Alexei, Likelihood-based confidence regions need not be intervals (according to Moreira in Ec 2110). The way in which I interpreted the section notation is in the context of quasi-concave likelihood functions--in these cases, there are two unique values of t such that the CI condition is satisfied. This suggests an interpretation for "calibration" since one needs to find the values of t that satisfy 2lnL(T^)-3.84=2lnL(t) (there are two such values of t if the likelihood function is quasi-concave. If not, it is possible that there are additional intervals that satisfy the constraint. I hope that this helps. Best, Martin Alexei Colin wrote:

Hi everyone, I still can't figure out this likelihood-based confidence interval. In the notes it says that the points in the interval must satisfy the condition 2ln(L(thetahat)/L(theta)) <= 3.84. However, given that the absolute value of L(thetahat) is less than the absolute value of L(theta), the fraction evaluated within the log must be between zero and one, yielding a negative number. Furthermore, if we used the expanded version of the expression with the ln(L(thetahat))-ln(L(theta)) we would have problems since all the likelihoods are negative and cannot be logged. Overall, the numbers just don't seem right. Any thoughts? Jon and Jane 2008/3/9, Alexei Colin <acolin at fas.harvard.edu>: -- Jon Bischof Graduate Student Department of Government Harvard University

I have finished the rest of the problem set, but I am having a very difficult time conceptualizing how to solve the Wilks confidence interval. Perhaps it is because I have spent way too much time looking at this computer screen, but I just can't get my head around L(thetahat) and L(theta). Is my algebra even correct? First, are we trying to find L(theta)? Second, I assume since 3.84 is the critical value, we are trying to solve for 3.84. (2)*ln(L(thetahat)/L(theta)=3.84 (2)*(lnL(thetahat)-lnL(theta))=3.84 (lnL(thetahat)-lnL(theta))=1.92 lnL(thetahat)=lnL(theta)+1.92 lnL(thetahat)-1.92=lnL(theta) -insert mental explosion here- Joe -----Original Message----- From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Jens Hainmueller Sent: Monday, March 10, 2008 5:50 PM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] Wilks confidence intervals Without having seen your code, my best guess is that you are using ln(ln(L(thetahat))/ ln(L(theta))) instead of ln(L(thetahat)/L(theta)). Notice L() refers to the likelihood, not the log likelihood. If you use the log-likelihood instead you'd log the thing twice. Hope this helps, jens _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l

Solve for lnL(thetahat); that is just a number. I hope that helps. I'm having problems with the bootstrap confidence interval Johannes Quoting Joseph Williams <william5 at fas.harvard.edu>:

Cat, THIS is referring to the use of the exponential model to model the political survival outcomes. This includes the whole log-likelihood, etc. since it is all part of the same model. There are various correct answers here. Think about the assumptions that underlie the exponential model and whether they are reasonable in this context. You can also discuss goodness of fit, etc. We don't ask you to consider alternative models, although you could if you want to (based on other distributions you may have read about in UPM). Hope this helps. Jens From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Catherine Kelly Sent: Thursday, March 13, 2008 12:58 AM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] Fisher and Hessian question Hi Jens, Jenn, et. al, I am confused about what problem j on the Homework is asking: When you say "Do you think THIS is a reasonable model for this data?" what is the THIS referring to--the log-likelihood/MLE model?? the use of the exponential distribution to describe political survival outcomes?? Ultimately, wondering what model is being referred to, and then as a corollary wondering what our alternative/competing models are.... Thanks, Cat On Sun, Mar 9, 2008 at 6:17 PM, Jens Hainmueller <jhainmueller at gmail.com> wrote: Jane, If you're analytical and numerical answers agree this should give you a strong indication that you're on the right track (they should not differ wildly). Re re-parameterization: The hessian changes with the re-parameterization scheme; it will give you the curvature of the re-parameterized LLfcn. To get the analytical variance for the de-reparameterized quantity of interest you normally need to use the delta method. However, here you can derive a closed from solution for the standard error so there is no need for that. For the simulations you should work with the reparametrized hessian as in the other example in the section code. Finally, you can also avoid re-paramterizatioin using L-BFGS-B. ?Hope this helps, jens _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l -- Catherine Lena Kelly Ph.D. Student Harvard University Department of Government