Error in Variables Parameter Estimation

Abstract

The application of the errors in variables method (EVM) to environmental engineering practice using, as an example, the determination of kinetic parameters from a laboratory biodegradability study is presented. Model parameters must often be estimated from field or laboratory observations to describe biological treatability studies, adsorption, and water quality modeling. Such models consist of one or more linear or nonlinear equations. Usually, a function of the observed variables is designated as the ``dependent.'' The model parameter values minimizing the sum of squares of deviations between the observed and predicted ``dependent'' variable is accepted as ``best.'' Even for linear models, this method is biased when the independent variables are measured with error. Forced linearization of instrinsically nonlinear models may produce biased point estimates or interval estimates of parameter. Nonlinear parameter estimation methods when some or all of the variables are measured with error, designated as EVM, recently have been developed and utilized in chemical engineering for the reduction of thermodynamic data.