Validation and comparison of geostatistical and spline models for spatial stream networks

Scientists need appropriate spatial-statistical models to account for the unique features of stream network data. Recent advances provide a growing methodological toolbox for modelling these data, but general-purpose statistical software has only recently emerged, with little information about when to use different approaches. We implemented a simulation study to evaluate and validate geostatistical models that use continuous distances, and penalised spline models that use a finite discrete approximation for stream networks. Data were simulated from the geostatistical model, with performance measured by empirical prediction and fixed effects estimation. We found that both models were comparable in terms of squared error, with a slight advantage for the geostatistical models. Generally, both methods were unbiased and had valid confidence intervals. The most marked differences were found for confidence intervals on fixed-effect parameter estimates, where, for small sample sizes, the spline models underestimated variance. However, the penalised spline models were always more computationally efficient, which may be important for real-time prediction and estimation. Thus, decisions about which method to use must be influenced by the size and format of the data set, in addition to the characteristics of the environmental process and the modelling goals