[R] SSweibull

[Philippe Grosjean]

Dr. Mirko Luedde wrote:
>Dear Prof Ripley,

>there was no (direct) answer to any of my questions in your post, but
>I think I'm getting the idea! Sorry for my ignorance.

I take the liberty to answer to these questions. Prof Ripley has certainly
many work answering questions about 1.3.0 installation and so on... but I am
sure he will add some nice tip to this answer if required.

>And I still seem to have a gross misunderstanding about the use of
>`SSweibull(nls)'.

SSweibull, like any Self-starting function in R (SSlogis, SS...) is just an
analytical function y = f(x) that returns y values for provided x values.
Under some circumstances, it returns also the gradient matrix, i.e.: the
Jacobian or if you prefer the matrix of partial derivatives according to
each parameters of the function. See ?SSweibull for more info. The equation
is provided. It is: Asym-Drop*exp(-exp(lrc)*x^pwr), with Asym, Drop, lrc and
pwr being parameters to estimate.

>Is it simply a means to calculate the Weibull
>distribution?

No. See answer to the previous question.

>What's the difference to `pweibull', then?

Idem.

>Which means could help me estimating the Weibull parameters from
>empirical data?

>And what does it mean that `[SSweibull is] intended to be used by a
>call to nls()'?

Self-starting objects are mostly intended to define a formula like y ~
SSweibull(x, Asym, Drop, lrc, pwr). This formula is used as first argument
of the nonlinear least-square regression function that evaluate parameters
from empirical data. See last line of example in the SSweibull help. It will
create a nls object with all you need to diagnose the fitting. Use
summary(nlsobjectname) for instance.

Usually with nls(), you also have to provide initial guess of parameters,
and convergence is dependent upon these initial guess. To ease the use of
nls(), Self-starting functions have a nice algorithm that evaluate good
guess for intial values of parameters and you don't need to provide them.
Many Self-starting functions of nls() library even got the parameters
estimation that correspond to the overall minima of the obective function.
In this case, initial evaluation _is_ also evaluation at convergence and it
is fast, easy, and secure (you are sure it is not just a local minimum).

Please, note thate library nlrq uses the same Self-starting functions than
nls(), but performs nonlinear quantile regression which could be useful for
study of survival (calculating curves corresponding to various quantiles,
see ?nlrq and the corresponding paper citer in help).

Otherwise, I am sure you will find very good stuff in survreg... but there I
cannot help you.

Regards,

Philippe Grosjean


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