Integrating spatial heterogeneity and dependence into landslide susceptibility modeling: a Gaussian-based regression framework

Landslide susceptibility assessment—defined here as the spatial prediction of relative landslide abundance—aims to identify where landslides are relatively more likely to occur. Landslide susceptibility assessment refers to a collection of methods aimed at predicting where landslides are likely to occur. In this study, we go beyond the traditional landslide susceptibility framework and use spatial regression methods to estimate landslide abundance (the number of mapped landslides per catchment) in 533 catchments in the Colombian Andes, based on predictors of rainfall, morphometry, geology, and land cover. Moran scatter plots and Lagrange Multiplier tests show that these predictors are spatially autocorrelated and clustered. We systematically compare Ordinary Least Squares (OLS) regression against several Gaussian-based spatial models using AIC, adjusted R², and Moran's I of residuals, and benchmark these against count-based Zero Inflated Negative Binomial and Gaussian models as references. We employ Geographically Weighted Regression (GWR) and Spatial Regimes to address spatial heterogeneity, and Simultaneous Autoregressive (SAR) models to account for spatial dependence. esIn this study, we model landslide abundance (the number of mapped landslides per catchment) across 533 catchments in the Colombian Andes using rainfall, morphometry, geology, and land cover as predictors. The data are prone to spatial heterogeneity and dependence, which, if ignored, can lead to biased and inaccurate estimates. Moran scatter plots and Lagrange Multiplier tests confirm that predictors and residuals are spatially autocorrelated and clustered. We systematically compare Ordinary Least Squares (OLS) regression against several Gaussian-based spatial models using AIC, adjusted R², and Moran's I of residuals and benchmark these against count-based Poisson and negative binomial models as references. We employ Geographically Weighted Regression (GWR) and Spatial Regimes to address spatial heterogeneity, and Simultaneous Autoregressive (SAR) models to account for spatial dependence. Our results show that accounting for spatial properties substantially improves model fit and provides deeper geomorphic insights. GWR and Spatial Regimes reveal distinct regions where relief and elevation exert spatially varying influences, while the superior performance of the Spatial Error Model highlights the impact of spatially autocorrelated, unobserved factors.We conclude that, despite the limitations of a Gaussian framework for count data, integrating spatial dependence and heterogeneity is essential for generating more statistically sound and geographically realistic models of regional landslide abundance.