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[jiangjuanjuan]

I have designed three models for one data set. Model1 has two differential equations and 4 parameter, conditonal number is several hundred, but the WRSS is the largest. Model2 has three differential equations and 5 parameter, and decreased WRSS to 25% of that in model1 with conditional number being several thousand. Model3 has two differential equations and 5 parameter, and similar WRSS with model2 ,but conditional number is up to ten thousand. so which model should I choose, model1 or model2? and why? and how to evaluated on the conditional number?

[Simon Davis]

Hi Jiang, the condition number associated with a problem is a measure of that problem's amenability to digital computation, that is, how numerically well-conditioned the problem is. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned.

Your target is have a condition number LESS THAN 10^{No. of parameters} i.e.for a model of Cl & V would be 10² = 100.

Personally I tend to concentrate on looking for the model with the lowest AIC, minimising CV% of parameter estimates as much as possible and overall visual assessment of fit.

Johan Gabrielsson & Dan Weiner's book, "Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications" can be useful as a hand book since it uses WinNonlin models and output to illustrate concepts. And luckily enough you can order it here if you want ;0)

http://www.pharsight...ca_textbook.php

Take a look at Chapter 4. " Parameter Estimation" from page 361
4.1 Background 361
4.2 Linear and Nonlinear Models 362
4.3 Criteria for Best Fit – Minimization Methods 364
4.3.1 Ordinary, weighted and extended least squares methods 364
4.3.2 Generalized least squares method 366
4.4 Considerations in the Choice of Weights 368
etc.

Simon