# Re: [R] maximum likelihood estimation of 5 parameters

From: Ken Beath <kbeath_at_efs.mq.edu.au>
Date: Fri 05 Jan 2007 - 20:48:42 GMT

Using the inverse logistic transform to replace p by exp(xp)/(1+exp(xp)) allows unconstrained fitting of xp. There may still be problems where xp tends to + or - infinity depending on starting values.

>>> francogrex <francogrex@mail.com> 01/05/07 11:54 PM >>>

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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