Order Matters: The Benefits of Ordinal Fragility Curves for Damage and Loss Estimation.

Probabilistic loss assessments from natural hazards require the quantification of structural vulnerability. Building damage data can be used to estimate fragility curves to obtain realistic descriptions of the relationship between a hazard intensity measure and the probability of exceeding certain damage grades. Fragility curves based on the lognormal cumulative distribution function are popular because of their empirical performance as well as theoretical properties. When we are interested in estimating exceedance probabilities for multiple damage grades, these are usually derived per damage grade via separate probit regressions. However, they can also be obtained simultaneously through an ordinal model which treats the damage grades as ordered and related instead of nominal and distinct. When we use nominal models, a collapse fragility curve is constructed by treating data of "near-collapse" and "no damage" the same: as data of noncollapse. This leads to a loss of information. Using synthetic data as well as real-life data from the 2015 Nepal earthquake, we provide one of the first formal demonstrations of multiple advantages of the ordinal model over the nominal approach. We show that modeling the ordering of damage grades explicitly through an ordinal model leads to higher sensitivity to the data, parsimony and a lower risk of overfitting, noncrossing fragility curves, and lower associated uncertainty.