Recall that sigma^2 is a parameter just like the betas. It is the variance of the normal distribution that the y's are drawn from. In our setup, we are trying to maximize over all the parameters (which include 4 betas and 1 sigma^2), so the last term of the parameter vector happens to be the sigma^2 in the way we set it up. It's no different than if we were trying to maximize for two pi's in the last HW, where the last item in the parameter vector was pi_2. On Fri, Mar 6, 2009 at 8:11 PM, charlotte cavaille <charlotte.cavaille at gmail.com Dear Miya I have a question on lectures notes: in the following piece of R code i don't get the part in bold: # Predicted Values set.seed(12345) M <- 1000 par.draws <- mvrnorm(M, mu=opt.new.par , Sigma=opt.new.vcv) beta.draws <- par.draws[,-5] sigma2.draws <- exp(par.draws[,5]) X.c <- apply(X.data, 2, mean) mu.c <- c() for(i in 1:nrow(beta.draws)){ mu.c[i] <- X.c %*% beta.draws[i,] } m <- 1 Y.c.predict <- c() for(i in 1:length(mu.c)){ Y.c.predict[i] <- rnorm(m, mean=mu.c[i], sd= sqrt(sigma2.draws[i])) } mean(Y.c.predict); sd(Y.c.predict) #84.92893 #2.005887 why is the 5th column of an output of a multivariate normal sampling that of the variances???? Thanks! Charlotte _______________________________________________ gov2001-l mailing list 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 _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l

Not sure what you mean by "specify error artificially" (perhaps you are talking about how we generated our fake data?) but I hope the following explanation helps. The model from section (specifically the part on simulating quantities of interest) was a linear regression model. So, sigma squared is part of the model and part of the likelihood that we maximize. It is a necessary parameter and must be estimated and simulated along with the other parameters (i.e. the beta coefficients). Whether or not there is a sigma squared parameter simply depends on your model -- your model tells you what parameters to estimate, simulate, etc. Best, Miya On Sat, Mar 7, 2009 at 6:16 PM, Bernard L. Fraga <bfraga at fas.harvard.edu Sounds good. Quick Question: How do we pull out the sigma^2 from a model when we don't specify error artificially (like in the section slides)? Thanks in advance. -Bernard ----------------------- Bernard L. Fraga Ph.D. Student, Harvard University Government and Social Policy bfraga at fas.harvard.edu ----------------------- On Mar 7, 2009, at 1:44 AM, Patrick Lam wrote: > Recall that sigma^2 is a parameter just like the betas. It is the > variance of the normal distribution that the y's are drawn from. > In our setup, we are trying to maximize over all the parameters > (which include 4 betas and 1 sigma^2), so the last term of the > parameter vector happens to be the sigma^2 in the way we set it > up. It's no different than if we were trying to maximize for two > pi's in the last HW, where the last item in the parameter vector > was pi_2. > > On Fri, Mar 6, 2009 at 8:11 PM, charlotte cavaille <charlotte.cavaille at gmail.com >> Dear Miya > > I have a question on lectures notes: in the following piece of R > code i don't get the part in bold: > > # Predicted Values > set.seed(12345) > M <- 1000 > par.draws <- mvrnorm(M, mu=opt.new.par , Sigma=opt.new.vcv) > beta.draws <- par.draws[,-5] > sigma2.draws <- exp(par.draws[,5]) > X.c <- apply(X.data, 2, mean) > mu.c <- c() > for(i in 1:nrow(beta.draws)){ > mu.c[i] <- X.c %*% beta.draws[i,] > } > m <- 1 > Y.c.predict <- c() > for(i in 1:length(mu.c)){ > Y.c.predict[i] <- rnorm(m, mean=mu.c[i], sd= sqrt(sigma2.draws[i])) > } > mean(Y.c.predict); sd(Y.c.predict) > #84.92893 > #2.005887 > > > why is the 5th column of an output of a multivariate normal > sampling that of the variances???? > > Thanks! > > Charlotte > > _______________________________________________ > gov2001-l mailing list > 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 > _______________________________________________ > gov2001-l mailing list > 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 http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l -- Miya Woolfalk Ph.D. Student Harvard University Government and Social Policy _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l