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?
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[sup][size=4]No. of parameters[/size][/sup] i.e. for a model of Cl & V would be 10[sup]2[/sup] = 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) Certara | Drug Development Solutions 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