R-beta: extreme value dose-response fit
Bill Simpson
wsimpson at uwinnipeg.ca
Wed Sep 9 16:39:39 CEST 1998
Here are my dose-response data:
contrast<-c(0,.1,.04,.02,.03)
yes<-c(0+3+2+6+0+4+0+8,49+45,42+37,12+3,40+27)
ntrials<-c(49+49+53+53+55+61+52+42,51+45,51+39,47+48,47+58)
Contrast is the physical variable (dose) being varied.
I can fit these data by MLE to a normal or logistic CDF no problem. I
have done it both with nlm and glm.
But I run into problems when I try to fit them with an extreme value
CDF. In nlm I have problems with NaNs when a log of a number close to zero
is taken. In glm the procedure does not converge, presumably for the same
reason. I see in Venables and Ripley 237-238 this is a fairly common
circumstance. They say to try nlm, which I have done and still have
problems. The only other solution I see is to fit via least squares
rather than MLE.
I wonder if anyone out there is familiar with this sort of problem and has
ways to deal with it.
Thanks very much for any help.
Bill Simpson
PS By graphical trial and error I see that the extreme value CDF actually
fits these data pretty well. If I use those eyeballed parameter values as
a starting point, it doesn't help (numerical problems with near-zeros).
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