Andrew Gelman will have a second blog. I don't yet understand the forthcoming principle of individuation across the two blogs.

So, how does the content differ? My plan was--is--for the Science Blog to be optional and a portal on to this main blog. Thus, I'll post links here to the Science Blogs content so you can click over and take a look at it if you'd like. I don't really have any plans to separate content, except of course that I won't be putting the technical statistical stuff over there.

I might just start crossposting everything there on to here--that's what I do when I post on New Majority, 538, and the Monkey Cage--but for now I'll try to have some material that's only over there. It seems only fair, since they gave me a blog there, that I post some unique content.

I'm still not sure if this new blog makes sense. New Majority is fine--I sent them material on occasion and they decide whether to post it--and 538 is great--again, most of my stuff doesn't really fit there, but every week or so I have something that's highly relevant to current political events, and then I post there. The Monkey Cage is no big deal because I can crosspost for them whenever--the blog has its own existence without needing too much from me. But this new blog . . . well, we'll see how it goes. It's a bid to spread the statistical gospel to a wider audience.

A new study found that rates of marriage outside the faith were sharply curbed among young Jews who have taken "birthright" trips to Israel . . . Over the past decade, Taglit-Birthright Israel, a U.S. nonprofit founded by Jewish businessmen, has sponsored nearly 225,000 young Jewish adults for free 10-day educational tours of Israel as a way to foster Jewish identity. . . .

A study [by Brandeis University researcher Leonard Saxe and partly funded by Taglit-Birthright] showed that 72% of those who went on the trip married within the faith, compared with 46% of people who applied for the trip but weren't selected in a lottery. . . . The Brandeis study looked at 1,500 non-Orthodox Jewish adults who took Taglit trips or applied for one between 2001 and 2004. . . . The Brandeis study looked at 1,500 non-Orthodox Jewish adults who took Taglit trips or applied for one between 2001 and 2004.

The article also said that 10,000 people participated in these trips last summer, which suggests that the 1,500 people in the research study represent a very small fraction of the participants from 2001-2004. I have no idea if this is a random sample, or what. Also I wonder about the people who participated in the lottery, were selected, but didn't go on the trip. Excluding these people (if there are many of them) could bias the results. The news article unfortunately doesn't link to any research report.

Most estimates of America's Jewish population place it a little higher than six million, although some demographers have argued it is higher. The U.S. census doesn't track people by faith.

I've seen estimates that are closer to 5 million. More to the point, I don't think that "tracking people by faith" is the right way to think about it. For this sort of counting exercise, Judaism is as much of an ethnicity or a nationality than a "faith." For example:

Taglit's founders and funders include Charles Bronfman, heir to the Seagram liquor empire, and Michael Steinhardt, a former hedge-fund manager. . . . Mr. Steinhardt, who describes himself as an atheist, has said he supports Taglit because he wants to pass along Judaism's humanistic values.

I am returning Assembly Bill 1176 without my signature.

For some time now I have lamented the fact that major issues are overlooked while many
unnecessary bills come to me for consideration. Water reform, prison reform, and health
care are major issues my Administration has brought to the table, but the Legislature just
kicks the can down the alley.

Yet another legislative year has come and gone without the major reforms Californians
overwhelmingly deserve. In light of this, and after careful consideration, I believe it is
unnecessary to sign this measure at this time.

Philp concludes:

The null hypothesis for testing "coincidences" matters. In this example, it is easy to get a wide spectrum of values for the "probability" of a coincidence. In the six calculations here, the probability ranges from about one in a couple of thousand to one in 487 billion: a factor of nearly 200 million--more than 8 orders of magnitude. News consumers should be wary of calculations of the "chance" of a coincidence, regardless of the context.

