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Math Forum » Discussions » sci.math.* » sci.stat.math.independent

Topic: Maximum Likelihood estimation
Replies: 16   Last Post: Nov 5, 2006 7:43 AM

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Glen Barnett

Posts: 643
Registered: 12/6/04
Re: Maximum Likelihood estimation
Posted: Oct 30, 2006 8:20 PM
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Charles,

One issue occurs to me that's a bit hard to tell from your time-free
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(t-1),....,P(1)|P(0)) = f(P(t)|P(t-1)) . f(P(t-1)|P(t-2)) ... .
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

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