Improving uncertainty analysis in kinetic evaluations using iteratively reweighted least squares.

ABSTRACT

Kinetic parameters of environmental fate processes are usually inferred by fitting appropriate kinetic models to the data using standard nonlinear least squares (NLS) approaches. Although NLS is appropriate to estimate the optimum parameter values, it implies restrictive assumptions on data variances when the confidence limits of the parameters must also be determined. Particularly in the case of degradation and metabolite formation, the assumption of equal error variance is often not realistic because the parent data usually show higher variances than those of the metabolites. Conventionally, such problems would be tackled by weighted NLS regression, which requires prior knowledge about the data errors. Instead of implicitly assuming equal error variances or giving arbitrary weights decided by the researcher, we use an iteratively reweighted least squares (IRLS) algorithm to obtain the maximum likelihood estimates of the model parameters and the error variances specific for the different species in a model. A study with simulated data shows that IRLS gives reliable results in the case of both unequal and equal error variances. We also compared results obtained by NLS and IRLS, with probability distributions of the parameters inferred with a Markov-Chain Monte-Carlo (MCMC) approach for data from aerobic transformation of different chemicals in soil. Confidence intervals obtained by IRLS and MCMC are consistent, whereas NLS leads to very different results when the error variances are distinctly different between different species. Because the MCMC results can be assumed to reflect the real parameter distribution imposed by the observed data, we conclude that IRLS generally yields more realistic estimates of confidence intervals for model parameters than NLS.