Re: [R] using nls to fit a four parameter logistic model

[Spencer Graves]

     In your second model, log(conc) is negative for conc = 0.001.  
This observation will generate NA for (log(conc)/xmid)^scal unless scal 
is an integer or xmid is also negative.  In the latter case, 
(log(conc)/xmid)^scal will be NA for all but that last value unless scal 
is an integer. 

     What do your biological references do with this model for 
concentrations less than 1? 

     If you delete that observation, the algorithm can still die 
testing a value for xmid <= 0.  To avoid these cases, I routine 
parameterize problems like this in terms of ln.xmid, something like the 
following: 
       
           log(il10)~A+(B-A)/(1+(log(conc)/exp(ln.xmid))^scal). 

     hope this helps.  spencer graves
[EMAIL PROTECTED] wrote:
Shalini Raghavan
3M Pharmaceuticals Research
Building 270-03-A-10, 3M Center
St. Paul, MN  55144
E-mail: [EMAIL PROTECTED]
Tel:  651-736-2575
Fax:  651-733-5096
----- Forwarded by Shalini Raghavan/US-Corporate/3M/US on 08/16/2004 11:25
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                                                                  Subject 
                                      Fw: using nls to fit a four         
                                      parameter logistic model            
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          
                                                                          




I am working on what appears to be a fairly simple problem for the
following data
test=data.frame(cbind(conc=c(25000, 12500, 6250, 3125, 1513, 781, 391,
195, 97.7, 48.4, 24, 12, 6, 3, 1.5, 0.001),
il10=c(330269, 216875, 104613, 51372, 26842, 13256, 7255, 3049, 1849, 743,
480, 255, 241, 128, 103, 50)))
 

test
   

       conc   il10
1  25000.000 330269
2  12500.000 216875
3   6250.000 104613
4   3125.000  51372
5   1513.000  26842
6    781.000  13256
7    391.000   7255
8    195.000   3049
9     97.700   1849
10    48.400    743
11    24.000    480
12    12.000    255
13     6.000    241
14     3.000    128
15     1.500    103
16     0.001     50
I am able to fit the above data to the equation
 

nls(log(il10)~A+(B-A)/(1+exp((xmid-log(conc))/scal)),data=test,
   

+  start = list(A=log(0.001), B=log(100000),
+ xmid=log(6000),scal=0.8))
Nonlinear regression model
 model:  log(il10) ~ A + (B - A)/(1 + exp((xmid - log(conc))/scal))
  data:  test
       A         B      xmid      scal
3.796457 14.705159  6.410144  2.507653
residual sum-of-squares:  0.1667462
But in attempting to achieve a fit to what is commonly known as the hill
equation, which is a four parameter fit that is used widely in biological
data analysis
nls(log(il10)~A+(B-A)/(1+(log(conc)/xmid )^scal),data=test,
+ start = list(A=log(0.001), B=log(100000),  xmid=log(6000),scal=0.8))
Nonlinear regression model
 model:  log(il10) ~ A + (B - A)/(1 + (log(conc)/xmid )^scal)
Error in numericDeriv(form[[3]], names(ind), env) :
       Missing value or an Infinity produced when evaluating the model

Please would someone offer a suggestion
Shalini
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