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Stochastic dominance tests are used to measure whether distributions are directionally‐distinct. Using stochastic dominance measures, an income distribution can be measured to be more favorable for its members at all income levels than another distribution. This contrasts with conventional σ and β‐convergence approaches that compare distributions at a set of predetermined income levels. Given this comprehensiveness, stochastic dominance measures can yield novel insight into the relationship between income distributions, and thus to the relative economic welfare of inhabitants of different societies. However, stochastic dominance measures used in the analysis of regional income convergence have ignored the complications of geography. In this paper we examine the properties of common tests for stochastic dominance using various descriptive models of geographically‐realistic income growth processes. We find that the false positive rate of stochastic dominance tests increases significantly when comparing spatially‐informed income distributions growing over time. Further, this over‐eager rejection rate requires only that one distribution be spatially‐dependent, unlike some other bivariate statistics. We demonstrate that both the parametric and non‐parametric spatial filtering procedures are effective at resolving these issues in restricted circumstances for higher‐order dominance tests. Overall, while providing a novel and useful perspective on income distribution dynamics, stochastic dominance measures are demonstrated to have undesirable properties when used in geographically‐realistic scenarios and they resist one common method to address these issues. Solutions to the concerns expressed here remain open. [ABSTRACT FROM AUTHOR]

Abstract: The United Nations expressed an interest in reducing subnational (i.e., province and state level) inequality. We propose using a spatial decomposition of the Gini coefficient (SDGC) to track changes in subnational inequality. Typically, agencies do not track summary measures of subnational clustering of development indicators. Tracking changes in the SDGC can help measure and reduce regional inequality. To illustrate the use of the SDGC, we first present data for 93 nations to obtain cross‐sectional variation. Next, to illustrate how the SDGC trends over time, changes in the Human Development Index in Mongolia are compared to Russia and China. The SDGC can show improvement, decline and persistent clustering of subnational level inequality. The SDGC is a useful measure for the United Nations' Sustainable Development Goals. [ABSTRACT FROM AUTHOR]

Discrete Markov chain models (DMCs) have been widely applied to the study of regional income distribution dynamics and convergence. This popularity reflects the rich body of DMC theory on the one hand and the ability of this framework to provide insights on the internal and external properties of regional income distribution dynamics on the other. In this paper we examine the properties of tests for spatial effects in DMC models of regional distribution dynamics. We do so through a series of Monte Carlo simulations designed to examine the size, power and robustness of tests for spatial heterogeneity and spatial dependence in transitional dynamics. This requires that we specify a data generating process for not only the null, but also alternatives when spatial heterogeneity or spatial dependence is present in the transitional dynamics. We are not aware of any work which has examined these types of data generating processes in the spatial distribution dynamics literature. Results indicate that tests for spatial heterogeneity and spatial dependence display good power for the presence of spatial effects. However, tests for spatial heterogeneity are not robust to the presence of strong spatial dependence, while tests for spatial dependence are sensitive to the spatial configuration of heterogeneity. When the spatial configuration can be considered random, dependence tests are robust to the dynamic spatial heterogeneity, but not so to the process mean heterogeneity when the difference in process means is large relative to the variance of the time series. [ABSTRACT FROM AUTHOR]

Abstract: Residential segregation is an inherently spatial phenomenon as it measures the separation of different types of people within a region. Whether measured with an explicitly spatial index, or a classic aspatial index, a region’s underlying spatial properties could manifest themselves in the magnitude of measured segregation. In this paper we implement a Monte Carlo simulation approach to investigate the properties of four segregation indices in regions built with specific spatial properties. This approach allows us to control the experiment in ways that empirical data do not. In general we confirm the expected results for the indices under various spatial properties, but some unexpected results emerge. Both the Dissimilarity Index and Neighborhood Sorting Index are sensitive to region size, but their spatial counterparts, the Adjusted Dissimilarity Index and Generalized Neighborhood Sorting Index, are generally immune to this problem. The paper also lends weight to concerns about the downward pressure on measured segregation when multiple neighborhoods are grouped into a single census tract. Finally, we discuss concerns about the way space is incorporated into segregation indices since the expected value of the spatial indices tested is lower than their aspatial counterparts. [Copyright &y& Elsevier]

The authors explore the effect of different topologies on properties of self-organizing maps (SOM). They suggest several diagnostics for measuring topology-induced errors in SOM and use these in a comparison of four different topologies. The results show that SOM is less sensitive to localized irregularities in the network structure than the literature may otherwise suggest. Further, the results support the use of spherical topologies as a solution to the boundary problem in traditional SOM. [ABSTRACT FROM AUTHOR]

This paper considers the intersection of academic spatial analysis with the open source revolution. Its basic premise is that the potential for cross-fertilization between the two is rich, yet some misperceptions about these two communities pose challenges to realizing these opportunities. The paper provides a primer on the open source movement for academicians with an eye towards correcting these misperceptions. It identifies a number of ways in which increased adoption of open source practices in spatial analysis can enhance the development of the next generation of tools and the wider practice of scientific research and education. [ABSTRACT FROM AUTHOR]

PySAL is an open source library for spatial analysis written in the object-oriented language Python. It is built upon shared functionality in two exploratory spatial data analysis packages--GeoDA and STARS--and is intended to leverage the shared development of these components. This paper presents an overview of the motivation behind and the design of PySAL, as well as suggestions for how the library can be used with other software projects. Empirical illustrations of several key components in a variety of spatial analytical problems are given, and plans for future development of PySAL are discussed. [ABSTRACT FROM AUTHOR]

Space–Time Analysis of Regional Systems (STARS) is an open-source package designed for the dynamic exploratory analysis of data measured for areal units at multiple points in time. STARS consists of four core analytical modules: Anselin (1995) exploratory spatial data analysis; Anselin (2003) inequality measures; Carlino and Mills (1993) mobility metrics; and Christakos, Bogaert, and Serre (2001) spatial Markov. Developed using the Python object-oriented scripting language, STARS lends itself to three main modes of use. Within the context of a command line interface (CLI), STARS can be treated as a package which can be called from within customized scripts for batch-oriented analyses and simulation. Alternatively, a graphical user interface (GUI) integrates most of the analytical modules with a series of dynamic graphical views containing brushing and linking functionality to support the interactive exploration of the spatial, temporal, and distributional dimensions of socioeconomic and physical processes. Finally, the GUI and CLI modes can be combined for use from the Python shell to facilitate interactive programming and access to the many libraries contained within Python. This article provides an overview of the design of STARS, its implementation, functionality, and future plans. A selection of its analytical capabilities are also illustrated that highlight the power and flexibility of the package. [ABSTRACT FROM AUTHOR]

Abstract: Common to all tests of space–time interaction is the assumption that the population underlying the events of interest exhibits a trajectory of growth that is consistent through time and across space. In practice, however, this assumption is often untenable and, when violated, can introduce population shift bias into the results of these tests. While this problem is widely recognized, more work remains to compare its effect across tests and to determine the extent to which it is a problem for study short periods. This paper quantifies and compares the population shift bias present in the results of the Knox, Mantel, and Jacquez tests of space–time interaction. A simulation study is carried out which quantifies the bias present in each test across a variety of population movement scenarios. Results show a positive relationship between population shift bias and the heterogeneity in population growth across all the tests. They also demonstrate variability in the size of the bias across the three tests for space–time interaction considered. Finally, the results illustrate that population shift bias can be a serious problem for short study periods. Collectively, these findings suggest that an unbiased approach to assessing the significance of space–time interaction test results is needed whenever spatially heterogeneous population change is identified within a study area. [Copyright &y& Elsevier]