
Re: Maximum Likelihood estimation
Posted:
Oct 30, 2006 8:20 PM


Charles,
One issue occurs to me that's a bit hard to tell from your timefree formulation  does your parameter estimation combine parameter estimates across all time periods, or are you trying to estimate for a single time period across all regions?
In the combined time period case the Markovian nature of the model makes it harder to combine into one large logistic regression, but as long as you can condition on an initial period, the likelihood should decompose. If P(s) is the vector of pi's at time s, then
f(P(t),P(t1),....,P(1)P(0)) = f(P(t)P(t1)) . f(P(t1)P(t2)) ... . f(P(2)P(1)) . f(P(1)P(0)),
so something may be possible. Of course to do it really properly, you'd want to include the original time as well, but the effect should not be very large.
Glen

