February 2009 Archives

I feel I have to respond to this item that people keep pointing me to:

John Antonakis and Olaf Dalgas presented photos of pairs of competing candidates in the 2002 French parliamentary elections to hundreds of Swiss undergrads, who had no idea who the politicians were. The students were asked to indicate which candidate in each pair was the most competent, and for about 70 per cent of the pairs, the candidate rated as looking most competent was the candidate who had actually won the election. The startling implication is that the real-life voters must also have based their choice of candidate on looks, at least in part. [emphasis added]

Nooooooooooooooooooooooooooooooooooo!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

This came up a couple of years ago, when, in response to a similar study, I wrote:

It's a funny result: at first it seems impressive--70% accuracy!--but then again it's not so impressive given that you can predict something on the order of 90% of races just based on incumbency and the partisan preferences of the voters in the states and districts [at least in the U.S.; I don't know about France]. If 90% of the races are essentially decided a year ahead of time, what does it mean to say that voters are choosing 70% correct based on the candidates' looks.

I can't be sure what's happening here, but one possibility is that the more serious candidates (the ones we know are going to win anyway) are more attractive. Maybe you have some goofy-looking people who decide to run in districts where they don't have a chance, whereas the politicians who really have a shot at being in congress take the time to get their hair cut, etc.

Anyway, the point of this note is just that some skepticism is in order. It's fun to find some scientific finding that seems to show the shallowness of voters, but watch out! I guess it pleases the cognitive scientists to think that something as important and seemingly complicated as voting is just some simple first-impression process. Just as, at the next level, it pleases biologists to think that something as important and seemingly complicated as psychology is just some simple selfish-gene thing.

And see here for a discussion of some research by Atkinson, Enos, and HIll on this topic.

Just one more thing

From the news article:

"These findings suggest that voters are not appropriately weighting performance-based information on political candidates when undertaking one of democracy's most important civic duties," the researchers said.

No, no, no. Unless you want to take a very weak interpretation of "suggest." Or, to put it another way, sure, I have no doubt that "voters are not appropriately weighting performance-based information on political candidates"--but I don't see the personal appearance study as relevant to even close to definitive on this point.

I'm as cynical as the next guy, but this sort of thing is going a step too far, even for me.

More pretty graphs from the 2008 Pew surveys, interspersed with discussion and concluding with the line, "One thing sophistication can give you is an appreciation for the simple things in life."

Below is one of the graphs; click on the link above for more.

I received the following email:

As a psychologist teaching and using Bayesian statistics, I've been pleased to see some of my colleagues endorsing Bayesian data analysis. But I've been very chagrined to see them champion Bayes factors for null-hypothesis testing, instead of parameter estimation. My question is simple: Are there any articles that head-on challenge the Bayes-factor approach to null-hypothesis testing, and instead favor parameter estimation?

Perhaps the most straight-forward example against Bayes factors for null hypotheses was given by Stone (1997), Statistics and Computing, 7, 263-264. He showed a simple case in which the BF prefers the null but the estimated posterior excludes the null value. I realize that the two approaches are asking different questions --- I've just never really been convinced that the answer provided by a null/alternative comparison really tells us anything we want to know, because no matter what it says, I always want to do the estimation anyway.

My reply: You won't be surprised that I agree with the above perspective. Here's my article with Rubin (from Sociological Methodology 1995) where we bang on Bayes factors for 8 straight pages. I really like this article.

Image via Wikipedia

Here is a chart by Johannes Ruf (using a bibliography prepared by Bernhard Ganglmair), listing a number of papers that list the value of life as estimated by such trade-offs:

So, allowing some tolerance for inflation and deflation, and taking the average of all of the above, we arrive to about 4 million dollars. If we assume that the average life expectancy is 78 years, and that half of the day is waking time, the value comes down to about $12 for a waking hour of life - arbitrary, but the right order of magnitude. Additional complexity can be entered into this model to improve it.

I will now address what we can do with these numbers.

Bilmes and Stiglitz estimate cost of the Iraq war to 3 trillion, while the US military casualties currently number 4250. So, the cost of lives lost is 17 billion, but the economic cost borne by the United States is 3 trillion. What is the true cost of the Iraq war in human lives? 3 trillion divided by 4.2 million comes down to over 720,000 lives. This is the true casualty count, which accounts for people having to work on stuff that explodes instead of spending time with their families. On the Iraqi side, there were about 100,000 civilian lives lost, but it's hard to estimate the full cost of war to Iraq - the Lancet study claims numbers considerably larger than this.

Andrew Gelman has also written about this - when is one's risk of radon to health sufficient to justify the cost of measurement or remediation. I'd again like to acknowledge Johannes and Bernhard's help with the research, but all flaws are solely my own. The difficulties of estimation shouldn't stop us from studying the problem - maybe better awareness of this will help save a million lives in the future.

