suggestions for nls error: false convergence

Hi,
  I'm trying to fit some data using a logistic function defined as

y ~ a * (1+m*exp(-x/tau)) / (1+n*exp(-x/tau)

My data is below:

x <- 1:100

y <- c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,1,1,2,2,2,2,2,3,4,4,4,5,
5,5,5,6,6,6,6,6,8,8,9,9,10,13,14,16,19,21,
24,28,33,40,42,44,50,54,69,70,93,96,110,127,127,141,157,169,
178,187,206,216,227,236,238,244,246,250,255,255,257,260,261,262,266,268,
268,270,272,272,272,273,275,275,275,276)

My first attempt was to use nls as below:

    d <- data.frame(x=x, y=y)
    model <- nls(y ~ a * (1+m*exp(-x/tau)) / (1+n*exp(-x/tau)), data=d,
    start=list(a=277,m=100,n=101,tau=10), 
    algorithm='port', trace=TRUE,
    control=nls.control(maxiter=5000, minFactor=1/2048))

Running the above code I get the following error message:

Convergence failure: function evaluation limit reached without
convergence (9).

To investigate this further I used nlminb() to get a set of starting
parameters. Thus I did:

func <- function( par ) {
    a = par[1]
    m = par[2]
    n = par[3]
    tau = par[4]
    a * (1+m*exp(-x/tau)) / (1+n*exp(-x/tau))
}
est <- nlminb( c(277, 100,101, 10), objective=func,
control=list(eval.max=400, iter.max=1000))

I get absolute convergence and a set of parameter values. Plugging these
into the nls call and trying again still gives me

 Convergence failure: function evaluation limit reached without
convergence (9)

I have tried a number of different starting values for the nls() call
but I usually end up getting the following error:

Convergence failure: false convergence (8)

After reading the PORT library docs, I see that this error can mean

1) gradient is calculated incorrectly
2) stopping tolerances are too tight
3) gradient is discontinous near some iterate

However, since nls() usually reports the above error after 30 to 40
iterations, the PORT docs suggest that it is not problem 1. I'm not sure
about (3) - I have other data which are somewhat similar to the above
data, but they lead to a straightforward fit.

In the end I tried a different starting value and lowered the tolerances
a little, and I got a valid fit

My questions are:

1) Why would the parameters that lead nlminb() to converge to work in
nls() (since I'm using the PORT algorithm in both cases)?

2) Is there a strategy to obtain starting values? In my case I know that
a should be around 277, but for the others I'm not sure. 

3) Is there a quick way to check whether the gradient is discontinous at
a point, numerically (rather than calculating the analytical
derivatives)? I did 

plot(diff(y))

and it certainly looks messy, but I also have other y vectors which look
equally jagged (though the jaggedness occurs at lower x)

Any suggestions would be appreciated.

Thanks,

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Rajarshi Guha <rxg218 at psu.edu> <http://jijo.cjb.net>
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After a number of decimal places, nobody gives a damn.