What Were We Thinking?

Abstract

This article outlines the context in geography and statistics in the mid 1960s, at the height of geography's so‐called “quantitative revolution,” that led us into a long‐term collaboration about spatial statistics, which has continued in surges and lulls for some 40 years. We focus upon problems in spatial autocorrelation, including the measurement of autocorrelation, distribution theory, and variable geographical lattices. This narrative may not describe how it was, but it does describe how we remember the events of the time.

SAM: a comprehensive application for Spatial Analysis in Macroecology

“…The problem of inflated type I error rates and model instability that may arise from violation of the assumption of residuals independence in ecological models are now well-known (Legendre 1993, Schabenberger and Gotway 2005, Diniz-Filho et al 2008, Cliff and Ord 2009. In SAM, this assumption can be easily checked for by evaluating the spatial correlogram of regression residuals that is automatically calculated when the regressed data is spatially explicit.…”

A classic that wasn’t: Statistical Geography and paths only later taken

“…DCD is not mentioned in any of these works (nor are Anderson and Stephan). 3 In a special issue of Geographical Analysis commemorating the fortieth anniversary of their first publication (Griffith, 2009), Cliff and Ord (2009) reflected on the origins and nature of their work, noting the major initial influence of Cliff’s mentor at Northwestern University, Dacey, and their focus on the use of contiguity matrices as developed by Geary and Moran (1950): DCD is not mentioned but Gould’s (1970) paper, presented at the same 1969 conference as their own, is. That commemorative issue contains 13 other papers, none of which mentions DCD .…”

Local Cost Surface Models of Distance Decay for the Analysis of Gridded Population Data

“…In spatial analyses involving spatial regression or spatial auto‐correlation of numerical population data it is the norm to adopt the convenient fiction of modelling these interactions as a simple function of Euclidean distance. Yet, as Cliff and Ord () noted, these simple functions of distance ignore anisotropy (directional variation) and assume spatial homogeneity. In reality, interactions between people are a function of multiple complex factors.…”

“…It has also been widely recognized that the applicable distance decay function may vary from place to place, leading to functions with locally varying parameters, such as the bisquare adaptive kernel (Fotheringham et al ., ). Cliff and Ord () further noted that the use of weight schemes (used in measuring spatial auto‐correlation, for example) which are not based on adjacency of areas is still underdeveloped; a shortcoming that this paper addresses. Getis and Aldstadt (), in a study concerned with deriving local weights matrices, have provided a useful summary of alternative forms of geographical weighting (distance decay) functions.…”