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Spatial regression analysis vs. Kriging methods for spatial estimation.

Article Excerpt
Abstract Due to the rapid development of Geographic Information Systems (GIS) in recent years, spatial data analysis has received considerable attention and played an important role in social science. Although many standard statistical techniques are attractive in traditional data analysis, they cannot be implemented uncritically for spatial data. Generally, most of the studies in spatial data analysis can be divided into two branches: the model-driven approach and the data-driven approach. The main aim of this paper is the comparison of both approaches. To carry out such a task, crime rate data in Columbus (Ohio), coming from a well-known database, have been used. The main aim of this paper is to illustrate how spatial effects can be viewed as spatial econometric models, which assess the limitations of standard techniques in a spatial context, suggesting alternative methods to deal with this problem. An application to the crime rate in Columbus (Ohio) has been carried out.

Keywords Weight matrix * Spatial correlation * Spatial econometrics * Econometric models * Autocorrelation. Kriging estimator

JEL C10 * C21 * C40 * E00

Introduction

The importance of space as the fundamental concept underlying the essence of social science is unquestioned. Since the 1950s, a large number of spatial theories and operational models have been developed, which have gradually disseminated into the practice of urban and regional policy and analysis. However, this theoretical contribution has not been matched by a similar advance in the methodology for the econometric analysis of georreferenced data.

Spatial Term Development

Spatial means each item of data has a geographical reference so we know where each case occurs on a map. A definition of spatial analysis is that it represents a collection of techniques and models that explicitly use the spatial referencing associated with each data value or object that is specified within the system under study. The main idea when spatial effects appear is how such effects can be measured. The term spatial econometrics was coined by Jean Paelinck and Klaasen (1979) to designate a growing body of the regional science literature that dealt primarily with estimation and testing problems encountered in the implementation of multiregional econometric models. On one hand, the distinction between spatial econometrics and statistical econometrics is easy and essential. If activities such as estimating spatial interaction models, statistically analyzing urban density functions and empirically implementing regional econometric models are analyzed by applying standard econometrics, the study of the models in question will tend to ignore specific spatial aspects. On the other hand, the distinction between spatial econometrics and spatial statistics is less straightforward and methods tend to be categorized as belonging to one field or the other depending on the personal preference of the researcher. One possible categorization can be extracted from Haining (1986) or Ansclin (1988). They refer to the data-driven orientation in spatial statistics (1) and to the model-driven approach in spatial econometrics (2). Moreover, spatial econometrics typically deals with models related to regional and urban economics, whereas a substantial body of the spatial statistics literature is primarily focused on physical phenomena in biology and geology.

This paper first addresses the model-driven approach (reviewing the definition of the spatial weight matrix). Secondly, the data-driven orientation (kriging methodology) is studied. Thirdly, an application to the crime rate in Columbus (Ohio) is presented and, finally, concluding remarks will be given.

The Traditional Econometric Approach

As Anselin (1988) pointed out, spatial effects are the essential reason for the existence of a separate field of spatial econometrics. Spatial effects can be divided into two general groups: spatial dependence or spatial autocorrelation and spatial heterogeneity. While spatial dependence can be considered as the existence of a functional relationship between what happens at one point in space and what happens elsewhere, spatial heterogeneity implies that functional forms and parameters vary by location and are not homogeneous throughout the data set.

The paper focuses on spatial dependence but, due to the multidirectional nature of dependence in space, a different methodological framework is required to that used in a one-directional situation in time. It is a well known fact that the consequence of spatial dependence and heterogeneity...

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