In building damage surveys conducted in the aftermath of earthquakes, trained earthquake engineers use damage scales to assign the level of damage caused to a building to a discrete grade or state. For example, the lowest grade typically refers to “No damage” while the highest grade refers to “Collapse”.
Fragility curves relate the probability of exceeding a damage state to an underlying ground motion intensity measure. While these curves are often estimated using separate model for the exceedance of each state (thus treating the states as nominal and unrelated), there are multiple benefits of modelling the exceedance of the damage states together and taking account of their ordering.
Through synthetic data experiments as well as damage data from the 2015 Nepal earthquake, David Lallemant and I illustrate the advantages that doing so via an ordinal or cumulative link model has over the common approach of separate probit regressions.