Introduction to parameter optimisation Sabine Beulke CSL York

Introduction to parameter optimisation Sabine Beulke, CSL, York, UK FOCUS Work Group on Degradation Kinetics Estimating Persistence and Degradation Kinetics from Environmental Fate Studies in EU Registration Brussels, 26 -27 January 2005

Curve fitting

Optimisation Least squares method: Minimises the sum of squared residuals (RSS) Measured datapoint Calculated line Residual = deviation between calculated and measured data

Optimisation Initial guess (starting value) Calculate curve Calculate RSS Modify parameter

Automatic optimisation Stops when: l Convergence criteria are met Comparison between RSS for actual and previous runs. Convergence reached if difference is smaller than user-specified difference l Termination criteria are met For example, when maximum number of runs has been carried out (user-specified) Good fit not guaranteed!

Non-uniqueness

Non-uniqueness Parameter correlation Parameters strongly related Effects on RSS of changes in one parameter can be compensated by changes in another parameter Inadequate model For example, selection of bi-phasic model not warranted if data follow SFO

Global versus local minimum RSS as a function of changes in 2 parameters From : http : //ww w. ss g-su rfer. c om/ The optimisation may find a local “valley” in the RSS surface, but not the absolute, global minimum. Different parameter combinations may be returned for different starting values. Good fit not guaranteed!

FOCUS recommendations l Always evaluate the visual fit l Avoid over-parameterisation l Aim at finding reasonable starting values l Always use different starting values l Constrain parameter ranges if appropriate l Plausibility checks for parameters and endpoints l Stepwise fitting where necessary l Be aware of differences between software packages

Goodness of fit - visual assessment

Goodness of fit - statistical criteria l 2 test where C = calculated value O = observed value = mean of all observed values err = measurement error percentage If calculated 2 > tabulated 2 then the model is not appropriate at the chosen level of significance Error percentage unknown Calculate error level at which 2 test is passed (e. g. with Excel spreadsheet provided by FOCUS)

Goodness of fit - statistical criteria l Confidence in parameter estimates Calculate e. g. from Model. Maker output A parameter is significantly different from zero if p (t) < alpha l Others (e. g. model efficiency, F-test)

FOCUS optimisation procedure Optimise Evaluate: Visual fit Statistics Parameters Endpoints Eliminate outliers, weighting? Initial guess (starting values) Change starting values Select kinetic model & parameters Change model, fix parameters? Enter measured data