Evaluation of debris flow susceptibility in El Salvador (CA): a comparison between Multivariate Adaptive Regression Splines (MARS) and Binary Logistic Regression (BLR)

Keywords: landslide susceptibility, debris flows, Multivariate Adaptive Regression Splines (MARS), Binary Logistic Regression (BLR), hurricane Ida, El Salvador


In the studies of landslide susceptibility assessment which have been developed in recent years, statistical methods have increasingly been applied. Among all, the BLR (Binary Logistic Regression) certainly finds a more extensive application while MARS (Multivariate Adaptive Regression Splines), despite the good performance and the innovation of the strategies of analysis, only recently began to be employed as a statistical tool for predicting landslide occurrence. The purpose of this research was to evaluate the predictive performance and identify possible drawbacks of the two statistical techniques mentioned above, focusing in particular on the prediction of debris flows. To this aim, we employed an inventory of debris flows triggered by the passage of the hurricane IDA and the low-pressure system associated with it 96E, on November 7thand 8th2009 in the Caldera Ilopango, El Salvador (CA). Two validation strategies have been applied to both statistical techniques thus obtaining four models (BLR(I), MARS(I), BLR(II), MARS(II)) to be compared in pairs. Model performance was assessed in terms of AUC (area under the receiver operating characteristic (ROC) curve), Sensitivity, Specificity, Positive Prediction Value and Negative Prediction Value. Moreover, to evaluate the robustness of the modeling procedure, 50 replicates were created for each model and the standard deviation was calculated for each of them. The results show that both techniques allow for obtaining good or excellent performances so that it is not possible to define one of the two techniques as absolutely better. However, the validation procedure reveals slightly better performance of the MARS models, with greater sensitivity and greater discrimination among TNs.


Atkinson, P.M. and Massari, R. 2011. Autologistic modelling of susceptibility to land sliding in the Central Apennines, Italy. Geomorphology 130. 55–64. https://doi.org/10.1016/j.geomorph.2011.02.001

Bai, S.B., Wang, J., Lü, G.N., Zhou, P.G., Hou, S.S. and Xu, S.N. 2010. GIS-based logistic regression for landslide susceptibility mapping of the Zhongxian segment in the Three Gorges area, China. Geomorphology 115. 23–31. https://doi.org/10.1016/j.geomorph.2009.09.025

Brabb, E.E. 1984. Innovative approaches to landslide hazard and risk mapping. In Proceedings 4th International Symposium on Landslides 1. Toronto, Canadian Geotechnical Society, 307–324.

Briand, L.C., Freimut, B. and Vollei, F. 2004. Using multiple adaptive regression splines to support decision making in code inspections. Journal of Systems and Software 73. (2): 205–217. https://doi.org/10.1016/j.jss.2004.01.015

Bui, D.T., Tuan, T.A., Klempe, H., Pradhan, B. and Revhaug, I. 2016. Spatial prediction models for shallow landslide hazards: a comparative assessment of the efficacy of support vector machines, artificial neural networks, kernel logistic regression, and logistic model tree. Landslides 13. 361–378. https://doi.org/10.1007/s10346-015-0557-6

Cama, M., Lombardo, L., Conoscenti, C., Agnesi, V. and Rotigliano, E. 2015. Predicting stormtriggered debris flow events: Application to the 2009 Ionian Peloritan disaster (Sicily, Italy). Natural Hazards and Earth System Sciences 15. (8): 1785–1806. https://doi.org/10.5194/nhess-15-1785-2015

Cama, M., Conoscenti, C., Lombardo, L. and Rotigliano, E. 2016. Exploring relationships between grid cell size and accuracy for debris-flow susceptibility models: a test in the Giampilieri catchment (Sicily, Italy). Environmental Earth Sciences 75. (238): 1–21. https://doi.org/10.1007/s12665-015-5047-6

Cama, M., Lombardo, L., Conoscenti, C. and Rotigliano, E. 2017. Improving transferability strategies for debris flow susceptibility assessment. Application to the Saponara and Itala catchments (Messina, Italy). Geomorphology 288. 52–65. https://doi.org/10.1016/j.geomorph.2017.03.025

Carrara, A., Cardinali, M., Guzzetti, F. and Reichenbach, P. 1995. GIS technology in mapping landslide hazard. In Geographical Information Systems in Assessing Natural Hazards. Eds.: Carrara, A. and Guzzetti, F., Dordrecht, Kluwer, 135–175. https://doi.org/10.1007/978-94-015-8404-3_8

Chung, C.J.F., Fabbri, A.G. and Van Westen, C.J. 1995. Multivariate regression analysis for landslide hazard zonation. In Geographical Information Systems in Assessing Natural Hazards. Eds.: Carrara, A. and Guzzetti, F., Dordrecht, Kluwer, 107–133. https://doi.org/10.1007/978-94-015-8404-3_7

Chung, C.J.F. and Fabbri, A.G. 2003. Validation of spatial prediction models for landslide hazard mapping. Natural Hazards 30. (3): 451–472. https://doi.org/10.1023/B:NHAZ.0000007172.62651.2b

