Ángel M. Felicísimo

Comparison of statistical methods commonly used in predictive modelling

Abstract Logistic Multiple Regression, Principal Component Regression and Classification and Regression Tree Analysis (CART), commonly used in ecological modelling using GIS, are compared with a relatively new statistical technique, Multivariate Adaptive Regression Splines (MARS), to test their accuracy, reliability, implementation within GIS and ease of use. All were applied to the same two data sets, covering a wide range of conditions common in predictive modelling, namely geographical range, scale, nature of the predictors and sampling method. We ran two series of analyses to verify if model validation by an independent data set was required or cross-validation on a learning data set sufficed. Results show that validation by independent data sets is needed. Model accuracy was evaluated using the area under Receiver Operating Characteristics curve (AUC). This measure was used because it summarizes performance across all possible thresholds, and is independent of balance between classes. MARS and Regression Tree Analysis achieved the best prediction success, although the CART model was difficult to use for cartographic purposes due to the high model complexity. Abbreviations: AUC = Area under the ROC curve; CART = Classification Regression Trees; FN = False negative; FP = False positive; GAM = Generalized Additive Model; GIS = Geographic Information System; GLM = Generalized Linear Model; LMR = Logistic Multiple Regression; MARS = Multivariate Adaptive Regression Splines; NDVI = Normalized Difference Vegetation Index; PCR = Principal Components Regression; ROC = Receiver Operating Characteristics.

Mapping landslide susceptibility with logistic regression, multiple adaptive regression splines, classification and regression trees, and maximum entropy methods: a comparative study

Four statistical techniques for modelling landslide susceptibility were compared: multiple logistic regression (MLR), multivariate adaptive regression splines (MARS), classification and regression trees (CART), and maximum entropy (MAXENT). According to the literature, MARS and MAXENT have never been used in landslide susceptibility modelling, and CART has been used only twice. Twenty independent variables were used as predictors, including lithology as a categorical variable. Two sets of random samples were used, for a total of 90 model replicates (with and without lithology, and with different proportions of positive and negative data). The model performance was evaluated using the area under the receiver operating characteristic curve (AUC) statistic. The main results are (a) the inclusion of lithology improves the model performance; (b) the best AUC values for single models are MLR (0.76), MARS (0.76), CART (0.77), and MAXENT (0.78); (c) a smaller amount of negative data provides better results; (d) the models with the highest prediction capability are obtained with MAXENT and CART; and (e) the combination of different models is a way to evaluate the model reliability. We further discuss some key issues in landslide modelling, including the influence of the various methods that we used, the sample size, and the random replicate procedures.

Ocean surface winds drive dynamics of transoceanic aerial movements.

Global wind patterns influence dispersal and migration processes of aerial organisms, propagules and particles, which ultimately could determine the dynamics of colonizations, invasions or spread of pathogens. However, studying how wind-mediated movements actually happen has been hampered so far by the lack of high resolution global wind data as well as the impossibility to track aerial movements. Using concurrent data on winds and actual pathways of a tracked seabird, here we show that oceanic winds define spatiotemporal pathways and barriers for large-scale aerial movements. We obtained wind data from NASA SeaWinds scatterometer to calculate wind cost (impedance) models reflecting the resistance to the aerial movement near the ocean surface. We also tracked the movements of a model organism, the Corys shearwater (Calonectris diomedea), a pelagic bird known to perform long distance migrations. Cost models revealed that distant areas can be connected through “wind highways” that do not match the shortest great circle routes. Bird routes closely followed the low-cost “wind-highways” linking breeding and wintering areas. In addition, we found that a potential barrier, the near surface westerlies in the Atlantic sector of the Intertropical Convergence Zone (ITCZ), temporally hindered meridional trans-equatorial movements. Once the westerlies vanished, birds crossed the ITCZ to their winter quarters. This study provides a novel approach to investigate wind-mediated movements in oceanic environments and shows that large-scale migration and dispersal processes over the oceans can be largely driven by spatiotemporal wind patterns.

Parametric statistical method for error detection in digital elevation models

Abstract We propose an automatic method for the detection and correction of anomalous values in matrix elevation digital models. This method uses statistical criteria and allows us to estimate the error probability of a point together with the statistical parameters derived from the same model, so that they are adapted to the characteristics of the area relief. This method has been programmed for an Arc/Info Geographical Information System environment, and thus the program is presented both in Arc Macro Language and a generic programming language.

Do stacked species distribution models reflect altitudinal diversity patterns

The objective of this study was to evaluate the performance of stacked species distribution models in predicting the alpha and gamma species diversity patterns of two important plant clades along elevation in the Andes. We modelled the distribution of the species in the Anthurium genus (53 species) and the Bromeliaceae family (89 species) using six modelling techniques. We combined all of the predictions for the same species in ensemble models based on two different criteria: the average of the rescaled predictions by all techniques and the average of the best techniques. The rescaled predictions were then reclassified into binary predictions (presence/absence). By stacking either the original predictions or binary predictions for both ensemble procedures, we obtained four different species richness models per taxa. The gamma and alpha diversity per elevation band (500 m) was also computed. To evaluate the prediction abilities for the four predictions of species richness and gamma diversity, the models were compared with the real data along an elevation gradient that was independently compiled by specialists. Finally, we also tested whether our richness models performed better than a null model of altitudinal changes of diversity based on the literature. Stacking of the ensemble prediction of the individual species models generated richness models that proved to be well correlated with the observed alpha diversity richness patterns along elevation and with the gamma diversity derived from the literature. Overall, these models tend to overpredict species richness. The use of the ensemble predictions from the species models built with different techniques seems very promising for modelling of species assemblages. Stacking of the binary models reduced the over-prediction, although more research is needed. The randomisation test proved to be a promising method for testing the performance of the stacked models, but other implementations may still be developed.

