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Published byJaden Hewitt Modified over 2 years ago

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Introduction to parameter optimization Sabine Beulke, Central Science Laboratory, York, UK Kinetic Evaluation according to Recommendations by the FOCUS Work Group on Degradation Kinetics Washington, January 2006

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Curve fitting

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

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

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

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Non-uniqueness

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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

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Global versus local minimum 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! From: RSS as a function of changes in 2 parameters

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

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Goodness of fit - visual assessment

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Goodness of fit - statistical criteria 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

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

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

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