BoundarySeer includes two methods for randomizing spatial data during Monte Carlo procedures: full randomization (also known as complete spatial randomness or CSR), and restricted permutations based on spatial proximity or similarity. These methods are for randomizing the observations among the data's original spatial locations. See Location models for a discussion of randomizing the spatial coordinates of the data set (used for data with location uncertainty).
This method corresponds to a null hypothesis of no spatial structure. Although commonly used, CSR is increasingly recognized as an untenable null hypothesis, because the complete absence of spatial structure is not a reasonable scenario for boundary-less surfaces. In essence, this method assumes spatial independence between samples, which is violated in data sets with spatial autocorrelation (Fortin and Jacquez 2000).
Restricted randomization procedures can provide more realistic randomizations and more realistic null hypotheses. We can account for more complex structure (spatial and otherwise) by restricting permutations based on distance (or similarity) relationships among observations. In practice, this method works like CSR, except that the observations are reallocated according to a probability matrix that is either defined by the user or calculated by BoundarySeer. This matrix, called a generator matrix, gives BoundarySeer instructions for how to randomize the data.
Spatial autocorrelation can be accounted for when constructing reference distributions of boundary statistics, by using measures of spatial autocorrelation to construct the generator matrix. This approach also allows attributes other than spatial relationships to restrict permutations.
See also: