[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

sraghavan at mmm.com wrote:

>
>Shalini Raghavan
>3M Pharmaceuticals Research
>Building 270-03-A-10, 3M Center
>St. Paul, MN  55144
>E-mail: sraghavan at mmm.com
>Tel:  651-736-2575
>Fax:  651-733-5096
>
>----- Forwarded by Shalini Raghavan/US-Corporate/3M/US on 08/16/2004 11:25
>AM -----
>                                                                           
>             Shalini                                                       
>             Raghavan/US-Corpo                                             
>             rate/3M/US                                                 To 
>                                       r-help at stat.math.ethz.ch.           
>             08/16/2004 08:57                                           cc 
>             AM                                                            
>                                                                   Subject 
>                                       Fw: using nls to fit a four         
>                                       parameter logistic model            
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>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)))
>  
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>>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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