Statistically rigorous, model-based inferences from maps

Statistically rigorous inferences in the form of confidence intervals for map-based estimates require model-based inferential methods. Model-based mean square errors (MSE) incorporate estimates of both residual variability and sampling variability, of which the latter includes population unit variance estimates and pairwise population unit covariance estimates. Bootstrapping, which can be used with any prediction technique, provides a means of estimating the required variances and covariances. The objectives of the study were to to demonstrate a method for estimating the sampling variability, Var̂samμ̂, that can be used with all prediction techniques, to develop an efficient method that map makers can use to disseminate metadata that facilitates calculation of Var̂samμ̂ for arbitrary subregions of maps, and to estimate the individual contributions of sampling variability and residual variability to the overall standard error of the prediction of the population mean. The primary results were fourfold: (i) map makers must provide metadata that facilitate estimation of population unit variances and covariances for arbitrary map subregions, (ii) bootstrapping was demonstrated as an effective means of estimating the variances and covariances, (iii) the very large matrix of pairwise population unit covariances can be aggregated into a much smaller matrix that can be readily communicated by map makers to map users, and (iv) MSEs that include only estimates of residual variability and/or estimates of population unit variances, but not estimates of the pairwise population unit covariances, grossly under-estimate the actual MSEs.