Building W Matrices Using Selected Geostatistical Tools: Empirical Examination and Application

Elżbieta Antczak

doi:10.3390/stats1010009

Abstract

This paper investigates how to determine the values (elements) of spatial weights in a spatial matrix (W) endogenously from the data. To achieve this goal, geostatistical tools (standard deviation ellipsis, semivariograms, semivariogram clouds, and surface trend models) were used. Then, in the econometric part of the analysis, the effect of applying different variants of matrices was examined. The study was conducted on a sample of 279 Polish towns from 2005–2015. Variables were related to the quantity of produced waste and economic development. Both exploratory spatial data analysis and estimations of spatial panel and seemingly unrelated regression models were performed by including particular W matrices in the study (exogenous-random as well as distance and directional matrices constructed based on data). The results indicated that (1) geostatistical tools can be effectively used to build Ws; (2) outcomes of applying different matrices did not exclude but supplemented one another, although the differences were significant; (3) the most precise picture of spatial dependence was achieved by including distance matrices; and (4) the values of the assessed parameter at the regressors did not significantly change, although there was a change in the strength of the spatial dependency.

Highlights

The construction of a spatial weight matrix (W) is an important problem of spatial econometrics [1].This matrix considers and expresses the potential for interactions between pairs of observations in various locations [2]
This study evaluates the effect of using different variants of spatial weight matrices on the results of exploratory spatial data analysis (ESDA) as well as econometric modelling, and identifies the differences that significantly occurred
In the structure of the spatial weight matrix based on the geographical distance, it can be difficult to determine the maximum distance to which units are autocorrelated

Summary

Introduction

The construction of a spatial weight matrix (W) is an important problem of spatial econometrics [1]. This matrix considers and expresses the potential for interactions between pairs of observations in various locations [2]. The W matrix could be set a priori (W specified exogenously) by the researcher (e.g., [3,4]). Kooijman [1] was one of the first to explicitly tackle the question of estimating the W matrix endogenously. He suggested that weights could be built by maximizing the value of Moran’s

Results

Discussion

Conclusion