon measured on a nominal level because the properties are not necessarily related to the nature of the spatial features. Thus, the contiguous neighbours of each object "district" can have identical properties.
  • Example 4 (spatial features produced by the distribution of classes of aptitude for agriculture of soil units; see Fig 2.3b): The numerical properties of the features express hierarchical position on a scale of soil quality, but their contents are thus of ordinal level level. It is then relevant to describe the way in which the level of quality varies according to the spatial proximity.

Discontinuous spatial distributions for predefined features Predefined spatial features (districts) Predefined spatial features (cells) Fig 2.3a: Categories of major economic sector (nominal scale) Fig 2.3b: Units of soil quality for agriculture (ordinal scale) Figure 2.3