Reformulating Classical Linear Statistical Models

Abstract

The problematic points in Chapter 1 can be reduced to a single issue, namely that inferential problems arise when statistical analyses are carried out on spatial data series having dependent observations. As Chapter 2 has suggested, this is a more trouble-some issue than its counterpart found in time series, because spatial interdependencies are both multidirectional and two-dimensional. The resulting complications are ones of accuracy, bias and nuisance. For instance, in the usual situation of positive spatial autocorrelation, the information contained in some observed value x _i is less than its independent counterpart, since spillover effects produce communalities amongst juxtaposed areal unit measures. An analogy can be made here between spatial data and a contrived classical situation. Suppose a random sample of size n is drawn, and the set of measures {x _i ; i = 1, 2, ..., n} is made. This set of measures contains a certain amount of information. Now if the sample size were to be increased merely by repeating each x _i measure twice, then it would become 2n. But the amount of information contained in the data would not change from that found in the original n observations.