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).

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 graphic design friends in Sydney suggested Meta to me a while ago. I was looking for something that would distinguish my papers from the lovely but ubiquitous Computer Modern, that wasn’t Times + mtimes etc (which I’ve come to appreciate more and more, btw, perhaps since my book was set in Times etc), something that was “modern” but not so starkly sans-serif as to degrade readability.

I was originally playing with Gill Sans, which does have a Greek character set. But (a) graphic designer friends thought it a bit lame; (b) it is lovely for signage (“Signs on the wall identify this as Euston in a tasteful sans-serif that screams official credibility” wrote Neal Stephenson in Cryptonomicon), but not great in gobs and gobs of text. Students would also complain about its starkness in lecture slides: upper-case “I” is what, exactly (lower-case el, the numeral one, a vertical bar, or upper-case eye…).

So FFMeta seemed like a good solution: a hint of a serif, works well at different sizes. If I were to do it again, I’d think also about Whitney by Tobias Frere-Jones, or the Futura-ish look of Verlag. National looks like a lovely typeface as well, a Grotesk-ish sans that could work for both headers and text (then again, I have days when I think everything should be in Didot.

The downside was that Meta didn’t come with an extended set of “expert” glyphs or Greek characters (at least none that I could find). So I use Gill Sans Greek (actually Monotype GillSansDualGreekMT) for my Greek characters (except lower case \alpha and \chi, which I never liked the look of in Gill Sans Greek, substituting the Euler \alpha that ships with most tex distributions). I use as many symbols from Meta as I can, to keep the look and kerning standard (e.g., \neq, \leq, \infty, \pm \times) , but with default is to fall back on Computer Modern for symbols (e.g., \partial, \int, \forall). I never got this perfect, but its good enough.

When you get new typefaces, they often come as AFM files (Adobe Font Metrics) or TTF (TrueType). [Update: or OTF these days]. I got 24 AFM files when I purchased FFMeta. To use them in LaTeX you have to convert all of them (or the ones you want to use) to TFM (TeX font metrics), and specify an encoding (e.g., 8r, the TeX Base 1 Encoding); use the afm2tfm utility that comes with your tex distribution (part of the dvips side of things). The “-v” option will produce a VPL (virtual property list) so you can create “virtual fonts”. It has been a while since I’ve done this, and you can also use afm2pl utility to convert the AFM file to the a “property list” PL file, then pltotf to get the TFM files, and vpl2vpl and vptovf to get the VPL.

All that is complicated. fontinst attempts to automate the process. I’ve never used it, and I end up writing scripts like this. You probably want to look at Fontforge too.

LaTeX needs font definition files, which tell LaTeX which TFM file it should use when it encounters things like \emph{} and \bold{} or \textsc{} etc; here is mine, for my FFMeta setup. pdfLaTeX/dvips also need a map file, telling them how to map from TFMs to actual fonts to be included in the Postscript or PDF file (pfb files); here is my meta.map file (which won’t display properly in a browser window).

You need to keep your wits about you with naming schemes for fonts (TeX is unforgiving about this), where you put all these files when you are done, and finally (a) making TeX aware that you have new fonts to use, and (b) writing a .sty file that gives you access to the new fonts from inside your LaTeX document. It is inside that .sty file (in my case, meta.sty) that I have all the other hacks that define other characters and things. Put it all together and you get this (made from this).

Resources: this page is pretty good if you are in the Mac world. I also learned a lot from TeX Unbound by Alan Hoenig, but that book could be out of date by now, I don’t know.

Update: see comment #1. Forget all the scripting and carry-on above. Go use xelatex. Its only 5 years old (where have I been?!), and it certainly takes the pain out of switching fonts…

As per comment #1: use it with Will Roberston’s fontspec and unicode-math. Stop before 4am in the morning…your family will thank you.

Good Lord how did I miss this?

Update: and yet another graphical rendering (click on the thumbnail for the PDF).

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.

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:

• 5 Democrats voting for the amendment: Baucus, Webb, McCaskill, Bayh, Nelson.
• 7 Republicans voting against the amendment: Bond, Alexander, Cochran, Gregg, Johanns, Cornyn, Burr.
• Voinovich (R OH) is predicted to vote against the amendment (ideal point lies to the left of the cutpoint), but voted Yea.

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…”

Light chop for much of the way after Denver, some mountain wave was coming off the Rockies as well.

Flying the Modesto 3 STAR, we entered a hold at CEDES along with a whole bunch of other aircraft, since SFO couldn’t do parallel ops on the 28s. Ch9 was up, and I was dismayed to hear that we could be out here for 30mins (I’m drafting this while we’re in the hold). We got a clearance pretty shortly after that, probably only 8 mins in the hold all up; a jink to the south-west, thence MEHTA and final approach up the Bay.

On final we were requested to go as slow as possible, which our pilots reported as 140 KTS. Landed on 28R.

Flightaware track, zoomed in on the hold and approach.

Ironically, I am at NSF and can’t do an analysis of the vote from behind the firewall etc (blogging my iPhone right now).

Not today. I took the late flight, 3.50pm departure. A morning of work in Palo Alto, ran a seminar at Stanford at noon, lunch with a colleague, then 2pm ride to airport. Got the upgrade, seat 2D on a 757. Seatguru is right about the equipment box under the seat in front, but its not a deal-breaker. Takeoff from 28R and a sharp right back onto the usual east-bound departure route over the Bay, Oakland (the SFO8 DP, with a 110 degree turn from the runway heading to 030, and I was on the right-hand side of the plane).

Lovely late afternoon views of the Sierra, with some snow cover starting to appear, Half Dome marking Yosemite Valley about two valleys to our south.

There is no in-seat power in the United 757s (hasn’t been for ages, at least in the 757s I’ve been getting out of SFO), and no channel 9 on this flight. The pilots did pipe through WFAN coverage of the last game of the World Series once we got, say, about an hour from Dulles, on ch9. Uneventful approach and landing, rolled out, no reverse thrust.

It lives.