[R] maximum likelihood estimation of 5 parameters

[Ingmar Visser]

Franco,
You can provide lower and upper bounds on the parameters if you use optim
with method="L-BFGS-B".
Hth, Ingmar


> From: francogrex <francogrex at mail.com>
> Date: Fri, 5 Jan 2007 04:54:50 -0800 (PST)
> To: <r-help at stat.math.ethz.ch>
> Subject: [R] maximum likelihood estimation of 5 parameters
> 
> 
Hi Guys, it would be great if you could help me with a MLE problem in R.

I
> am trying to evaluate  the maximum likelihood estimates of theta = (a1,
b1,
> a2, b2, P) which defines a mixture of a Poisson distribution and two
gamma
> prior distributions (where the Poisson means have a gamma
distribution,
> actually 2 gammas and P is the mixing factor). The likelihood
function for
> theta is L(theta) = Pi,j{P f(Nij; a1, b1, Eij) + (1 ­ P) f(Nij;
a2, b2, Eij),}
> 
The maximum likelihood estimate of theta is the vector that maximizes
> the
above equation (the values of N and E are given). The authors of the
> article
I read say that the maximization involves an iterative search in the
> five
dimensional parameter space, where each iteration involves
> computing
log[L(theta)] and its first and second-order derivatives. In test
> runs it is
suggested that the maximization typically takes between 5 and 15
> iterations
from the starting point theta = (a1 = 0.2, b1 = 0.1, a2 = 2, b2 =
> 4, P =
1/3). 

Now I have done maximization of a gamma-poisson mixture before
> (1 poisson, 1
gamma) successfully and I could determine correctly alpha (a)
> and beta(a).
But this one above is giving me ridiculously large unusable
> values (for
example P should not be above 1 and sometimes I get values of
> 500!) or even
negative values! I know the values I should be obtaining with my
> samples
shouldn't be far from the staring points. Is there a way to help me
> solve
this issue? Thanks.
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