A generalised approach for identifying influential data in hydrological modelling

Abstract

Influence diagnostics are used to identify data points that have a disproportionate impact on model parameters, performance and/or predictions, providing valuable information for use in model calibration. Regression-theory influence diagnostics identify influential data by combining the leverage and the standardised residuals, and are computationally more efficient than case-deletion approaches. This study evaluates the performance of a range of regression-theory influence diagnostics on ten case studies with a variety of model structures and inference scenarios including: nonlinear model response, heteroscedastic residual errors, data uncertainty and Bayesian priors. A new technique is developed, generalised Cook's distance, that is able to accurately identify the same influential data as standard case deletion approaches (Spearman rank correlation: 0.93–1.00) at a fraction of the computational cost (<1%). This is because generalised Cook's distance uses a generalised leverage formulation which outperforms linear and nonlinear leverage formulations due to less restrictive assumptions. Generalised Cook's distance has the potential to enable influential data to be efficiently identified on a wide variety of hydrological and environmental modelling problems.