The second type of spatial effect, spatial heterogeneity, pertains to the spatial or regional differentiation which follows from
the intrinsic uniqueness of each location. This is a special case of the general problem of structural instability. As is well known, in
order to draw conclusions with a degree of general validity from the study of a spatial sample, it is necessary that this sample
represents some type of equilibrium. In the analysis of cross-sectional data in the social sciences this assumption is typically made.
However, this assumption is considered with respect to the time dimension only, and systematic instability or structural variation that
may be exhibited across different locations in space is mostly ignored. Such spatial heterogeneity may be evidenced in various aspects of the statistical analysis: it may occur in the form of different distributions holding for spatial, subsets of the data, or more simply, in
the form of different means, variances or other parameter values between the subsets. I will refer to discrete changes over the
landscape, such as a difference in mean or variance between inner city and suburb, or between northern and southern states as spatial
regimes, where each regime corresponds to a well-defined subset of locations. Alternatively, I will call a continuous variation with
location spatial drift. This would be the case if the parameters of a distribution vary in a smooth fashion with location, for example,
when their mean follows a polynomial expression in the x and y coordinates (this is referred to as a trend surface). As is the case for
spatial dependence, spatial heterogeneity can also be considered either as a nuisance or as substantive heterogeneity.