I haven't done problem 2 yet, so I can't help you there. If you recall from lecture last week, vertical shifts don't matter because we're not concerned with the value of the likelihood function; rather, we are interested in the parameter value which maximizes that likelihood. What you should see when you do some arbitrary vertical shirts is that the N=100 and N=1000 are both maximized at the same parameter value, but that the curvature of one sample is much great/stepper in one case, implying the MLE is more certain in that case. Zac On Sun, Mar 1, 2009 at 9:53 PM, Lai, Ronald <rolai at hbs.edu> wrote:

It is actually the x-axis that needs to be scaled the same. Ronald, you're right that technically you can do the same by plotting the two curves on two different graphs and then eyeballing them, as long as the x-axis is the same. However, since we can shift likelihoods up and down, it's easier to compare by putting them on the same graph, which is what the problem is asking. On Sun, Mar 1, 2009 at 11:05 PM, John-Paul Ferguson <jpferg at mit.edu> wrote: -- Patrick Lam Department of Government and Institute for Quantitative Social Science, Harvard University http://www.people.fas.harvard.edu/~plam

Thanks all. I get it! Best. From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Patrick Lam Sent: Monday, March 02, 2009 3:11 AM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] PS4#2 & 1f whoops, John-Paul is also right, the y-axis should be on the same scale. On Mon, Mar 2, 2009 at 3:06 AM, Patrick Lam <plam at fas.harvard.edu<mailto:plam at fas.harvard.edu>> wrote: It is actually the x-axis that needs to be scaled the same. Ronald, you're right that technically you can do the same by plotting the two curves on two different graphs and then eyeballing them, as long as the x-axis is the same. However, since we can shift likelihoods up and down, it's easier to compare by putting them on the same graph, which is what the problem is asking. On Sun, Mar 1, 2009 at 11:05 PM, John-Paul Ferguson <jpferg at mit.edu<mailto:jpferg at mit.edu>> wrote: If you plot the two using par(mfrow=c(2,1)), the curvature will look almost the same, but the scale of the y-axis will be quite different. You have to plot them on the same scale in order to compare the curvature. Shifting one of them vertically so that their maxima have the same y-value makes it easy to plot them on the same graph. --John-Paul On Sun, Mar 1, 2009 at 9:53 PM, Lai, Ronald <rolai at hbs.edu<mailto:rolai at hbs.edu>> wrote: All, Since both distributions are Binomials with N=10, the log likelihood f(x) would be the same for both. Why is it necessary to even have an indicator variable? Essentially f(x)^d * f(x)^(1-d) = f(x).. I guess if one distr was Bin w/ N=10 and the other was N<>10, having the indicator variable makes sense. I'll operate on the assumption that the user of my R code can alter Ns for the two distributions. I'm a bit confused about PS4#1f 1) I'm assuming reparameterization is not necessary for plotting so I rewrote the f(x) to deal w/ this 2) Vertical shifts? Is it not the same as using par(mfrow=c(2,1)) and eyeballing the results? Feel like I'm missing something. Best. PS. Sparsha, in your f(x) below, you have not defined n or g. to my knowledge, the function also does not require an iterative process (per your for-loop) From: gov2001-l-bounces at lists.fas.harvard.edu<mailto:gov2001-l-bounces at lists.fas.harvard.edu> [mailto:gov2001-l-bounces at lists.fas.harvard.edu<mailto:gov2001-l-bounces at lists.fas.harvard.edu>] On Behalf Of sparsha saha Sent: Friday, February 27, 2009 3:41 PM To: gov2001-l at lists.fas.harvard.edu<mailto:gov2001-l at lists.fas.harvard.edu> Subject: [gov2001-l] R hates me is anyone getting this error message for problem 2 on this week's problem set Error in pnorm(pa3) : element 1 is empty; the part of the args list of '.Internal' being evaluated was: (q, mean, sd, lower.tail, log.p) I get this when I run my log likelihood function in R and then try to use optim on it: + pies2 <- pnorm(pa2) + pies3 <- pnorm(pa3) + for (i in 1:n) { + blaba <- ifelse(g > 0, sum(y2 * log(pies2) + (n - y2) * log(1 - pies2)), sum(y2 * log(pies3) + (n - y2) * log(1 - pies3))) + } + roe <- sum(blaba) / n + return(roe) + } Error in pnorm(pa3) : element 1 is empty; the part of the args list of '.Internal' being evaluated was: (q, mean, sd, lower.tail, log.p) _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu<mailto:gov2001-l at lists.fas.harvard.edu> http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu<mailto:gov2001-l at lists.fas.harvard.edu> http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l -- Patrick Lam Department of Government and Institute for Quantitative Social Science, Harvard University http://www.people.fas.harvard.edu/~plam -- Patrick Lam Department of Government and Institute for Quantitative Social Science, Harvard University http://www.people.fas.harvard.edu/~plam