Smoothing Regional Maps Using Empirical Bayes Predictors

Maps are one of the geographer's basic tools. Suppose the data to be mapped are values of a variable (for example, sudden infant deaths per thousand live births, percentage undercount in a census, etc.) that are known only by region (for example, counties, enumeration districts). From the point of view of pure data summary, a map of the regions coded or colored according to the values of the variable is a very effective way of presenting both the data and the regional geography. However, it is tempting to use such a map for other purposes, such as cluster detection and comparison with previous time periods. This article will concentrate on the important case where the variable mapped is a rate. Since such rates have a nonconstant base, one is faced with a statistical comparison of regional data whose variances may be highly different. Thus, if the regional map is to be used to look for spatial patterns in the data, it is important to map smoothed values that take into account the spatial inhomogeneity of variances, as well as any spatial dependence between regions.