Several risk-managers have expressed concern for the limited scope of the additive model. They argue that the relevance of some risks factors depend on the presence or the magnitude of other risk factors. For instance, the animal mobility presents an actual risk only in regions with high animal density, or maybe in regions in the borders of the country, etc.
These arguments sound sensible to me. They are talking about interactions between factors.
Once all the risk factors are loaded and scaled, we could offer the possibility to add interactions between them by multiplying the risk maps and incorporating these products as additional (additive) terms. Just as in any regression model. Then, the user can weight the importance of the "main effects" and also of these interactions.
Since the final outcome is a risk map with values in an interval [say (0,1), for the matter], it would make sense to model the contributions in a logit scale and the scale back to risk-scale.
This would introduce dependence among all factors (the "effect" of A depends on the value of B). But is not exactly an interaction (if B has a very low risk, the effect of A is exaggerated, rather than suppressed).
In fact, (2) will simply exaggerate extreme risks and attenuate average risks. I worry whether it would be too much. On the other hand, the manual assignment of weights to the factors becomes more difficult because of the change of scale. I need to think about this and make some tests.
Both changes are thus complementary, and the whole model would share the structure of a logistic regression. This has the appeal that it is more comparable to a model fit with data. Moreover, this allows to interpret the whole approach as a model fit only with priors on the parameters, handle the uncertainty more formally and allow to build upon the prior risk-maps with observed data.
Several risk-managers have expressed concern for the limited scope of the additive model. They argue that the relevance of some risks factors depend on the presence or the magnitude of other risk factors. For instance, the animal mobility presents an actual risk only in regions with high animal density, or maybe in regions in the borders of the country, etc.
These arguments sound sensible to me. They are talking about interactions between factors.
Once all the risk factors are loaded and scaled, we could offer the possibility to add interactions between them by multiplying the risk maps and incorporating these products as additional (additive) terms. Just as in any regression model. Then, the user can weight the importance of the "main effects" and also of these interactions.
Since the final outcome is a risk map with values in an interval [say (0,1), for the matter], it would make sense to model the contributions in a logit scale and the scale back to risk-scale. This would introduce dependence among all factors (the "effect" of A depends on the value of B). But is not exactly an interaction (if B has a very low risk, the effect of A is exaggerated, rather than suppressed).
In fact, (2) will simply exaggerate extreme risks and attenuate average risks. I worry whether it would be too much. On the other hand, the manual assignment of weights to the factors becomes more difficult because of the change of scale. I need to think about this and make some tests.
Both changes are thus complementary, and the whole model would share the structure of a logistic regression. This has the appeal that it is more comparable to a model fit with data. Moreover, this allows to interpret the whole approach as a model fit only with priors on the parameters, handle the uncertainty more formally and allow to build upon the prior risk-maps with observed data.