Modified Weights-of-Evidence Modeling with Example of Missing Geochemical Data

Abstract

Weights of evidence (WofE) and logistic regression (LR) are two loglinear methods for mineral potential mapping. Both models are limited by their respective basic assumptions in application. Ideally, WofE indicator patterns have the property of conditional independence (CI) with respect to the point pattern of mineral deposits to be predicted; in LR, there supposedly are no interactions between the point pattern and two or more of the indicator patterns. If the CI assumption is satisfied, estimated LR coefficients become approximately equal to WofE contrasts and the two methods produce similar results; additionally, bias then is avoided in that the sum of all estimated posterior probabilities becomes approximately equal to the number of observed discrete events. WofE allows construction of input layers that have missing data as a separate category in addition to known presence-absence type input, while logistic regression as such is not capable of handling missing data. As an improved WofE model based on LR, modified weights of evidence (MWofE) inherit the advantages of both LR and WofE, i.e., eliminates bias due to lack of CI and can handle missing data as well. Pixel or unit area input for MWofE consists of positive and negative weights for presence and absence of a pattern plus zeros for missing data. MWofE first is illustrated by application to simple examples. Next, it is applied to a study area with 20 known gold occurrences in southwestern Nova Scotia in relation to four input layers based on geological and lake geochemical data. Assuming that geochemical data were missing for the northern part of the study area, MWofE, like WofE but unlike LR, provides posterior probabilities for the entire area.