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Parameter Variability

Another criteria that can help in deciding if you have the right model is the reported variability in the parameter values. Most non linear regression model will provide some indication of parameter variability. This might include standard deviation, confidence interval or coefficient of variation. These numbers may be reported as zero, some reasonable number or a very large number or even NaN. Anything other than a reasonable number may mean a serious problem with the model. A value of zero is not good. A low number is OK but 0 usually means some computational problem, including wrong model, weighting scheme, insufficient data.

If the coefficient of variation (CV) is below 10% for all your parameters then your model is probably doing quite well. Occasionally one or two or the parameters may have higher CV values. This indicates that the program is not able to provide more precise estimates for these parameters. Maybe these parameters are not necessary. As the CV increases above 15%, above 25%, greater than 100% you are provided with the evidence that the model may be too large. You should consider looking at a smaller model, removing or replacing parameters with larger CV values.

Some non linear regression programs provide a table of correlation coefficients between the adjustable parameters of the model. A high correlation (> 0.90 or > 0.95) between two parameters suggests that one parameter may replace both or that an otherwise smaller model maybe worth exploring.

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