Favorability functions based on kernel density estimation for logistic models: A case study

Susceptibility or hazard models are often established by means of logistic regression techniques in order to describe the effect of a group of explanatory variables on the probability of a dichotomous or binary response. Since the available variables do not always meet the assumptions of logit-linearity of the logistic regression, a modified approach is proposed. Firstly a favorability function associated with each explanatory variable based on the conditional probability measures is introduced. Next, a simple transformation based on the empirical probability function for non-continuous variables is suggested, while nonparametric kernel estimation is considered for continuous ones. The favorability-based transformations lead to new explanatory variables for the logistic regression model. The performance of the method is evaluated using simulated data. In addition, a real case-study is presented, in which a GIS-based landslides susceptibility model is carried out.