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?
question about the conditional number
Started by
jiangjuanjuan
, Mar 29 2010 01:57 AM
1 reply to this topic
#2
Posted 29 March 2010 - 12:03 PM
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 10No. 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
Your target is have a condition number LESS THAN 10No. 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
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