Conoscenti, C., Di Maggio, C. and Rotigliano, E. 2008. GIS analysis to assess landslide susceptibility in a fluvial basin of NW Sicily (Italy). Geomorphology 94. 325–339. https://doi.org/10.1016/j.geomorph.2006.10.039

Conoscenti, C., Ciaccio, M., Caraballo-Arias, N.A., Gómez-Gutiérrez, Á., Rotigliano, E. and Agnesi, V. 2015. Assessment of susceptibility to earth-flow landslide using logistic regression and multivariate adaptive regression splines: a case of the Belice River basin (western Sicily, Italy). Geomorphology 242. 49–64. https://doi.org/10.1016/j.geomorph.2014.09.020

Conoscenti, C., Rotigliano, E., Cama, M., Caraballo-Arias, N.A., Lombardo, L. and Agnesi, V. 2016. Exploring the effect of absence selection on landslide susceptibility models: A case study in Sicily, Italy. Geomorphology 261. 222–235. https://doi.org/10.1016/j.geomorph.2016.03.006

Conoscenti, C., Agnesi, V., Cama, M., Caraballo-Arias, N.A. and Rotigliano, E. 2018. Assessment of Gully Erosion Susceptibility Using Multivariate Adaptive Regression Splines and Accounting for Terrain Connectivity. Land Degradation and Development 29. 724–736. https://doi.org/10.1002/ldr.2772

Costanzo, D., Chacón, J., Conoscenti, C., Irigaray, C. and Rotigliano, E. 2014. Forward logistic regression for earth-flow landslide susceptibility assessment in the Platani river basin (southern Sicily, Italy). Landslides 11. (4): 639–653. https://doi.org/10.1007/s10346-013-0415-3

Craven, P. and Wahba, G. 1979. Smoothing noisy data with spline functions. Numerische Mathematik 31. (4): 377–403. https://doi.org/10.1007/BF01404567

Felicísimo, Á.M., Cuartero, A., Remondo, J. and Quirós, E. 2013. Mapping landslide susceptibility with logistic regression, multiple adaptive regression splines, classification and regression trees, and maximum entropy methods: a comparative study. Landslides 10. 175–189. https://doi.org/10.1007/s10346-012-0320-1

Friedman, J.H. 1991. Multivariate adaptive regression splines. The Annals of Statistics 19. (1): 1–141. https://doi.org/10.1214/aos/1176347963

Garosi, Y., Sheklabadi, M., Porghasemi, H.R., Besalatpour, A.A., Conoscenti, C. and Van Oost, K. 2018. Comparison of differences in resolution and sources of controlling factors for gully erosion susceptibility mapping. Geoderma 330. 65–78. https://doi.org/10.1016/j.geoderma.2018.05.027

Gómez-Gutiérrez, Á., Schnabel, S. and Lavado Contador, F. 2009. Using and comparing two nonparametric methods (CART and MARS) to model the potential distribution of gullies. Ecological Modelling 220. (24): 3630–3637. https://doi.org/10.1016/j.ecolmodel.2009.06.020

Gómez-Gutiérrez, Á., Conoscenti, C., Angileri, S.E., Rotigliano, E. and Schnabel, S. 2015. Using topographical attributes to evaluate gully erosion proneness (susceptibility) in two Mediterranean basins: advantages and limitations. Natural Hazards 79. (1): 291–314. https://doi.org/10.1007/s11069-015-1703-0

Goodenough, D.J., Rossmann, K. and Lusted, L.B. 1974. Radiographic applications of receiver operating characteristic (ROC) curves. Radiology 110. 89–95. https://doi.org/10.1148/110.1.89

Guzzetti, F., Carrara, A., Cardinali, M. and Reichenbach, P. 1999. Landslide hazard evaluation: a review of current techniques and their application in a multi-scale study, Central Italy. Geomorphology 31. 181–216. https://doi.org/10.1016/S0169-555X(99)00078-1

Heckmann, T., Gegg, K., Gegg, A. and Becht, M. 2014.mSample size matters: investigating the effect of sample size on a logistic regression susceptibility model for debris flows. Natural Hazards and Earth System Sciences 14. 259–278. https://doi.org/10.5194/nhess-14-259-2014

Hanley, J.A. and McNeil, B.J. 1982. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143. 29–36. https://doi.org/10.1148/radiology.143.1.7063747

Hosmer, D.W. and Lemeshow, S. 2000. Applied logistic regression. Wiley Series in Probability and Statistics, Wiley. https://doi.org/10.1002/0471722146

Jebur, M.N., Pradhan, B. and Tehrany, M.S. 2014. Optimization of landslide conditioning factors using very high-resolution airborne laser scanning (LiDAR) data at catchment scale. Remote Sensing of Environment 152. 150–165. https://doi.org/10.1016/j.rse.2014.05.013

