[R] regression for poisson distributed data

[Gabor Grothendieck]

On Tue, Apr 3, 2012 at 9:58 AM, Joachim Audenaert
<Joachim.Audenaert at pcsierteelt.be> wrote:
> Hello all,
>
> I would like to get parameter estimates for different models. For one of
> them I give the code in example. I am estimating the parameters (i,j and
> k) with the nls function, which sees the error distribution as normal, I
> would however like to do the same as nls with the assumption that the
> errors are poisson distributed.
>
> Is there a way to do this with R? Are there packages designed for this? I
> tried with the gnm package, but don't understand how to transform my
> equation to a generalised equation. Is there an option for nls to choose
> family = poisson?
>
> Lower in the mail the code with the model and visualisations I use to
> check my results. I also copied the test dataset from my txt file.
>
> I am using R 2.15 and Rstudio to visualise it.
>
>
> plot(FR~N0)
> x <-
> nls(FR~(exp(i+j*N0)/(1+exp(i+j*N0)))*(k*N0/(k+N0)),start=list(i=0.02,j=0.002,k=6))
> summary(x)
> hatx <- predict(x)
> lines(spline(N0,hatx))
>

Just minimize the negative log likelihood from first principles.
Define the mean function and then define the negative log likelihood
in terms of that:

Mean <- function(p) { i <- p[1]; j <- p[2]; k <- p[3];
exp(i+j*N0)/(1+exp(i+j*N0))*(k*N0/(k+N0)) }
ll <- function(p) - sum(dpois(FR, Mean(p), log = TRUE))
out <- optim(c(1, 1, 1), ll); out

plot(FR ~ N0, pch = 20)
lines(Mean(out$par) ~ N0)

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