On Sun, 14 Nov 2004, Olivia Lau wrote:
Good questions, Kate.
In PS 7, #1, part c, we are supposed to calculate
first differences using
simulation (and not using Zelig).
Correct
In lecture, Gary said that we are supposed to
re-use the random draws when
we are going through the expected value algorithm. I can see why this
would save time for the computer but would it actually give a different
answer for first diffs or CI's? (i.e. if we don't mind being a bit
patient, do we need to do this way?)
You need to resue the random draws. A first difference is
FD = g(X1 %*% beta) - g(X %*% beta)
if you reuse the beta's here, then the only variation in FD across draws
is due to estimation variation. each draw varies only due to that, and
that's exactly what we want (recall that we average over, or use this
trick, to get rid of fundamental uncertainty when looking at first diffs
or expected rather than predicted values).
if you don't reuse the draws, then your sims of FD will include BOTH
estimation uncertainty AND simulation variation. i.e., for any sized M,
you'll have too much variability in FD (tho larger M will be better). if
this isn't clear, or maybe even if it is, try both. you should see the
difference.
Gary
where g() is the parameterization of the systematic component. If the
betas are different, the calculation doesn't make sense and you rely on
distributional assumptions to make the distribution of FD's converge. So
just reuse the draws.
Also, which values in particular would we be
re-using on the way through
the simulation of expected values. Just the ones for gamma-squiggle, right?
Beta tilde and any other simulated parameters. I think for logit and
probit they're just the betas.
Olivia.
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