Parameter estimation for non-linear environmental models using below-detection data

Abstract

Problems requiring regression analysis of below-detection or censored data frequently arise in the field of environmental engineering. Detection limits of analyzing instruments are the main reason for censored observations of pollutant concentrations. An iterative least-squares method for regression analysis is developed to suit the doubly censored data for non-linear models commonly used in environmental engineering. The algorithm developed, non-linear iterative least squares (NILS), utilizes the values expected for censored observations estimated from probability density functions of doubly censored data in the regression process. It has been shown through extensive simulation that the NILS method proposed returns estimates of model parameters close to those estimated with complete information, even for probability of censoring (POC) equal to 0.7 (i.e. 70% of the data are censored). Simulation results of 500 runs (sample size 20, 40 and 80 data points with POC 0.2, 0.4 and 0.7, respectively) from the algorithm developed are also compared to results obtained using some obvious simplifications on censored data, such as: (i) ignoring censored data; (ii) taking censored data as the detection limit; and (iii) taking censored data as equal to half of the difference between the lower limit (e.g. background level) and the detection limit. These simplifications have no scientific basis. It is shown that these simplifications on censored data cause substantial bias in the parameters estimated, and thus model predictions become uncertain. In addition to simulation analysis, the methodology is also established for actual observations for environmental models taken from the literature.