[R] Bioassays Yielding concentration-Mortality data

[Thomas Lumley]

On Mon, 27 Oct 2003, Ing. Michael Rost wrote:

> Dear all, I'm trying reproduce an example of bioassays Yielding
> Concentration-Mortality Data particularly control - adjustment model
> from book Bioassay of Entomopathogenic Microbes and Nematodes chapter 7
> with R.
>
> I used glm with family=binomial and link=probit, but I do not know how
> to implement parameter gamma (control mortality - mortality of the
> untreated control insect in this exaple) into model formula.
>
> Model in book:
> pi(x)=gamma+(1-gamma)F(alpha+beta log(x))

This is a generalised linear model but isn't one of the built-in link
functions.  You would have to modify one of the glm family objects to use
this link function, changing the components
linkfun:  the link function
linkinv: the inverse of the link function
mu.eta: the derivative of the inverse of the link function

As a starting point you probably want the family object returned by
binomial(link=probit).

	-thomas

> F....cumulative probability distribution function
> data:
> x=concentration
> n=number of insect at each run
> y=number of death among n in given batch run at given concentration
>
>
> Xmat<-data.frame(x=rep(c(0.01,0.1,1,10,100),2),n=rep(100,10),y=c(19,20,21,45,80,25,25,27,56,91))
>
>
>
> Reults from book (obtained from SAS) are
>
> intercept  -1.6597 , beta =0.5586, control mortality --- gamma =0.2172
>
> Thanks for any advice.
> Michael
>
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Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle