[R] classification by nls and anova

Maciej.Hoffman-Wecker@evotecoai.com Maciej.Hoffman-Wecker at evotecoai.com
Wed May 29 16:42:30 CEST 2002

Dear R-users, 

I'd appreciate your statistical opinion on the following problem. 

I'm fitting the four parameter logistic model [f(x) = a + (b - a)/(1 + 
exp((c - x)*d))] to assay data. 
We have a lot of samples to fit and my aim is to classify these samples 
into following groups: 

  1. no interrelation 
     all results about =~ 0 
     too low concentration 

  2.   only full saturation 
     all results about =~ 1 
     too high concentration 

  3. only starting interrelation 
     results going up, not reaching the turning point 
     too low concentration 

  4. only starting saturation 
     results starting above the turning point, going up, reaching the 
     hence too high concentration 

  5. only the linear area 
     no start and saturation 
     hence too low concentration range 

  6. full interrelation 
     including starting interrelation and saturation 

Is there a way to model these classes, and compare their significance by 
means of an 
analysis of the residuals (ANOVA)? 

Something like 

  model 1 = linear & constant =~ 0 & slope = 0 
  model 2 = linear & constant =~ 1 & slope = 0 
  model 3 = ???? some curvature 
  model 4 = ???? some curvature 
  model 5 = linear & slope > 0 
  model 6 = full four parameter logistic model 

with the procedure: 

Starting with the linear model and testing for any curvature. 
 -> curvature not significant 
    ==> result = model 1, 2 or 3, depending on significance of slope and 
 -> curvature significant   
   -> testing for full logistic model 
    -> logistic model significant     
    ==> result = logistic model 
    -> logistic model not significant   
    ==> result = a curvature model (model 3 or 4), depending on the 

Is this a reasonable and feasible procedure? And if so, what kind of model 
might be appropriate 
for the classes 3 and 4? 

Hope someone has the time to give me an answer or any advice on any other 

Thanks in advance 

Maciej Hoffman-Wecker 

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