Lasko, T.A., Bhagwat, J.G., Zou, K.H. and Ohno-Machado, L. 2005. The use of receiver operating characteristic curves in biomedical informatics. Journal of Biomedical Informatics 38. 404–415. https://doi.org/10.1016/j.jbi.2005.02.008

Lombardo, L., Cama, M., Maerker, M. and Rotigliano, E. 2014. A test of transferability for landslides susceptibility models under extreme climatic events: Application to the Messina 2009 disaster. Natural Hazards 74. (3): 1951–1989. https://doi.org/10.1007/s11069-014-1285-2

MARN 2010. Síntesis de los informes de evaluación técnica de las lluvias del 7 y 8 de noviembre 2009 en El Salvador: Análisis del impacto físico natural y vulnerabilidad socio ambiental (Technical report of the tropical storm event of 7–8 November 2009 in El Salvador: Physical impact and social vulnerability analysis). San Salvador, Ministerio de Medio Ambiente y Recursos Naturales de Salvador.

Menard, S. 1995. Applied Logistic Regression Analysis. London, Sage Publications.

Milborrow, S. 2015. Notes on the earth package. An online www document. http://www.milbo.org.doc/earth-notes.pdf

Milborrow, S., Hastie, T. and Tibshirani, R. 2011. Earth: Multivariate Adaptive Regression Spline Models. R Software Package.

Naimi, B. 2015. Uncertainty Analysis for Species Distribution Models. R Software Package.

Ohlmacher, G.C. and Davis, J.C. 2003. Using multiple logistic regression and GIS technology to predict landslide hazard in northeast Kansas, USA. Engineering Geology 69. 331–343. https://doi.org/10.1016/S0013-7952(03)00069-3

Prokos, H., Baba, H., Lóczy, D. and El Kharim, Y. 2016. Geomorphological hazards in a Mediterranean mountain environment – Example of Tétouan, Morocco. Hungarian Geographical Bulletin 65. (3): 283–295. https://doi.org/10.15201/hungeobull.65.3.6

R Core Team 2017. R: A language and environment for statistical computing. Vienna, R Foundation for Statistical Computing. https://www.R-project.org/

Rotigliano, E., Agnesi, V., Cappadonia, C. and Conoscenti, C. 2011. The role of the diagnostic areas in the assessment of landslide susceptibility models: a test in the Sicilian chain. Natural Hazards 58. (3): 981–999. https://doi.org/10.1007/s11069-010-9708-1

Rotigliano, E., Cappadonia, C., Conoscenti, C., Costanzo, D. and Agnesi, V. 2012. Slope unitsbased flow susceptibility model: Using validation tests to select controlling factors. Natural Hazards 61. (1): 143–153. https://doi.org/10.1007/s11069-011-9846-0

Rotigliano, E., Martinello, C., Hernandéz, M.A., Agnesi, V. and Conoscenti, C. 2018. Predicting the landslides triggered by the 2009 96E/Ida tropical storms in the Ilopango caldera area (El Salvador, C.A.): optimizing MARS-based model building and validation strategies. Environmental Earth Sciences (in press)

Van Westen, C.J., Rengers, N. and Soeters, R. 2003. Use of geomorphological information in indirect landslide susceptibility assessment. Natural Hazards 30. (1): 399–419. https://doi.org/10.1023/B:NHAZ.0000007097.42735.9e

Van Westen, C.J., Castellanos, E. and Kuriakose, S.L. 2008. Spatial data for landslide susceptibility, hazard, and vulnerability assessment: an overview. Engineering Geology 102. 112–131. https://doi.org/10.1016/j.enggeo.2008.03.010

Verstappen, H.T. 1983. Geomorphology of the Agri valley, Southern Italy. ITC Journal 4. 291–301.

Von Ruette, J., Papritz, A., Lehmann, P., Rickli, C. and Or, D. 2011. Spatial statistical modeling of shallow landslides-validating predictions for different landslide inventories and rainfall events. Geomorphology 133. 11–22. https://doi.org/10.1016/j.geomorph.2011.06.010

Vorpahl, P., Elsenbeer, H., Märker, M. and Schröder, B. 2012. How can statistical models help to determine driving factors of landslides? Ecological Modelling 239. 27–39. https://doi.org/10.1016/j.ecolmodel.2011.12.007

Weber, H.S., Wiesemann, G., Lorenz, W. and Schmidt-Thome, M. 1978. Mapa geologico de la Republica de El Salvador/America Central, 1:100,000 (Geological map of the El Salvador Republic/Central America, 1:100,000). Hannover, Bundesanstalt für Geowissenschaften und Rohstoffe.

Youden, W.J. 1950. Index for rating diagnostic tests. Cancer 3. (1): 32–35. https://doi.org/10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3

How to Cite
Rotigliano, E., Martinello, C., Agnesi, V., & Conoscenti, C. (2018). Evaluation of debris flow susceptibility in El Salvador (CA): a comparison between Multivariate Adaptive Regression Splines (MARS) and Binary Logistic Regression (BLR). Hungarian Geographical Bulletin, 67(4), 361-373. https://doi.org/10.15201/hungeobull.67.4.5