The effective variance weighting for least squares calculations applied to the mass balance receptor model

The effective variance weighted least squares solution to the mass balance receptor model is derived from the theory of maximum likelihood. The solution is one which contains the effects of random uncertainties in both the receptor concentrations and the source compositions. The solution involves trancendental equations of the unknown source contribution variables, and an iterative solution is required. This solution and the ordinary weighted least squares solution are applied to ten sets of simulated data generated from known source contributions and source compositions, perturbed by random experimental errors typical of those to be found in environmental sampling. The standard deviation of the source contributions calculated from each of these data sets is compared with the uncertainty obtained from the ordinary and effective variance least squares solutions; the effective variance solution provides the more accurate estimate. Extensions of this method to other least squares treatments of environmental data are proposed.