Re: probit analysis with natural response

On Jun 19, 10:05 pm, Aniko <aniko123...@xxxxxxxxx> wrote:

You are running into boundary and discontinuity issues, mostly because
of the log(0)=-Inf input. I would be really surprised if SAS dealt
with it gracefully without error messages in the log file (unless it
is a built-in model - are you using PROC NLIN?) and/or a good choice
of starting values. It's not complaining about log(0)? Or 0*log(0)?
Perhaps the SAS answer was different because it just plain dropped
that value.
For example, with any beta<0 your likelihood is infinite, while with
beta=0 it is finite (as long as 0*log(0)=0). You can try bounded
optimization (since c should not go out of the 0-1 range either). The
other issue is the finite differencing: R calculates the derivatives
itself, and apparently it is sometimes running into trouble (perhaps
when it tries to use negative beta?). You could help it by supplying
the gradient function which should be pretty straightforward to
calculate for this model.
But the real difficulty is that P should be bounded, and the model
does not make it so. Cutting it a 0 and 1 is not perfect, and with P=0
or 1 you get infinite likelihood if the observed probability is not 0
or 1. A possible solution is to define the likelihood function so that
when P leaves its range the likelihood decreases smoothly (so that the
maximum is never there).

Aniko

Thank you very much, Aniko. I will make more test according to your
suggestions.

For I am not familiar with statistics and R language, so I sent a
message
to R-help mailing list, and hope to get a hand.

I will post solution here, if I get it.

Jinsong
.