Not what you might think.
Take the MNL model (with IIA etc) and add a probit link. It is odd that they would call that multinomial probit. Most people would understand “multinomial probit” as a model for multinomial outcomes with multivariate normal disturbances (in general, with non-zero covariances). A screen full into the documentation for Stata’s mprobit it says:
The error terms are assumed to be independent, standard normal, random variables. See [R] asmprobit for the case where the latent-variable errors are correlated or heteroskedastic and you have alternative-specific variables.
A trap for the hasty, the unwary…?
This said, the “real” multinomial probit function in Stata uses some funky options for controlling he nasty integrations necessary to evaluate the likelihood for this model (i.e., simulated MLE a la GHK, with an option for Halton sequences to drive the quasi-Monte Carlo integration). It would be fun to play with this Stata function, alongside the fully Bayesian/MCMC implementations in R for this model (e.g., MNP and bayesm).
A recent e-mail correspondent writes:
I have a degree in applied statistics, and I’m really interested in the lectures notes you put on your website about Bayesian approaches and simulations. That’s something i need to discover and it looks really rich and interesting. I also use R on a very regular basis.
The purpose of this email is that I’m using LaTeX to write some documents, and i can’t find anything on how to install the FF Meta police, which is very clear and easy to read.
Have you anything about that by any chance?
First of all, I should take the Bayes notes down and point you in the direction of The Book (done!).
On FFMeta, I don’t quite get the references to “FF Meta police”. But here is how I did it (below the fold).
Some graphs looking at the voting on the Stupak amendment. This roll call sliced up the Democrats pretty nicely. Thumbnails below link to PDFs. Democrats only in the 1st graph, looking at the relationship between the Ayes and Noes and Obama vote share in the representatives’ respective districts.
And one more look at last night’s vote, this time with each representative’s estimated ideal point (based on the entire 111th House thus far) as the predictor, similar to what I did for the Coburn amendment in the Senate.
Update: and yet another graphical rendering (click on the thumbnail for the PDF).
Here is a quick look at how Democrats split on the House vote on the Affordable Health Care for America Act, as a (logistic) function of Obama vote in their district.
Davis (AL-7) and Kucinch (OH-10) are the big “errors” among the “Noe” votes; Kucinch had been telegraphing his opposition to a too meek reform bill for some time. Davis is the same boat (“is this the best we can do?“).
Marion Berry (AR-1) is the biggest “error” among the “Aye” votes; he voted yes while representing an Arkansas district where McCain got 59% of the vote and Obama just 38% (but, perhaps reflecting much about that part of Arkansas, he was unopposed in the 2008 Congressional elections) and he seems to have long history of being in the forefront of Democratic reform efforts on health care.
Update: a nice take on the Dems voting Noe from the NYTimes.
I did a little work on the Coburn amendment rollcall. The vanilla spatial voting model fits the roll call reasonably well; I use all 341 roll calls cast by the 111th U.S. Senate (at least as of this morning when I ran the analysis) to estimate the ideal points, and then look at the fit to the roll call on the Coburn amendment.
The graph (thumbnail below) summarizes the fit, with the curve tracing out the predicted probabilities as a function of estimated ideal point (these come a simple probit regression of the actual votes on the ideal points). The estimated cutpoint — the point where a legislator is indifferent, on average — is between the ideal points of Voinovich (R OH) and Murkowski (R AK).
The “surprises” (or deviations from “pure” spatial voting) are show on the graph:
Snowe (R ME) and Collins (R ME) are to the left of the cutpoint and voted in accordance with the model prediction.
Bayh is up for re-election in 2010, as is Voinovich; for what it is worth, both are in Midwestern states. The splits in the MO and NE delegations are interesting.
In the spirit of trying to explain “errors” here, I’m wondering if any of our political science colleagues engaged in lobbying (seriously). For instance, did the Vandy people email Lamar Alexander? Did the UT/UH/Rice/Texas A&M people contact Cornyn’s office? And a lot of Federal research money finds it way to North Carolina, too (e.g., SAS, RTI, UNC & Duke, etc); Burr (R-NC) voted against the amendment, with an ideal point a long way to the right of the estimated cutpoint. Of course, it would also be interesting to consider cases where lobbying might have failed (McCaskill?).
Conversations with colleagues I was with yesterday (at the NSF!) had the more sensible take on this, probably to chalk it up to “position-taking”; with such a small amount of money at stake, the vote is largely symbolic (were that it were otherwise). That is, this is the kind of roll call that incumbents will add to their respective tallies in campaign statements to the effects of “I voted against waste and fraud n times…”
Some slides from a talk I gave at a conference sponsored by the American Political Science Association on “Democracy Audits and Governmental Indicators” at the University of California, Berkeley, October 30-31, 2009. The graphic below shows the estimates of country-level democracy for the year 2000 (with marginal 95% credible intervals) that Shawn Treier and I estimated using the Polity IV indicators (a better quality version appears in the slides).
Plus an early attempt at cross-national measurement of regime type (complete with uncertainty bounds), a nice parting gift from our host, Henry Brady.
I’m speaking at a conference at Berkeley sponsored by the American Political Science Association on “Democracy Audits and Governmental Indicators”. In getting some remarks together — on the the reliability of country-level measures of democracy etc — I wanted to compare the performance of measures of democracy against things like GRE scores, legislative ideal points.
ETS has a background document providing some technical data on GRE scores. The standard deviation of GRE-V scores issued in the 2003-08 period is 121 points, while the GRE-Q scores have a standard deviation of over 150 points. The standard errors of measurement are pretty small, relative to this cross-subject variation in the scores, and surprisingly uniform over the range of scores.
Usually you get a U-shape relationship between standard errors of measurement (or — if you are a Bayesian — standard deviations of marginal posterior densities of latent scores) and the scores; we have greater uncertainty about test subjects in the tails of the ability distribution, since the test items tend to be less informative about those subjects (as they rack up a lop-sided pattern of right/wrong answers).
The administered-by-computer, adaptive, version of the GREs helps smooth out that U-shape, with the computer administering items that have “cut-points” close to the running estimate of the subject’s ability.
To look at this I plotted the “conditional standard errors of measurement” for the GREs (as reported by the ETS) against scores; see below.
There is something of an inverted U, which is weird. We’re actually getting less precision in the middle of the scales than in the tails. The other thing is that we’ve got standard errors of measurement that are about 20%-35% of the between-subject score variation, which tails away to about 5-15% in the upper tails.
I wish those standard errors of measurement were smaller, and that is really only a function of the length of the test, given that ETS has near-perfect knowledge of the item parameters. So, does the GRE need to be longer?
Into Bayes? Into music? Into wicked coding? Want to live in France for a couple of years? Read on below the fold. (more…)
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