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Abstract
One of the key concerns in spatial analysis and modeling is to study and analyze the processes that generate our observations of the real world. The typical global models employed to do this, however, fail to identify spatial variations in these processes because they assume that the processes being investigated are spatially stationary. In many real-life situations, spatial variations in relationships seem plausible and at least worth examining so that the assumption of global stationarity is, at best, unhelpful and, at worst, unrealistic. In contrast, local spatial models allow for potential variations in relationships over space leading to greater insights into the data-generating processes. In this study, a framework for localizing spatial interaction models, based on geographically weighted techniques, is developed. Using the framework, we construct a family of spatially weighted interaction models (SWIM) that can help in detecting, visualizing, and analyzing spatial nonstationarity in spatial interaction processes. Using custom-built algorithms, we apply both traditional interaction models and SWIM to a journey-to-work data set in Switzerland. The results of the model calibrations are explored using matrix visualizations, which suggest that SWIM provide useful information on the nature of spatially nonstationary processes leading to spatial patterns of flows.
空间分析与模式化的其中一个重要考量，便是研究与分析生产我们对真实世界的观察之过程。但用来从事上述活动的典型全球模式，却预设这些被探讨的过程在空间上是固定的，因而无法指认这些过程中的变异性。在诸多真实生活的情境中，关係中的空间变异似乎是相当真实的，且至少是值得分析的，所以全球固定性的预设是没有帮助的，甚至是不切实际的。反之，地方空间模型，考量空间关係上的潜在变异，并对数据产生的过程提出了更佳的洞见。本研究根据地理权重技术，建构一个地方化空间互动模型的架构。我们运用此一架构来建立在空间上加权的互动模型（SWIM）家族，该模型可以协助侦测、可视化，以及分析空间互动过程中的空间非固定性。我们运用客户建构的演算法，同时将传统的互动模型与 SWIM 应用至瑞士工作通勤旅次的数据集。我们并运用矩阵可视化，探讨该模型校正的结果，并指出 SWIM 可对导向流动的空间模式之空间非固定过程的本质提出有用的数据。
Una de las preocupaciones claves en análisis y modelización espacial es estudiar y analizar los procesos que generan nuestras observaciones del mundo real. Sin embargo, los típicos modelos globales que se emplean para hacer esto fallan en identificar las variaciones espaciales en estos procesos porque asumen que los procesos que se están investigando son espacialmente estacionarios. En muchas situaciones de la vida real, las variaciones espaciales en las relaciones parecen ser plausibles y por lo menos dignas de ser examinadas, por lo que la presunción de una estacionaridad global es de poca ayuda, en el mejor de los casos y, en el peor, impráctica. Por el contrario, los modelos espaciales locales dan cabida a variaciones potenciales en las relaciones en el espacio, que llevan a percepciones de mayor profundidad en los procesos generadores de datos. En este estudio se desarrolla una infraestructura para localizar los modelos de interacción espacial, con base en técnicas ponderadas geográficamente. Usando esta infraestructura construimos una familia de modelos de interacción espacialmente ponderados [SWIM, por el acrónimo en inglés] que pueden ayudar a detectar, visualizar y analizar la no estacionaridad espacial en los procesos de interacción espacial. Utilizando algoritmos diseñados a la medida, aplicamos tanto los modelos tradicionales de interacción como los SWIM a un conjunto de datos de viaje al trabajo en Suiza. Los resultados de las calibraciones del modelo se exploraron usando visualizaciones matrices, que sugieren que los SWIM suministran información útil sobe la naturaleza de procesos espacialmente no estacionarios que conducen a patrones espaciales de flujo.
Notes
1. A Poisson model is deemed to be appropriate here because commuting flows are likely to result from independent decision-making behavior. If migration flows were being modeled, however, where flows are less likely to be independent (e.g., family members migrate together), a negative binomial model might be more appropriate. Alternatively, if the numbers of the flows in each of the cells are large, a Gaussian model might be deemed appropriate and such models are often encountered in the spatial interaction literature. For this reason, we also discuss a Gaussian spatial interaction framework later.
2. In the specific case of a Poisson GWR model, the AICc formula is defined by Nakaya et al. (Citation2005) as
where k(b) is the effective number of parameters in the model with bandwidth b.
Additional information
Notes on contributors
Maryam Kordi
MARYAM KORDI is a researcher in the Institute of Geography and Sustainability at University of Lausanne, 1015, Lausanne, Switzerland. She also works as a researcher for the private company NAXiO in Stäfa near Zurich, Switzerland. E-mail: [email protected]. Her research interests include mathematical models in spatial analysis and in spatial interaction and spatial decision making.
A. Stewart Fotheringham
A. STEWART FOTHERINGHAM is Professor of Computational Spatial Science in the School of Geographical Sciences and Urban Planning at Arizona State University, Tempe, AZ 85287. E-mail: [email protected]. His research interests include spatial analysis, geographic information science, and spatial interaction modeling.