Uncertainties in spatially aggregated predictions from a logistic regression model

Abstract

This paper presents a method to assess the uncertainty of an ecological spatial prediction model which is based on logistic regression models, using data from the interpolation of explanatory predictor variables. The spatial predictions are presented as approximate 95% prediction intervals. The prediction model is based on logistic regression analysis of field data of a wetland area in the central parts of the Netherlands. The model predicts block average probability of occurrences of 78 wetland plant species for 500 m×500 m blocks. The explanatory variables comprise groundwater chemistry, hydrological characteristics, and land use management. The uncertainty of the spatial model output is assumed to be a function of the uncertainty in the estimated regression coefficients and uncertainty in the interpolated values of explanatory variables. Monte Carlo analysis was used to assess the model output error due to uncertainty in both the regression coefficients and the explanatory variables. Correlation between errors in regression coefficients and spatial autocorrelation in explanatory variables are accounted for in the Monte Carlo analysis. Spatial patterns of the relative contribution of uncertainty of the regression coefficients to the total model uncertainty are presented. The patterns of the relative contributions of uncertainty to the total model uncertainty give information on the most effective way to reduce error, i.e. either by reducing uncertainty in the regression coefficients or in the interpolated input patterns. The spatial patterns and values of the 95% prediction intervals vary widely between species but are in general large and the relative contribution of the uncertainty of the regression coefficients is in general large (over 80%).