Amusing--but I don't think the 1 in 2520 model makes a lot of sense! As Philip writes, "a better 'null model; would pull full sentences at random from Governor Schwartzenegger's other vetoes, string them together, and see where the linebreaks fell." I expect the model of random words from the Gutenburg corpus would come pretty close to that. Then you have to multiply by some factor to correct for multiplicity, but considering you're starting with a probability of about 1 in a trillion, it seems unlikely that any correction for multiplicity could make this sort of thing very likely.

A good classroom or homework example, in any case.

I write to you with a question about the construction of informative priors in Bayesian analysis. Since most Bayesians at the statistics department here are more of the 'Objective' Bayes persuasion, I wanted some outside opinions as well.

My question is therefore the following: why is there so little literature on systematically combining existing results from earlier studies (to obtain priors, or more generally as a meta-analysis)? I did quite extensive searches so it seems unlikely that it is there and I just missed it. It also doesn't seem like a trivial problem to me. Even if the informed consensus is that it is for some reason not worth the effort, I still would expected to find some papers on the subject. Consequently I am thoroughly puzzled as to why I can't find anything, what I am overlooking.

My reply: I know what you mean. For our 1996 article, Frederic Bois and I constructed prior distributions based on the medical literature, but as you put it, we did it in an ad hoc way. My main advice on this point is that a good parameterization can help: if the parameters mean something, and if their meaning transfers well across people, they it's a more reasonable task to try to put together a prior distribution.

More generally, yes, there is a literature on meta-analysis--we even have a couple examples in Bayesian Data Analysis. The general idea, as formulated by Rubin and others a few decades ago, is to set up a group-level regression model. I don't think that there's any consensus that it's "not worth the effort" (as you put it). Maybe you're not looking in the right places.

Logistic regression does not have a direct equivalent to the R2 that is found in ordinary least squares (OLS) regression that represents the proportion of variance explained by the predictors. However, it is possible to use an analog, so-called a pseudo-R2, to mimic the OLS-R2 in evaluating the goodness-of-fit and the variability explained, which is the approach we used (ref 14). Using this approach we estimated that rs12979860 could account for 58% of the ethnicity-explained variability by estimating the difference between the expected variability if the IL28B SNP does not account for the variability explained by ethnicity at all, and the observed variability explained by both ethnicity and rs12979860.

While these details are somewhat vague, I trust that you will join me in finding this very suspicious.

The pseudo-R2 simply compares the log-likelihood from the null model (only an intercept) to the log-likelihood from the full model (all covariates included). I would call neither the R2 nor the pseudo-R2 a measure of "goodness of fit", but at least the R2 in a linear model does mean something straightforward. The pseudo-R2 in a logistic model, however, seems to me to have no straightforward interpretation at all, and I was under the impression that no serious statistician uses this statistic.

The authors wrote that they used this statistic to ascertain that the exposure (allele) "could account for 58% of the ethnicity-explained variability" and yet the pseudo-R2 does not measure variability at all. They claim to have come up with the 58% number by "by estimating the difference between the expected variability if the IL28B SNP does not account for the variability explained by ethnicity at all, and the observed variability explained by both ethnicity and rs12979860." I am not sure I quite follow that, but it sounds like they are computing the pseudo-R2 statistic twice, once for a model that contains ethnicity and the allele of interest, and once for the model that contains only ethnicity. Perhaps one of these numbers that results is 58% as big as the other, or something like that. If this is indeed what they did, I see no logical connection between this analysis and their claim that 58% of the ethnic disparity is due to the differential distribution of the allele. I have to assume that Nature has careful statistical review, but this doesn't make a lot of sense to me, based on what I can glean from this description.

My reply: I've never used pseudo-R-squared myself, but I can't speak for the general population of "serious statisticians" here. I know that a lot of statisticians don't like regular R-squared, but I find it helpful sometimes (see graphs on page 42 of ARM) and even wrote a research article (with Iain Pardoe) on the topic. So I'd be wary about slamming pseudo-R-squared in general terms.

