ABSTRACT
Special weights operations illustrate ways to incorporate weights information in the construction of spatially explicit variables, such as spatially lagged variables and spatially smoothed rates. This contrasts with other operations in GeoDa that use spatial weights, where by convention only the binary contiguity relationship is used (and then row-standardized). In the transformations covered in this chapter, the actual weights are employed, such as inverse distance weights and kernel weights. Five different kernel functions are supported, including a uniform kernel, triangular, quadratic or Epanechnikov, quartic and Gaussian.
Spatially lagged variables are weighted averages (or sums) of values observed at neighboring locations. These can be used in a spatial regression but also to create spatially smoothed rates. A special case of rate smoothing is introduced as spatial empirical Bayes smoothing, based on a reference rate in a spatial reference frame, such as a larger region.
