Monte Carlo Permutation Tests for Assessing Spatial Dependence at Different Scales

Spatially dependent residuals arise as a result of missing or misspecified spatial variables in a model. Such dependence is observed in different areas, including environmental, epidemiological, social and economic studies. It is crucial to take the dependence into modelling consideration to avoid spurious associations between variables of interest or to avoid wrong inferential conclusions due to underestimated uncertainties. An insight about the scales at which spatial dependence exist can help to comprehend the underlying physical process and to select suitable spatial interpolation methods. In this paper, we propose two Monte Carlo permutation tests to (1) assess the existence of overall spatial dependence and (2) assess spatial dependence at small scales, respectively. A p-value combination method is used to improve statistical power of the tests. We conduct a simulation study to reveal the advantages of our proposed methods in terms of type I error rate and statistical power. The tests are implemented in an open-source R package variosig.