Imagined communities: Reflections on the origin and spread of nationalism

The capabilities for visualization, rapid data retrieval, and manipulation in geographic information systems (GIS) have created the need for new techniques of exploratory data analysis that focus on the “spatial” aspects of the data. The identification of local patterns of spatial association is an important concern in this respect. In this paper, I outline a new general class of local indicators of spatial association (LISA) and show how they allow for the decomposition of global indicators, such as Moran's I, into the contribution of each observation. The LISA statistics serve two purposes. On one hand, they may be interpreted as indicators of local pockets of nonstationarity, or hot spots, similar to the Gi and G*i statistics of Getis and Ord (1992). On the other hand, they may be used to assess the influence of individual locations on the magnitude of the global statistic and to identify “outliers,” as in Anselin's Moran scatterplot (1993a). An initial evaluation of the properties of a LISA statistic is carried out for the local Moran, which is applied in a study of the spatial pattern of conflict for African countries and in a number of Monte Carlo simulations.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-4632.1995.tb00338.x

Local Indicators of Spatial Association—LISA

计量经济分析 = Econometric analysis

Statistics for Spatial Data.

This paper proposes simple tests of error cross section dependence which are applicable to a variety of panel data models, including stationary and unit root dynamic heterogeneous panels with short T and large N. The proposed tests are based on average of pair-wise correlation coefficients of the OLS residuals from the individual regressions in the panel, and can be used to test for cross section dependence of any fixed order p, as well as the case where no a priori ordering of the cross section units is assumed, referred to as CD(p) and CD tests, respectively. Asymptotic distribution of these tests are derived and their power function analyzed under different alternatives. It is shown that these tests are correctly centred for fixed N and T, and are robust to single or multiple breaks in the slope coefficients and/or error variances. The small sample properties of the tests are investigated and compared to the Lagrange multiplier test of Breusch and Pagan using Monte Carlo experiments. It is shown that the tests have the correct size in very small samples and satisfactory power, and as predicted by the theory, quite robust to the presence of unit roots and structural breaks. The use of the CD test is illustrated by applying it to study the degree of dependence in per capita output innovations across countries within a given region and across countries in different regions. The results show significant evidence of cross dependence in output innovations across many countries and regions in the World.

General Diagnostic Tests for Cross Section Dependence in Panels

1: Introduction.- 2: The Scope of Spatial Econometrics.- 3: The Formal Expression of Spatial Effects.- 4: A Typology of Spatial Econometric Models.- 5: Spatial Stochastic Processes: Terminology and General Properties.- 6: The Maximum Likelihood Approach to Spatial Process Models.- 7: Alternative Approaches to Inference in Spatial Process Models.- 8: Spatial Dependence in Regression Error Terms.- 9: Spatial Heterogeneity.- 10: Models in Space and Time.- 11: Problem Areas in Estimation and Testing for Spatial Process Models.- 12: Operational Issues and Empirical Applications.- 13: Model Validation and Specification Tests in Spatial Econometric Models.- 14: Model Selection in Spatial Econometric Models.- 15: Conclusions.- References.

Spatial Econometrics: Methods and Models

The development of specialized software for spatial data analysis has seen rapid growth since the lack of such tools was lamented in the late 1980s by Haining (1989) and cited as a major impediment to the adoption and use of spatial statistics by GIS researchers. Initially, attention tended to focus on conceptual issues, such as how to integrate spatial statistical methods and a GIS environment (loosely vs. tightly coupled, embedded vs. modular, etc.), and which techniques would be most fruitfully included in such a framework. Familiar reviews of these issues are represented in, among others, Anselin and Getis (1992), Goodchild et al. (1992), Fischer and Nijkamp (1993), Fotheringham and Rogerson (1993, 1994), Fischer et al. (1996), and Fischer and Getis (1997). Today, the situation is quite different, and a fairly substantial collection of spatial data analysis software is readily available, ranging from niche programs, customized scripts and extensions for commercial statistical and GIS packages, to a burgeoning open source effort using software environments such as R, Java and Python. This is exemplified by the growing contents of the software tools clearing house maintained by the U.S.- based Center for Spatially Integrated Social Science [CSISS] (see http://www.csiss.org/clearinghouse/).

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.0016-7363.2005.00671.x

Luc Anselin

Papers

Local Indicators of Spatial Association—LISA

Spatial Econometrics: Methods and Models

GeoDa: An Introduction to Spatial Data Analysis

Local Geographic Spillovers between University Research and High Technology Innovations

Simple diagnostic tests for spatial dependence