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understanding the 4 parameter logisitc regression

3 messages · 1Rnwb, Dieter Menne

1Rnwb
# 
I have questions regarding  
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)))

nls(log(il10)~A+(B-A)/(1+(conc/xmid )^scal),data=test,
+             start = list(A=3.5, B=15,
+               xmid=600,scal=1/2.5))
Nonlinear regression model
  model:  log(il10) ~ A + (B - A)/(1 + (conc/xmid)^scal) 
   data:  test 
          A           B        xmid        scal 
 14.7051665   3.7964534 607.9822962   0.3987786 
 residual sum-of-squares:  0.1667462 

I did not understand how these values  A=3.5, B=15,xmid=600,scal=1/2.5  were 
obtained by Jim in the posting here
http://www.mail-archive.com/r-help at stat.math.ethz.ch/msg25500.html.

I would appreciate a little help here to understand the 4-parameter
logisitic regression for processing of standard curve for ELISA/MUltiplex
Immunoassays.

Thanks and happy holidays
sharad
Dieter Menne
#
1Rnwb wrote:
The easiest way is to plot the function for several parameters with the
original data superimposed. It shows you, that either you copied


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)))

fn = function(conc, A,B,xmid,scal) {
  A+(B-A)/(1+(conc/xmid )^scal)
}

plot(test$conc,fn(test$conc,15,3.5,600,1/2.5),type="l") # looks good
#plot(test$conc,fn(test$conc,3.5,15,600,1/2.5),type="l") # bad
points(test$conc,log(test$il10))

Which tells you that the example you cited has a typo, or the author had
mixed up parameters A and B.

Dieter
1Rnwb
# 
Thanks Dieter for the help. This is how I want
plot(log(test$conc),fn(test$conc,15,3.5,600,1/2.5),type="l") # looks good

points(log(test$conc),log(test$il10)) 

regards and happy holidays
sharad