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

Abstract

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, an inventory of debris flows triggered by the passage of the hurricane IDA and the low-pressure system associated with it 96E, on 7 th and 8 th November 2009, in an area of about 26 km 2 close to the Caldera Ilopango, El Salvador (CA), was employed. Two validation strategies have been applied to both statistical techniques, thus obtaining four models -BLR (I), MARS (I), BLR (II) and 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 modelling procedure, 50 replicates were created for each model and 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 True Negatives (TNs).

The Relative Importance of Globalization and Public Expenditure on Life Expectancy in Europe: An Approach Based on MARS Methodology

“…In addition, its implementation usually improves the results obtained by other types of methodologies such as the logistic models [ 110 , 111 ], multiple linear regression models [ 112 ] and, in general, classical Gaussian models that assume a uniform relationship between response and predictors [ 113 ]. Likewise, Sephton [ 114 ] established that MARS is especially appropriate in the non-linear modeling of time series, while Zhang and Goh [ 100 ] showed that it is more reliable in terms of computational efficiency and interpretability than other approaches in the field of artificial intelligence such as Back Propagation Neural Network (BPNN), even outperforming the reliability of the CART models they come from [ 113 ].…”

“…MARS can be focused within the new scientific paradigm [ 115 ] of the “data driven-modeling” [ 100 , 116 , 117 ], one of the foundations of machine learning techniques, being defined on a bi-objective algorithm (elaborated from a “two-stage process”) [ 118 ] in which two different phases are distinguished [ 108 , 109 , 111 , 119 , 120 ]: forward selection and backward deletion. Formally, following Koc and Bozdogan [ 102 ] and Zhang and Goh [ 100 ], its working-schema can be defined from Y , the output or objective-dependent variable response, and , a matrix of j input variables (predictors), assuming that the data are generated under an “unknown and true model”.…”

Gully Erosion Susceptibility Mapping Using Multivariate Adaptive Regression Splines—Replications and Sample Size Scenarios

“…In this research, two scenarios were used: these scenarios were selected after altering different sample sizes and the number of replications, including 90%/10% and 80%/20% with 10 replications. To assess the robustness of the model's data sensitivity [8,22,35], 5, 10, and 15 sample data sets, (replicates) for 70%/30% sample size, were prepared through randomly multi-extracting of various data sets in the calibration and validation subsets [36]. Every set was adjusted through addition to positives (i.e., pixels having hedcut points) an equal number of randomly selected negative points, corresponding to pixels without hedcut [37].…”

Building Extraction Using Orthophotos and Dense Point Cloud Derived from Visual Band Aerial Imagery Based on Machine Learning and Segmentation

“…We applied five classifiers, of which RF, SVM, and MARS resulted in the best performance with >99% OAs; differences among them were only 1-5%, while OAs of PLS and KNN were even 40% worse. Although all algorithms proved their efficiency in different tasks [102,[125][126][127], we observed that accuracy depended on the similarity of the spectral characteristic of the objects and the input data. Deep learning (DL) algorithms such as artificial neural network (ANN) [128], convolutional neural network (CNN) [129], and recurrent neural network (RNN) [130] became popular and their efficiency can be higher than ML techniques.…”

“…Non-linearity is captured by knots as cutpoints. The classification works in two steps: (1) forward pass: a model is calculated involving all variables considering all possible knots; (2) backward pass: the algorithm removes the variables having the least contribution (prunes to optimal number of knots) to gain the best model using general leaving-one-out cross-validation error metrics [102,103]. We applied RKCV to obtain the optimal number of knots and degree (number of interactions) based on 30 models.…”