A Conditional Dependence Adjusted Weights of Evidence Model

Abstract

One of the key assumptions in weights of evidence (WE) modelling is that the predictor patterns have to be conditionally independent. When this assumption is violated, WE posterior probability estimates are likely to be biased upwards. In this paper, a formal expression for the bias of the contrasts will be derived. It will be shown that this bias has an intuitive and convenient interpretation. A modified WE model will then be developed, where the bias is corrected using the correlation structure of the predictor patterns. The new model is termed the conditional dependence adjusted weights of evidence (CDAWE) model. It will be demonstrated via a simulation study that the CDAWE model significantly outperforms the existing WE model when conditional independence is violated, and it is on par with logistic regression, which does not assume conditional independence. Furthermore, it will be argued that, in the presence of conditional dependence between predictor patterns, weights variance estimates from WE are likely to understate the true level of uncertainty. It will be argued that weights variance estimates from CDAWE, which are also bias-corrected, can properly address this issue.