I also don't know enough about genetics to try to interpret the 58%. But, yes, my guess is that this difference isn't really 58% of something. Maybe it makes sense as some approximation, though. My recommendation in this sort of situation is to forget about log-likelihoods and R-squares and just attack the comparison more directly, perhaps through an ROC curve or some similar approach.

Hello, my name is Lauren Schmidt, and I recently graduated from the Brain & Cognitive Sciences graduate program at MIT, where I spent a lot of time doing online research using human subjects. I also spent a lot of time being frustrated with the limitations of various existing online research tools. So now I am co-founding a start-up, HeadLamp Research, with the goal of making online experimental design and data collection as fast, easy, powerful, and painless as can be. But we need your help to come up with an online research tool that is as useful as possible!

We have a short survey (5-10 min) on your research practices and needs, and we would really appreciate your input if you are interested in online data collection.

I imagine they're planning to make money off this start-up and so I think it would be only fair if they pay their survey participants. Perhaps they can give them a share of the profits, if any exist?

1.a. If my likely use of Bayesian stats is econometrics, do you think it'd be good to use an "Intro to Bayesian Econometrics" textbook (like Lancaster's) or a general introduction textbook like your "Bayesian Data Analysis."

1.b. If you think the latter (and I'm inclined to think a general introduction would be better) would you recommend supplementing your textbook with any other book, perhaps one on BUGS, or another general textbook? I'm not trying to put you in the difficult spot here of either listing the shortcomings of the textbook or sounding over-confident. My question really comes from the fact that I won't have a teacher to bolster my understanding.

2. You've mentioned a few times that "to do statistical research [now]... you have to be a computer programmer." Are there any programming languages I could supplement my "course" with to better prepare me?

3. As a side note, I recently read your older review of Axelrod and the misapplication of the "prisoner's dilemma" model. Is it a coincidence that such a critique came from a Bayesian? It seems indeed that thinking hard about the model with which one is working, and said model's applicability to the subject, is one of the great strengths of applied Bayesianism.

My reply:

1. I like Tony Lancaster's book, and, of course, I like my own. I think either book would be fine, if your advisor is comfortable with it. If you want stuff on Bugs, I'd recommend looking into my book with Hill.

2. R or Matlab for statistics, But Stata is what's popular in economics. And then of course there are C and Python. I think the best way to learn a language is to have to learn it; that is, to have a problem that you need to program to solve. Fortunately (or unfortunately), there are a lot of problems like that. Just about any applied statistics problem requires programming if you want to do it right.

3. I did the prisoner's dilemma stuff as a senior in college, before I knew much about Bayesian statistics. I certainly didn't perceive any connection at the time. (And, back then, people dind't casually throw around the term "Bayesian" as a synonym for "rationality" the way they do today.) But perhaps the same seriousness-about-models that inspired me to criticize Axelrod also made me sympathetic to Donald Rubin's approach to Bayesian statistics.

Culture wars, voting and polarization: divisions and unities in modern American politics

On the night of the 2000 presidential election, Americans sat riveted in front of their televisions as polling results divided the nation's map into red and blue states. Since then the color divide has become a symbol of a culture war that thrives on stereotypes--pickup-driving red-state Republicans who vote based on God, guns, and gays; and elitist, latte-sipping blue-state Democrats who are woefully out of touch with heartland values. But how does this fit into other ideas about America being divided between the haves and the have-nots? Is political polarization real, or is the real concern the perception of polarization?

This work is joint with David Park, Boris Shor, Joseph Bafumi, Jeronimo Cortina, and Delia Baldassarri.

(Here's a video version of the talk, from when I gave it at Google.)

I'll be interested to see if people can explain to me the relevance (or lack thereof) of this work to politics in Britain and other countries.

P.S. I'm speaking at LSE on Monday also (on a different topic).

P.P.S. I'll be speaking again a couple times in London later in the academic year, but on other topics. All my talks there will be different.