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Predictive spatial modelling is an important task in natural hazardassessment and regionalisation of geomorphic processes or landforms. Logisticregression is a multivariate statistical approach frequently used inpredictive modelling; it can be conducted stepwise in order to select from anumber of candidate independent variables those that lead to the best model.In our case study on a debris flow susceptibility model, we investigate thesensitivity of model selection and quality to different sample sizes in lightof the following problem: on the one hand, a sample has to be large enough tocover the variability of geofactors within the study area, and to yieldstable and reproducible results; on the other hand, the sample must not betoo large, because a large sample is likely to violate the assumption ofindependent observations due to spatial autocorrelation. Using stepwise modelselection with 1000 random samples for a number of sample sizes between<i>n</i> = 50 and <i>n</i> = 5000, we investigate the inclusion and exclusion of geofactorsand the diversity of the resulting models as a function of sample size; themultiplicity of different models is assessed using numerical indices borrowedfrom information theory and biodiversity research. Model diversity decreaseswith increasing sample size and reaches either a local minimum or a plateau;even larger sample sizes do not further reduce it, and they approach the upperlimit of sample size given, in this study, by the autocorrelation range ofthe spatial data sets. In this way, an optimised sample size can be derivedfrom an exploratory analysis. Model uncertainty due to sampling and modelselection, and its predictive ability, are explored statistically andspatially through the example of 100 models estimated in one study area andvalidated in a neighbouring area: depending on the study area and on samplesize, the predicted probabilities for debris flow release differed, onaverage, by 7 to 23 percentage points. In view of these results, we arguethat researchers applying model selection should explore the behaviour of themodel selection for different sample sizes, and that consensus models createdfrom a number of random samples should be given preference over modelsrelying on a single sample

Sample size matters: investigating the effect of sample size on a logistic regression susceptibility model for debris flows