Logistic regression applied to natural hazards: rare event logistic regression with replications

Abstract. Statistical analysis of natural hazards needs particular attention, as most of these phenomena are rare events. This study shows that the ordinary rare event logistic regression, as it is now commonly used in geomorphologic studies, does not always lead to a robust detection of controlling factors, as the results can be strongly sample-dependent. In this paper, we introduce some concepts of Monte Carlo simulations in rare event logistic regression. This technique, so-called rare event logistic regression with replications, combines the strength of probabilistic and statistical methods, and allows overcoming some of the limitations of previous developments through robust variable selection. This technique was here developed for the analyses of landslide controlling factors, but the concept is widely applicable for statistical analyses of natural hazards.

[1]  Gary King,et al.  Logistic Regression in Rare Events Data , 2001, Political Analysis.

[2]  H. Sipman,et al.  Paramos: A Checklist of Plant Diversity, Geographical Distribuion, and Botanical Literature , 1999 .

[3]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[4]  Fausto Guzzetti,et al.  Rainfall thresholds for the possible occurrence of landslides in Italy , 2010 .

[5]  P. Reichenbach,et al.  Combined landslide inventory and susceptibility assessment based on different mapping units: an example from the Flemish Ardennes, Belgium , 2009 .

[6]  Santiago Beguería,et al.  Validation and Evaluation of Predictive Models in Hazard Assessment and Risk Management , 2006 .

[7]  Veerle Vanacker,et al.  Using Monte Carlo simulation for the environmental analysis of small archaeologic datasets, with the mesolithic in northeast Belgium as a case study , 2001 .

[8]  Veerle Vanacker,et al.  Linking hydrological, infinite slope stability and land-use change models through GIS for assessing the impact of deforestation on slope stability in high Andean watersheds , 2003 .

[9]  P. Reichenbach,et al.  Landslide hazard evaluation: a review of current techniques and their application in a multi-scale study, Central Italy , 1999 .

[10]  M. Greiner,et al.  Principles and practical application of the receiver-operating characteristic analysis for diagnostic tests. , 2000, Preventive veterinary medicine.

[11]  Fuchu Dai,et al.  Landslide risk assessment and management: an overview , 2002 .

[12]  Trevor J. Davis,et al.  Modelling Uncertainty in Natural Resource Analysis Using Fuzzy Sets and Monte Carlo Simulation: Slope Stability Prediction , 1997, Int. J. Geogr. Inf. Sci..

[13]  P. Atkinson,et al.  GENERALIZED LINEAR MODELLING IN GEOMORPHOLOGY , 1998 .

[14]  Rodrigo Sierra,et al.  The Dynamics and Social Organization of Tropical Deforestation in Northwest Ecuador, 1983-1995 , 1998 .

[15]  Stéphane Garambois,et al.  Characterization and comparison of landslide triggering in different tectonic and climatic settings , 2010 .

[16]  J A Swets,et al.  Measuring the accuracy of diagnostic systems. , 1988, Science.

[17]  David G. Kleinbaum,et al.  Introduction to Logistic Regression , 2010 .

[18]  Chang-Jo Chung,et al.  Mapping landslide susceptibility from small datasets: A case study in the Pays de Herve (E Belgium) , 2007 .

[19]  Shibiao Bai,et al.  GIS-based rare events logistic regression for landslide-susceptibility mapping of Lianyungang, China , 2011 .

[20]  S. Beguería,et al.  Changes in land cover and shallow landslide activity: a case study in the Spanish Pyrenees , 2006 .

[21]  J. Godt,et al.  Early warning of rainfall-induced shallow landslides and debris flows in the USA , 2010 .

[22]  Martin A. Andresen.  Testing for similarity in area-based spatial patterns: A nonparametric Monte Carlo approach , 2009 .

[23]  Matthew C. Larsen,et al.  The frequency and distribution of recent landslides in three montane tropical regions of Puerto Rico , 1998 .

[24]  Maher Maalouf,et al.  Computational Statistics and Data Analysis Robust Weighted Kernel Logistic Regression in Imbalanced and Rare Events Data , 2022 .

[25]  Andrea G. Fabbri,et al.  Validation of Spatial Prediction Models for Landslide Hazard Mapping , 2003 .

[26]  Rudolf Schmid,et al.  Páramos: A Checklist of Plant Diversity, Geographical Distribution, and Botanical Literature@@@Paramos: A Checklist of Plant Diversity, Geographical Distribution, and Botanical Literature , 1999 .

[27]  Paul D. Allison,et al.  Logistic Regression Using the SAS System : Theory and Application , 1999 .

[28]  P. Reichenbach,et al.  Landslide hazard assessment in the Collazzone area, Umbria, Central Italy , 2006 .

[29]  M. Summerfield.  Global geomorphology: An introduction to the study of landforms , 1992 .

[30]  C. F. Lee,et al.  Landslide characteristics and, slope instability modeling using GIS, Lantau Island, Hong Kong , 2002 .

[31]  Xu Weiya,et al.  GIS-based landslide hazard assessment: an overview , 2005 .

[32]  Jean-François Parrot,et al.  Landsliding related to land-cover change: A diachronic analysis of hillslope instability distribution in the Sierra Norte, Puebla, Mexico , 2006 .

[33]  C. F. Lee,et al.  Assessment of landslide susceptibility on the natural terrain of Lantau Island, Hong Kong , 2001 .

[34]  P. Atkinson,et al.  Generalised linear modelling of susceptibility to landsliding in the Central Apennines, Italy , 1998 .

[35]  M. Komac.  A landslide susceptibility model using the Analytical Hierarchy Process method and multivariate statistics in perialpine Slovenia , 2006 .

[36]  Jean Poesen,et al.  Using sequential aerial photographs to detect land-use changes in the Austro Ecuatoriano / Utilisation de photographies aériennes séquentielles pour détecter les changements d'utilisation du sol dans l'Austro Equateur , 2000 .

[37]  Esmeralda A. Ramalho.  Regression models for choice-based samples with misclassification in the response variable , 2002 .

[38]  L. Ayalew,et al.  The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains, Central Japan , 2005 .

[39]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[40]  Shlomo S. Sawilowsky,et al.  You Think You’ve Got Trivials? , 2003 .

[41]  M. Eeckhaut,et al.  Prediction of landslide susceptibility using rare events logistic regression: A case-study in the Flemish Ardennes (Belgium) , 2006 .

[42]  Gary King,et al.  Explaining Rare Events in International Relations , 2001, International Organization.

[43]  C. F. Lee,et al.  A spatiotemporal probabilistic modelling of storm‐induced shallow landsliding using aerial photographs and logistic regression , 2003 .

[44]  M. Eeckhaut,et al.  Spatial analysis of factors controlling the presence of closed depressions and gullies under forest: Application of rare event logistic regression , 2008 .

[45]  A. Brenning.  Spatial prediction models for landslide hazards: review, comparison and evaluation , 2005 .