I received the following email:

I am working on a paper for a political course which I must discuss "a what if" Pennsylvania transformed into a state of rationality. Everything is the same except that all the citizens, all the candidates for state office, all the state legislators, and all the lobbyists in the state behave rationally in a economic sense. Of these groups, which one is most likely to be the most politically powerful.

I am not sure how to exactly get started and thought I would see if you might have any suggestions or thoughts on the subject.

Sounds like a good assignment to me. I only teach statistics and methods courses, so I never think about this sort of interesting political-science homework problem.

In honor of Darwin's 200th birthday, some research by psychologist Laura Novick on the presentation of evolutionary trees ("cladograms"):

Her research shows that students are much better at understanding the diagram on the left than the one on the right. She calls the one on the left a "tree" and the one on the right a "ladder," which confuses me a bit: the one on the right looks more like tree branches to me.

Tyler Cowen links to this report that "economists comprised only 6 percent of guest appearances discussing stimulus on cable news, Sunday shows."

That sounds pretty good to me! I can't imagine that political scientists make up anything close to 6% of the TV commenters on political topics. I doubt it's 0.6%. My recommendation to economists: quit complaining and treasure the 6% you have!

Related: Why are there so few economists in elected office?:

There were 139,000 economists employed in the United States, which reprsented 0.1% of the employed population. 1% of 535 is about 1/2, so with at least two economists in Congress, the profession is hardly unrepresented. . . . even throwing in economics professors and various other practicing economists, I still don't think it would add up to the half-million that would be necessary to reach 2/535 of the employed population. . . . perhaps Congress would indeed be better if it included more economists--but rather to note that people with this sort of job are a small minority in the U.S. (In contrast, there were 720,000 physicians, 170,000 dentists, and 2.1 million nurses, and 1.7 million health technicans in the U.S.)

To put it another way, without reference to economists (or to the 2.1 million "mathematical and computer scientists" out there): the Statistical Abstract has 260,000 psychologists. Certainly Congress would be better off with a few psychologists, who might understand how citizens might be expected to react to various policies. . . . and what about the 114,000 biologists? A few of these in Congress might advance the understanding of public health. And then there are the 290,000 civil engineers--I'd like to have a few of them around also. I'd also like some of the 280,000 child care workers and 620,000 pre-K and kindegarten teachers to give their insight on deliberations on family policy. And the 1.1 million police officers and 340,000 prison guards will have their own perspectives on justice issues. . . .

Seth points to this wonderful suggestion by Tim Hartford on "how to enjoy the thrill of the lottery without the fool's bet":

Choose your numbers, but don't buy a ticket. You'll win almost every week - the fear that your number might actually come up is an adrenaline rush to beat them all.

I love this. But now I want to return to Seth, who draws a connection to what scientists do. I don't quite agree with what Seth writes--I think he gets his argument tangled up--but it's interesting, so let me repeat it and then follow up with my own comments. Seth writes:

It is the average [lottery] consumer who is gullible and makes the whole thing work . . . Scientists are no less gullible. Self-experimentation, like Hartford's advice, takes advantage of that gullibility. Because scientists essentially play the lottery in their research -- devote considerable resources (their careers) to looking for discoveries in one specific way (scientists are hemmed in by many rules, which also slow them down) -- this leaves a great deal to be discovered by research that doesn't cost a lot and can be done quickly. All of my interesting self-experimental discoveries have involved treatments that conventional scientists couldn't study because their research has to be expensive. Could a conventional scientist study the effect of seeing faces in the morning? No, because you couldn't get funding. And all research must require funding. (Research without funding is low status.) In practice, this means you can't take risks and you can't do very much. Like the lottery, this is a poor bet.

Let me untangle this. Seth is saying that the typical scientist is like a lottery player whereas, by doing self-experimentation, Seth is more like Tim Hartford's reverse lottery player, going for the near-sure thing rather than investing time in the hope of a hypothetical breakthrough.

It's funny that Seth says this, because I've always told him the opposite: conventional scientists such as myself are the plodders, squeezing out little research results each year, publishing in journals and getting grants, whereas Seth has always seemed to me to be the gambler, stepping away from the near-sure thing of the scientific treadmill and risking something like 10 years of his life on self-experimentation--it was about 10 years after he began that he started to get useful results. I've always admired Seth for his gamble.

Right now I can see that Seth views self-experimentation as a grind-it-out way to make discovery after discovery, but 20 years ago, not so much. Conversely, I don't think of conventional scientists as staking their careers on the chance of making a single big discovery. Rather, we make no risks at all! To paraphrase Paul Erdos, a scientist is a machine for turning hard work into little bits of publishable research.

P.S. I don't buy Seth's claim that "research without funding is low status." My impression is that people seek funding because they feel their research is important and they want help getting it done faster. I don't see that status has anything to do with it.

