1. Introduction to parameter optimization
Soils & Environmental Exposure Assessment
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
PSD, 6-7 March 2003

2. Curve fitting

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

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

5. 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!

6. Non-uniqueness

7. Non-uniqueness Parameter correlation Inadequate model
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

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

9. 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

10. Goodness of fit - visual assessment

11. 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

12. Goodness of fit - statistical criteria
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)

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