Testing for spatial association of qualitative data using symbolic dynamics |
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| Authors: | Manuel Ruiz Fernando López Antonio Páez |
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| Institution: | 1. Facultad de C.C. de la Empresa, Dpto. Métodos Cuantitativos e Informáticos, Universidad Politécnica de Cartagena, Cartagena, Spain
2. Centre for Spatial Analysis, School of Geography and Earth Sciences, McMaster University, Hamilton, ON, Canada
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| Abstract: | Qualitative spatial variables are important in many fields of research. However, unlike the decades-worth of research devoted
to the spatial association of quantitative variables, the exploratory analysis of spatial qualitative variables is relatively
less developed. The objective of the present paper is to propose a new test (Q) for spatial independence. This is a simple, consistent, and powerful statistic for qualitative spatial independence that
we develop using concepts from symbolic dynamics and symbolic entropy. The Q test can be used to detect, given a spatial distribution of events, patterns of spatial association of qualitative variables
in a wide variety of settings. In order to enable hypothesis testing, we give a standard asymptotic distribution of an affine
transformation of the symbolic entropy under the null hypothesis of independence in the spatial qualitative process. We include
numerical experiments to demonstrate the finite sample behaviour of the test, and show its application by means of an empirical
example that explores the spatial association of fast food establishments in the Greater Toronto Area in Canada. |
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