Chris Masse pointed me to this blog by Panos Ipeirotis, who argues that some online prediction markets give probabilities that are too good to be true:

What happened in 2008? Exit polls were made available immediately--as of election night. The next step is to go to individual-level data, which we recently obtained from the Pew Research Center's pre-election polls.

Here's the income and voting pattern at the national level: Republicans did better among upper-income voters--except possibly for the over-200,000's. (The highest income category from the Pew surveys is "$150,000+", so we can't do a direct comparison at the top.)

Red and blue states

Now let's look at red, blue, and purple states (which we define, following our book, as those states where George W. Bush won by more than 10 points in both his campaigns, those where he lost by more than 10 points both time, and the states in between): As in previous elections, income predicts Republican vote more strongly in red than in blue states. (For this and following graphs, I'm switching the x-axis from numerical incomes to income categories.)

Or, to put it another way, the red-state/blue-state divide is happening among the rich (actually, the upper middle class, since surveys don't tell us much about the truly rich) more than the poor.

Andy Sutter writes:

It's been a while (~2 years?) since I was last reading your blog semi-regularly and submitted a comment or two, but I was reading something today that made me recall those days.

At the time, I was curious about why social scientists present data as charts of regression coefficients, since I'd never seen such a presentation in the physical sciences.

On the front page of Suday's New York Times, the primest of prime real estate, Hiroko Tabuchi writes:

As recession-wary Americans adapt to a new frugality, Japan offers a peek at how thrift can take lasting hold of a consumer society, to disastrous effect. . . . Today, years after the recovery, even well-off Japanese households use old bath water to do laundry, a popular way to save on utility bills. Sales of whiskey, the favorite drink among moneyed Tokyoites in the booming '80s, have fallen to a fifth of their peak. And the nation is losing interest in cars; sales have fallen by half since 1990.

How is this "disastrous"? Using bath water to do laundry makes sense to me. Unfortunately our apartment is not set up to do this, but why not? Cars are much better made than they used to be, probably most people in Japan who want a car badly enough have one already, so it makes sense that car sales would fall--people can continue driving their dependable old cars. Finally, I have nothing against whiskey, but is it really "disastrous" that sales have fallen to a fifth of their peak? Fads and all that.

Sure, I can see that this is all evidence that Japan's economy is far from booming, but I'm a bit disturbed to see frugality treated as a "disaster" in itself.

What really bothers me, though, is that the assumptions in the article are completely unstated. I'd be happier if the reporter had written something like this:

You might think that it's a good thing that the Japanese have become more energy-efficient and less into trendy conspicuous consumption: even well-off Japanese households use old bath water to do laundry, a popular way to save on utility bills, and sales of whiskey, the favorite drink among moneyed Tokyoites in the booming '80s, have fallen to a fifth of their peak.

Even the notorious Japanese tendency to buy new cars and appliances every two years, whether they need it or not, has abated. The nation is losing interest in cars--sales have fallen by half since 1990--and people are sticking with old-fashioned television sets rather than snapping up expensive flat-screen TVs.

But this frugal behavior is having a disastrous effect [or, is symptomatic of an underlying economic disaster]. . . .

This puts the assumptions front and center, at which point they could quote experts on both sides of the issue or whatever.

P.S. Just to be clear: my point here is not that a newspaper reporter wrote something I might disagree with, but rather that sometimes people seem trapped within their unstated assumptions. (Yes, I'm sure that happens to me too.)

Image by jurvetson via Flickr

Thus, a master's degree actually hurts performance, and seniority was irrelevant as a factor. But master's degree and seniority are the only two factors that will increase a teacher's pay.

Now, Gates is pushing a lot for gathering and analyzing data. So there might be opportunities for those interested in doing research in education to get grants from the Gates foundation.

Helen DeWitt, commenting on about friends/colleagues/acquaintances who ask her for reference letters, writes of "a mythical entity: a reference that can just be dashed off in half an hour and popped in the post / fired off in an e-mail. There is no such thing."

Jenny Davidson follows up with:

I [Jenny] do not know why someone thinks that it is possible to write a good letter of recommendation without a HUGE amount of supplementary paperwork . . .

What's my experience? I get asked for a fair number of letters of recommendation or evaluation, and I take about 15 minutes to write such a letter and email it off (to someone who prints it on letterhead paper and mails it). From the remarks above, I suspect that it's considered a norm to spend more time than that, but I think it's a bit of an arms race: your letter has to be long so it can compete with other people's letters. So by writing short letters, I'm doing my part to make the process more sane. There's a well-known statistician who always writes letters for his students saying essentially that they're the second coming of Cauchy; he's recognized for doing this. As long as people have the expectation that my letters will be short, everything should work out fine.

Yair showed me this. It's simply amazing. Click on the link RIGHT AWAY and be awed. Great examples and all the code you'll ever need.

