Testing non-stationarity of spatial relationships under the multiscale effects

Testing spatial non-stationarity is a fundamental research topic in geographical analysis. Ignoring the multiscale effects may mislead the non-stationarity test. In this article, we concentrate on the test of non-stationarity of spatial relationships derived by the multiscale geographically weighted regression (MGWR) model. We consider the multiscale effects in this work so that it can greatly benefit the: (1) understanding of regression relationships and operational scales of geographical processes; (2) improvement of coefficient estimation; (3) enhancement of model specification. To mitigate the deficiencies in current inferential studies on this topic, we develop a bootstrap method for more effective inference. The proposed method is validated by the simulation experiment in either the Type I error or statistical power, with little dependence on the types of the error distribution of models. Besides, the proposed method can identify constant coefficients better than the traditional residual-based test developed for the GWR model which ignores the multiscale effects, particularly when the operational scales of their corresponding processes are very different. In a real-life case study of the morning peak-hour metro usage in Shenzhen, the proposed test can specify a reasonable mixed MGWR model, justifying its effectiveness and applicability in empirical modeling.