[R] Poisson Maximum Likelihood Estimation

Paul Sweeting
Fri, 25 Jan 2008 12:35:22 -0000

Hi

I am trying to carry out some maximum likelihood estimation and I'm not
making much headway, and I'm hoping that someone will be able to point me in
the right direction.

I am modelling mortality statistics.  One way to do this is to model the
mortality rate (or, more accurately, log of the mortality rate, log_m) as
(say) a constant plus a proportion of age, plus time, so:

r_1 <- lm(formula=log_m ~ age + time)
summary(r_1)

However, an alternative approach is to use try and estimate the number of
deaths from the poisson mean mortality rate, and the number of people, with
the poisson mean being defined in terms of age and time (And a constant).
Conceptually I can see how this should work, in terms of linking the poisson
probabilities together at each age and optimising the coefficients on age
and time to maximise the log likelihood, but I cannot work out how to
express this in R.  Hopefully this outlines what I'm trying to do - any
ideas gratefully received.