Beyond Moran's I: Testing for Spatial Dependence Based on the Spatial Autoregressive Model

The statistic known as Moran's I is widely used to test for the presence of spatial dependence in observations taken on a lattice. Under the null hypothesis that the data are independent and identically distributed normal random variates, the distribution of Moran's I is known, and hypothesis tests based on this statistic have been shown in the literature to have various optimality properties. Given its simplicity, Moran's I is also frequently used outside of the formal hypothesis-testing setting in exploratory analyses of spatially referenced data; however, its limitations are not very well understood. To illustrate these limitations, we show that, for data generated according to the spatial autoregressive (SAR) model, Moran's I is only a good estimator of the SAR model's spatial-dependence parameter when the parameter is close to 0. In this research, we develop an alternative closed-form measure of spatial autocorrelation, which we call APLE , because it is an approximate profile-likelihood estimator (APLE) of the SAR model's spatial-dependence parameter. We show that APLE can be used as a test statistic for, and an estimator of, the strength of spatial autocorrelation. We include both theoretical and simulation-based motivations (including comparison with the maximum-likelihood estimator), for using APLE as an estimator. In conjunction, we propose the APLE scatterplot, an exploratory graphical tool that is analogous to the Moran scatterplot, and we demonstrate that the APLE scatterplot is a better visual tool for assessing the strength of spatial autocorrelation in the data than the Moran scatterplot. In addition, Monte Carlo tests based on both APLE and Moran's I are introduced and compared. Finally, we include an analysis of the well-known Mercer and Hall wheat-yield data to illustrate the difference between APLE and Moran's I when they are used in exploratory spatial data analysis.     

The geographical lives of commodities: problems of analysis and critique

In two programmatic essays, Peter Jackson has reviewed new critical research on the geographical lives of commodities. This paper offers a constructive critique of his particular reading of this research. It is argued that three major issues require urgent attention if critical geographers and fellow‐travellers are to take their commodity research forward. First, there is too much imprecision in the use of the related terms ‘commodities’, ‘commodification’ and ‘commoditization’. This threatens to render all three terms meaningless or at the very least confusing. Secondly, this lack of conceptual clarity is linked to the problem of superficial engagements with normative issues. It is argued that the recent geographical research on commodities has thus far glossed over important questions of both academic and lay judgement. Finally, the paper suggests that the ‘modest’ role for critical academics envisaged by Jackson and other commodity researchers is only defensible if questions of voice, message and audience are addressed systematically. Overall, the paper presents a menu of explanatory and normative issues that require attention if critical commodity analysts like Jackson are to maximize the potential of their research agenda.     

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.     

Review

“DEMOCRACY IN WORLD POLITICS”, By Lester B. Pearson. (Oxford University Press.)     

Envisioning Capitalism: Geography and the Renewal of Marxian Political Economy

This paper offers a reinterpretation of what critical theorist Moishe Postone calls 'the fundamental core of capitalism'. In so doing, it seeks to lay a set of theoretical foundations for a renewed Marxian political economy in geography, at a time when Marxism has been eclipsed as a leading critical paradigm within the discipline. The argument works on two fronts simultaneously. On the one hand, the ongoing hegemony of economic and political neo-conservatism is occluding the violent realities of a capitalist world economy behind the anodyne logics of free-market theory. These realities suggest the continued relevance of, and need for, a strong Marxian critique of political economy. But on the other hand, Marxism has been reprimanded by its erstwhile allies on the Left of geography for being too 'modern' and too capital- and class-centred. In light of this double challenge, the paper seeks to develop a 'both/and' Marxism for geography that can chart a third way between the antinomies of modern and after-modern modes of theorizing capitalism and class. A project of 'envisioning capitalism' is suggested on this basis, which combines the 'power' of modern theory with the epistemological reflexivity of after-modern theory. At the same time, capitalism and class are rethought at an ontological level and shown still to be essential features of the fin-de-millennium world, but far less closed and hegemonic than is suggested by modern modes of Marxism. Finally, a return to a class politics of redistribution is suggested, but in a way that draws in more recent Left geographical concerns with identity, difference and recognition.