spTest: An R Package Implementing Nonparametric Tests of Isotropy

TL;DR

The paper introduces spTest, an R package that provides nonparametric hypothesis tests for assessing isotropy in spatial data, offering a more reliable alternative to graphical diagnostics.

Contribution

It implements multiple nonparametric tests of isotropy in R, facilitating more accurate spatial dependence analysis without assuming specific covariance models.

Findings

spTest enables hypothesis testing of isotropy in spatial data.

The package includes tests based on spatial and spectral methods.

Practical examples demonstrate the use of tests and graphical techniques.

Abstract

An important step of modeling spatially-referenced data is appropriately specifying the second order properties of the random field. A scientist developing a model for spatial data has a number of options regarding the nature of the dependence between observations. One of these options is deciding whether or not the dependence between observations depends on direction, or, in other words, whether or not the spatial covariance function is isotropic. Isotropy implies that spatial dependence is a function of only the distance and not the direction of the spatial separation between sampling locations. A researcher may use graphical techniques, such as directional sample semivariograms, to determine whether an assumption of isotropy holds. These graphical diagnostics can be difficult to assess, subject to personal interpretation, and potentially misleading as they typically do not include a measure of uncertainty. In order to escape these issues, a hypothesis test of the assumption of isotropy may be more desirable. To avoid specification of the covariance function, a number of nonparametric tests of isotropy have been developed using both the spatial and spectral representations of random fields. Several of these nonparametric tests are implemented in the R package spTest, available on CRAN. We demonstrate how graphical techniques and the hypothesis tests programmed in spTest can be used in practice to assess isotropy properties.