I have a very general question regarding variography and kriging interpolation. The first order stationarity assumes that the mean value of the attribute is same over the entire region. This assumption is violated when there are clusters with usually higher or lower values at different locations within the study region. This results in a coordinates dependent trend-surface. Variogram (and hence kriging interpolation) is then computed by removing this trend-surface by modeling attribute as a function of coordinates. It's called universal kriging. Also, if we have other (environmental) covariates/predictors, then external drift can also be checked for, resulting in kriging with external drift (KED). Besides trend-surface and external drift, one can also check for directional bias (anisotropic structure).
Since I have binary data, all the values are either 1s or 0s. Even if there are clusters of 1s, still they have the same mean everywhere (no higher or lower values). Same is true for external drift. The existence of directional bias is also confusing. In either direction, the values are same 1s or 0s. My data exhibit both the external drift and a clear anisotropic structure.
How do I justify KED and anisotropy in this case?
First, this interpolation techniqie assumes normal data because variance is independent of mean. This is not the case with binary data. However an approach to this problem will be regresion krigging. First you fit a generalized model to take into account mean trend and after krigging over the residuals.
@Monica, thanks for the response. It's indeed very useful information. For binary response with continuous predictors we fit a glm with binomial family. However the residuals will still be non-normal (quite skewed with extreme values) and a very large standard deviation (sigma_error = 120). Instead I have done another thing. I have employed a linear regression model (OLS) and used those residuals as they still were looking normally distributed within the range (-1, 1) and very small standard deviation (sigma_error = 0.32). So, if the residuals from glm are not normally distributed then how do we proceed?
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