Modelos de distribución de especies: Una revisión sintética

Fondo Social Europeo y la Junta de Comunidades de Castilla-La Mancha (Programa Operativo FSE 2007-2013), la Fundacion BBVA y la Oficina Espanola de Cambio Climatico (Ministerio de Medio Ambiente y Medio Rural y Marino), cuyo patrocinio economico ha hecho posible la realizacion de este trabajo. Jesus Munoz agradece ademas al Ministerio de Ciencia e Innovacion de Espana el apoyo economico a traves del proyecto CGL2009-09530-BOS.

Testing multivariate adaptive regression splines (MARS) as a method of land cover classification of TERRA-ASTER satellite images.

This work proposes a new method to classify multi-spectral satellite images based on multivariate adaptive regression splines (MARS) and compares this classification system with the more common parallelepiped and maximum likelihood (ML) methods. We apply the classification methods to the land cover classification of a test zone located in southwestern Spain. The basis of the MARS method and its associated procedures are explained in detail, and the area under the ROC curve (AUC) is compared for the three methods. The results show that the MARS method provides better results than the parallelepiped method in all cases, and it provides better results than the maximum likelihood method in 13 cases out of 17. These results demonstrate that the MARS method can be used in isolation or in combination with other methods to improve the accuracy of soil cover classification. The improvement is statistically significant according to the Wilcoxon signed rank test.

Analysis of Uncertainty and Repeatability of a Low-Cost 3D Laser Scanner

Portable 3D laser scanners are a valuable tool for compiling elaborate digital collections of archaeological objects and analysing the shapes and dimensions of pieces. Although low-cost desktop 3D laser scanners have powerful capacities, it is important to know their limitations. This paper performs an analysis of the uncertainty and repeatability of the NextEngine™ portable low-cost 3D laser scanner by scanning an object 20 times in two different resolution modes—Macro and Wide. Some dimensions of the object were measured using a digital calliper, and these results were used as the “true” or control data. In comparing the true and the scanned data, we verified that the mean uncertainty in the Macro Mode is approximately half that of the Wide Mode, at ±0.81 mm and ±1.66 mm, respectively. These experimental results are significantly higher than the accuracy specifications provided by the manufacturer. An analysis of repeatability shows that the successive replicates do not match in the same position. The results are better in Macro Mode than in Wide Mode; it is observed that the repeatability factor is slightly larger than the corresponding mode accuracy, with ±0.84 vs. ±0.81 mm in Macro Mode and ±1.82 vs. ±1.66 mm in Wide Mode. We suggest several improvements, such as adding an external reference scale or providing a calibrated object to allow for a self-calibration operation of the scanner.

Estimating the Uncertainty of Terrestrial Laser Scanner Measurements

At present, several papers discuss the accuracy and precision of terrestrial laser scanners (TLSs), but the research continues to focus on the behavior of the TLSs. The purpose of this paper is to propose a method to evaluate the uncertainty of a TLS (FARO Photon 80). A rigid and transportable aluminum structure with 28 black-and-white targets was designed for this purpose. The structure was scanned 12 times at several distances from 2 to 70 m, and the x, y, and z coordinates of the center of the targets were automatically identified. Data were analyzed by means of circular and spherical statistics using R modules programmed in our research group. Analysis reveals that 3-D spatial distribution has a stratified pattern in the Z-axis. Regardless of the scanner status, these results indicate that these analyses should be performed periodically because they can have an impact on some studies. The proposed methodology is robust and simple and can be performed with free software such as the R modules used in this work.

Positional Accuracy Analysis of Satellite Imagery by Circular Statistics

The proposed method in this paper uses circular statistics for the analysis of errors in the positional accuracy of geometric corrections satellite images using Independent Check Lines (ICL) instead of Independent Check Points (ICP). Circular statistics has been preferred because of the vectorial nature of the spatial error. A study case has been presented and discussed in detail. From the TERRA-ASTER images of Extremadura area (Spain), the Ground Control Point (GCP), ICP, and ICL data were acquired using differential GPS through field survey, and the planimetric positional accuracy was analyzed by both the conventional method (using ICP) and the proposed method (using 1CL). Comparing conventional and proposed methods, the results indicated that modulus statistics are similar (e.g., RMSE of Geometric Correction 1 were 17.5 for the conventional method and 17.2 m for proposed method). But as additional results, azimuthal component statistics was calculated (e.g., mean direction: 247.2° in Geometric Correction 1), and several tests were made which showed the error distribution are not uniform and normal.