Sensitivity Analysis of Spatial Autocorrelation Using Distinct Geometrical Settings: Guidelines for the Quantitative Geographer

Sensitivity Analysis of Spatial Autocorrelation Using Distinct Geometrical Settings: Guidelines for the Quantitative Geographer

António Manuel Rodrigues (Faculty of Social Sciences and Humanities, Universidade Nova de Lisboa, Lisbon, Portugal) and José António Tenedório (Faculty of Social Sciences and Humanities, Universidade Nova de Lisboa, Lisbon, Portugal)
DOI: 10.4018/IJAEIS.2016010105
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Abstract

Inferences based on spatial analysis of areal data depend greatly on the method used to quantify the degree of proximity between spatial units - regions. These proximity measures are normally organized in the form of weights matrices, which are used to obtain statistics that take into account neighbourhood relations between agents. In any scientific field where the focus is on human behaviour, areal datasets are greatly relevant since this is the most common form of data collection (normally as count data). The method or schema used to divide a continuous spatial surface into sets of discrete units influences inferences about geographical and social phenomena, mainly because these units are neither homogeneous nor regular. This article tests the effect of different geometrical data aggregation schemas - administrative regions and hexagonal surface tessellation - on global spatial autocorrelation statistics. Two geographical variables are taken into account: scale (resolution) and form (regularity). This is achieved through the use of different aggregation levels and geometrical schemas. Five different datasets are used, all representing the distribution of resident population aggregated for two study areas, with the objective of consistently test the effect of different spatial aggregation schemas.
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Introduction

The common feature between any geographical phenomena is the possibility to identify its location in relation to any model which represents the surface of the Earth. Moreover, any individual or collective action is conditioned (and conditions) actions taken by agents located nearby (Miller, 2004). Hence, we may speak of a contagious or spill over effect which result in clear spatial patterns. Distance is a chief component in any geographical model, because it quantifies the relation in space between intervening agents.

Most human activities are continuous in nature. Individual actions and in general spatial individual attributes (e.g. where someone works, lives or goes shopping) take place in a specific point-location. Yet, in the Geographical Information Sciences (GIS), it is common for spatial information to be compiled and made available for a set in spatial units/regions. Available datasets aggregate such attributes according to pre-defined geometrical regional settings. Geography is technically absent from these datasets as each record is independent. In order to overcome this assumption of independence between observations, a set of Exploratory Spatial Data Analysis (ESDA) tools has been developed which measure the relations between these units (Anselin,1992). The backbone of ESDA statistics is the use of spatial weights matrices where each cell represents the geographical relation between a pair of spatial units (Getis, 2007).

The same variable, the same spatial phenomenon may be studied using different levels of aggregation. This is analogous to the concept of image resolution. Hence, the term geographical or spatial resolution may be used as referring to how detailed aggregates are. In practice, for a fixed study-area, resolution is higher as the greater the number of spatial units for which counts is compiled.

The consequence of variations in spatial resolution and level of regularity is that an exploratory analysis of the same phenomenon may yield different results (Dykes 1998). Although the aggregation level may lead to distinct conclusions, these are not necessarily wrong; nonetheless, awareness for such differences is important as spatial diffusion occurs at different speeds according to the level of detail. In effect, diffusion speed may be the same, only distances are different.

Given the relevance of small-area analysis for the understanding of local and regional social patterns, problems related to the effects of distinct spatial resolutions and boundaries inconsistencies have been explored when exploring social segregation and polarisation. Some classic texts include Bracken (1994), Dorling (1995) and Dykes (1998).

There are several problems related to these aggregation exercises and the resulting geometrical schemas: first, using summary statistics which refer to the average behaviour of individuals or the sum of some demographic attribute may lead to mis-interpretations of social phenomena since the internal area of each spatial unit is not homogeneous. This is known in the literature as the ecological fallacy (Freedman, 2001; Rogerson, 2001). In practice, aggregation means that part of the information is lost.

The second problem highlights the consequences of using different geometrical schema and is known in the literature as the Modifiable Areal Unit Problem MAUP (Anselin, 1992). What are the reasons behind the multitude of geometrical boundaries which aggregate data for the same geographical plane? Different criteria or motivations normally result in different sets of boundaries and spatial forms. Regions may be defined as natural units (ex. a river basin), functional units (ex. a metropolitan area), anthropic units (ex. agricultural landscapes) or administrative units (ex. Nomenclature of Territorial Units for Statistics – NUTS). In the Geographical Information Sciences, MAUP related problems have long been acknowledged and explored - see for example Openshaw (1984).

For any spatial resolution, as any set of boundaries, MAUP may seriously hamper the strength of statistical results. Moreover, cross-section and time-series analysis of geographical data is often not possible due to geometric inconsistencies (Rodrigues, 2012 and 2015. Common solutions often involve areal interpolation techniques, of which dasymetric mapping algorithms are well documented (Goodchild, 1993; Eicher & Brewer, 2001; Mennis, 2003, Rodrigues, 2015).

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