[R] Fitting binomial data to a probit distribution without an equation

[mort459]

Hey everyone,

I've been reading an old scientific paper (well, not that old, about 15
years) and I want to verify the authors' statistical results. The paper is
fairly unclear about what exactly they did, and none of the relatively
simple commands I'm familiar with are producing results similar to theirs. 

The data is dose-response, recorded as binomial data:

structure(list(X1 = c(10, 10, 12, 13, 14, 15, 16, 18, 20, 20, 
23, 23, 25, 30, 45, 46, 46, 48, 50, 52), X2 = c(0, 1, 0, 1, 1, 
1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1)), .Names = c("X1", 
"X2"), row.names = c(NA, 20L), class = "data.frame")

The quote(s) from the paper is as follows: 

"Maximum likelihood was applied to probit models (normal, lognormal,
weibull, logistic, and
log-logistic) and the data to determine the incidence relationships. The
lognormal and loglogistic
models best represent the data."

and later:

"Binary data are utilized for the maximum likelihood dose response
calculations"

I tried using a simple glm() with a probit linker, but that produced
border-line nonsense results. This made sense when I thought about it more,
as R was trying to fit a regression line to raw binary data as opposed to
binned/high repetition binary data. 

I've also messed around with maximum likelihood but they're not clear about
what equation they're using. 

In the end, I guess what I'm trying to do is:  figure out how they're
estimating their probit parameters from a binary data set. To me, estimating
parameters seems very different from doing a GLM. Is this even possible to
do? Is there a package out there than performs this function or is it in the
basic functionality of R and I'm just being dumb??

-Mort

(apologies if this is too much theoretical statistics and not enough 'R')

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