Análisis Espacial de Vecindad Continua y regresión logística en el modelado espacial de probabilidad de ocurrencia de deslizamientos

• Autores: Rutilio Castro Miguel, Gabriel Legorreta Paulín
• Localización: Investigaciones geográficas, ISSN 0188-4611, ISSN-e 2448-7279, Nº. 98, 2019
• Idioma: español
• Títulos paralelos:
  • Application of the Continuum Neighborhood Spatial Analysis and Logistic Regression in the Spatial Modeling of Probability of Occurrence of Landslides
• Enlaces
  • Texto completo
• Resumen
  • español

    Este trabajo presenta un análisis comparativo de dos modelos estadísticos de probabilidad de procesos gravitacionales (PG) aplicando regresión logística (RL), utilizando la variable pendiente del terreno. En un primer modelo se analizó información in situ de sitios con deslizamientos y áreas estables; en el segundo, se analizó la información de los mismos sitios utilizando Análisis Espacial de Vecindad Continua (AEVC). La precisión que reportaron ambos modelos (in situ y AEVC), se evaluó estadísticamente con la medida de ajuste de -2 Logaritmo de la Verosimilitud (-2LL).Para la calibración de los modelos se utilizó un inventario de deslizamientos y el Continuo de Elevación Mexicano versión 3.0 (CEM 3.0) del Instituto Nacional de Estadística y Geografía (INEGI).Los resultados muestran que utilizando la información de las áreas de vecindad se obtiene un mayor nivel de ajuste de la ecuación en comparación con el modelo elaborado utilizando la información in situ.El valor de -2LL para el modelo con datos de vecindad fue de 264.312 y para los datos in situ fue de 269.573. Del mismo modo, la tabla de clasificación global del modelo de vecindad reportó un 58.5 %, mientras que para el análisis in situ fue de 51.8 %, lo anterior muestra un aumento de la correcta clasificación en el modelo estadístico del 6.7 % al utilizar el análisis de vecindad.El área de estudio es la cuenca del río La Ciénega, ubicada en la ladera este del volcán Nevado de Toluca, en el Estado de México.

  • English

    Spatial models of probability based on the Logistic Regression (RL) usually collect data for model calibration directly from the location of the sampling site. This data collection method involves the isolation of the site, leading to loss of information, as the neighborhood area is not considered; therefore, the LR model may be less representative of reality.Aiming to construct spatial models of higher accuracy when using the RL statistical model, this work addresses the analysis and integration of data on independent variables for areas surrounding the sampling sites used for the calibration of the statistical model.A few works have conducted a statistical evaluation of how the areas adjacent to calibration sites may yield a higher relationship with the occurrence of landslides processes, leading to higher precision in the classification of areas based on the probability of occurrence, as compared to in-situ data collection at the sampling site. Hence the importance of considering the relationship between the sampling site and its neighborhood area when gathering information for calibrating the probability model.This paper reports a comparative analysis of two statistical models of probability of occurrence of gravitational processes (PG) involving the application of RL and using terrain slope as the independent variable. A first model analyzed data collected in situ on the independent variable from sampling sites with landslides and in stable areas; the second analyzed information for these same sites using Spatial Analysis of Continuum Neighborhood (AEVC) to derive information about the terrain slope variable.The implementation of AEVC for the elaboration of the statistical model provided information for a detailed assessment of how the area surrounding sampling sites is statistically related to the process studied. The neighborhood area was estimated by using a circular shape centered in the sampling point, the radius of which was increased gradually in 1-pixel increments to 20 pixels.The data of the terrain slope variable were analyzed separately for the site location (in situ) and for each of the neighboring areas, from a distance of 1 to 20 pixels in diameter. This approach was used for calibrating the RL statistical models for each distance analyzed, which were then evaluated in statistical terms aiming to identify the model(s) that yield the best classification level.The precision of in-situ and AEVC models was evaluated using -2 Logarithm of Likelihood (-2LL) as a goodness-of-fit measure. This measure facilitates the comparison of two models, where the difference between the values obtained represents the shift in prediction level between models. A lower value of -2LL indicates better goodness of fit of the model; therefore, the size of the neighborhood area analyzed and the value of -2LL were both used for selecting the area for which the terrain slope contributed to better goodness of fit of the probability model.Models were calibrated using an inventory of landslides, and the terrain slope variable was derived from the Continuo de Elevación Mexicano version 3.0 (CMS 3.0). The results show that using data for neighboring areas yields higher goodness of fit of the equation relative to the model developed using in-situ data.The value of -2LL for the model was 264.3 using neighborhood data and 269.5 using in-situ data. The table on overall classification reported 58.5 % for the neighborhood model and 51.8 % for the in-situ analysis, showing a 6.7 % increase in the classification of the statistical model when the neighborhood analysis is used.The information used for the selection of the optimal distance for AEVC and the calibration of the statistical model can be depicted spatially; therefore, the results from the LR model can be represented in a map of the distribution of probability of landslides in the study area.The study area is the La Ciénega river basin located on the eastern slope of the Nevado de Toluca volcano, in the State of Mexico.