Exploring the effect of inventory un-completeness in landslide susceptibility assessment: a test for conditional analysis- and regression-based models.

Landslide susceptibility can be evaluated by using different statistical approaches. Among these, the methods based on conditional analysis exploit the observed incidence of landslides into homogeneous statistical domains (corresponding to single classes of each geo-environmental variable or to multivariate Unique Condition Units) to estimate their landslide susceptibility. Thus, the results of these types of analysis can be heavily compromised by the completeness or representativeness of the adopted landslide archive. On the other hand, inference-based frequentist methods allow scoring landslide susceptibility by using limited samples of cases, provided the calibration samples are statistically representative of the whole population, assuming that the lacking cases are missing completely at random.

This research aims to evaluate the effect of incomplete inventories in assessing landslide susceptibility, by using conditional analysis (Weight of Evidence, WoE; Frequency Ratio, FR) and inference-based (Binary Logistic Regression, BLR; Multivariate Adaptive Regression Splines, MARS) methods. In particular, we analysed the effects in terms of prediction skill of each of the four methods by reducing and randomly hiding the training calibration cases (and increasing the related validation cases).

The study was conducted in the Imera Settentrionale river basin (Sicily, Italy), by exploiting two different landslide archives (5134 earth flow and 1608 rotational/translational slides) and a set of 10 physical-environmental predictors. Cutoff-dependent and -independent metrics (ROC-curve analysis and confusion matrixes) were used to estimate the performance of the models.

As general assumptions, MARS and BLR modeling resulted as markedly more performing with moderately and asymptotically AUC improving up to 30-40% of the whole dataset, corresponding to the reaching of the relative optimal performance. A similar asymptotic AUC-increasing trend is described for WoE and FR, but with a lower performance. In particular, the optimal AUC values for rotational/translational slides range between 0.77 and 0.90, for BLR, 0.82 and 0.90, for MARS, 0.78 and 0.80, for FR, 0.76 and 0.78, for WoE. At the same time, a general lower model performance resulted for earth flows, with AUC values ranges of 0.69 and 0.75, for BLR; 0.75 and 0.79 for MARS; 0.67 and 0.70 for FR; 0.56 and 0.6, for WoE. Furthermore, differences in the selected predictors produced by the cases reduction were also explored through the analysis of the variable importance and the response curves.