Sure. Basically the procedure works like this.
1. Optimize to get the MLEs and the Hessian.
2. Take the negative-inverse of the Hessian to get the variance co-variance
matrix.
3. Simulate N draws from the multivariate normal centered at the MLE using
the variance-covariance matrix as Sigma.
4. Set two sets of X values (we'll call them X1 and X2) as well as two sets
of Z values (Z1 and Z2)
5. For each of the N draws:
5a. Convert from the parameters beta and gamma to the natural parameters
pi and lambda by pushing everything through the systematic component.
5b. You should now have 4 numbers: pi_1, pi_2, lambda_1, lambda_2
5c. Use the formula for the expectation to calculate the first
difference: E(Y|pi_2, lambda_2) - E(Y|pi_1, lambda_1)
6. Now you have N first differences. This is the sampling distribution.
7. Report the mean of your distribution as the point estimate, the standard
deviation as the SE, and any quantile as a confidence interval.
Brandon
On Wed, Mar 30, 2011 at 3:26 PM, Yanfang Su <suyanfang(a)gmail.com> wrote:
Thanks, Brandon! I still have a hard time in
calculating the s.e. of the
first difference. Would you please offer some hint? Best, Yanfang
*From:* gov2001-l-bounces(a)lists.fas.harvard.edu [mailto:
gov2001-l-bounces(a)lists.fas.harvard.edu] *On Behalf Of *Brandon Stewart
*Sent:* Tuesday, March 29, 2011 11:04 PM
*To:* Class List for Gov 2001/E-2001
*Subject:* Re: [gov2001] Problem 2.5
They are first differences and we gave you the form of the expectation so
you can take the shortcut. That being said, its quite easy to simulate from
the distribution so you absolutely can if you want to be sure!
Brandon
On Tue, Mar 29, 2011 at 10:57 PM, Yanfang Su <suyanfang(a)gmail.com> wrote:
Hi all,
In 2.5, why it is unnecessary to simulate from the zero-inflated poisson
distribution?
Thanks, Yanfang
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