Weighted random-effects regression models with application to interlaboratory calibration

In this article, we present a general random-effects regression model for t he case of heteroscedastic measurement errors. The model is both motivated by and illustrated with a problem from analytical chemistry in which measur ement errors art constant for near-zero concentrations and increase proport ionally with higher concentrations. The parameters of the calibration curve that relate instrument responses to true concentration are allowed to vary over laboratories. The estimation of model parameters is accomplished by i teratively reweighted maximum marginal likelihood estimation, Properties of the method are examined in a limited simulation study anti are applied to a typical interlaboratory calibration example for copper in distilled water . We illustrate a few applications of the model that include (1) determinin g if an analyte is present in a new sample, (2) approximate confidence boun ds for true concentration given a new measurement, and (3) determination of the minimum concentration that supports quantitative determination.