Los Angeles Tar Yields Mammoth's Skeleton

I'm working on a project involving the evaluation of social service innovations, and the other day one of my colleagues remarked that in many cases, we really know what works, the issue is getting it done. This reminded me of a fascinating article by Atul Gawande on the use of checklists for medical treatments, which in turn made me think about two different paradigms for improving a system, whether it be health, education, services, or whatever.

The first paradigm--the one we're taught in statistics classes--is of progress via "interventions" or "treatments." The story is that people come up with ideas (perhaps from fundamental science, as we non-biologists imagine is happening in medical research, or maybe from exploratory analysis of existing data, or maybe just from somebody's brilliant insight), and then these get studied (possibly through randomized clinical trials, but that's not really my point here; my real focus is on the concept of the discrete "intervention"), and then some ideas are revealed to be successful and some are not (with allowances taken for multiple testing or hierarchical structure in the studies), and the successful ideas get dispersed and used widely. There's then a secondary phase in which interventions can get tested and modified in the wild.

The second paradigm, alluded to by my colleague above, is that of the checklist. Here the story is that everyone knows what works, but for logistical or other reasons, not all these things always get done. Improvement occurs when people are required (or encouraged or bribed or whatever) to do the 10 or 12 things that, together, are known to improve effectiveness. This "checklist" paradigm seems much different than the "intervention" approach that is standard in statistics and econometrics.

The two paradigms are not mutually exclusive. For example, the items on a checklist might have had their effectiveness individually demonstrated via earlier clinical trials--in fact, maybe that's what got them on the checklist in the first place. Conversely, the procedure of "following a checklist" can itself be seen as an intervention and be evaluated as such.

And there are other paradigms out there, such as the self-experimentation paradigm (in which the generation and testing of new ideas go together) and the "marketplace of ideas" paradigm (in which more efficient systems are believed to evolve and survive through competitive pressures).

I just think it's interesting that the intervention paradigm, which is so central to our thinking in statistics and econometrics (not to mention NIH funding), is not the only way to think about process improvement. A point that is obvious to nonstatisticians, perhaps.

This 2006 article by Alan Abramowitz, Brad Alexander, and Matthew Gunning finds, consistent with our earlier research, that declining competitiveness in U.S. House elections cannot be explained by gerrymandering:

Competition in U.S. House elections has been declining for more than 50 years and, based on both incumbent reelection rates and the percentage of close races, the 2002 and 2004 House elections were the least competitive of the postwar era. This article tests three hypotheses that attempt to explain declining competition in House elections: the redistricting hypothesis, the partisan polarization hypothesis, and the incumbency hypothesis.We find strong support for both the partisan polarization hypothesis and the incumbency hypothesis but no support for the redistricting hypothesis. Since the 1970s there has been a substantial increase in the number of House districts that are safe for one party and a substantial decrease in the number of marginal districts. However, this shift has not been caused by redistricting but by demographic change and ideological realignment within the electorate. Moreover, even in the remaining marginal districts most challengers lack the financial resources needed to wage competitive campaigns. The increasing correlation among district partisanship, incumbency, and campaign spending means that the effects of these three variables tend to reinforce each other to a greater extent than in the past. The result is a pattern of reinforcing advantages that leads to extraordinarily uncompetitive elections.

So that's the story. Don't blame gerrymandering.

P.S. They didn't cite our 1991 AJPS article! A regrettable oversight, I'm sure. . . .

Matthew Yglesias quotes Richard Cohen presenting a common misconception:

Reality is real. No amount of lofty rhetoric is going to change the way members of Congress are elected. Most of them come from exquisitely gerrymandered districts created by computers that could, if good taste allowed, part the marital bed, separating husband from wife if they were of different political parties. This system created districts that are frequently reliably liberal or conservative. The computer has deleted the middle.

I can't disagree with Cohen's first sentence above, but I part company with him after that.

From Jessica, I saw a review by "Econjeff" of my review of Joshua Angrist and Jorn-Steffen Pischke's new book, "Mostly Harmless Econometrics: An Empiricist's Companion."

Econjeff pretty much agrees with what I wrote, but with one comment:

I [Econjeff] am a bit surprised by Gelman's call for more on hierarchical models; I think economists are right to treat these as a combination of useful pedagogical tool for education research design and an unnecessarily functional-form dependent way to get the standard errors right when then the unit of treatment differs from the units available in the data.

I think this is a common perception of multilevel (hierarchical) models among economists. Regular readers of this blog will not be surprised to hear that I disagree completely! The purpose of a multilevel model is not to "get the standard errors right" but rather to model structure in the data.

An analogy that might help here for economists is time series analysis. If you have data with time series structure and you ignore it, you can get over-optimistic standard errors. But that's not the main reason people do time series modeling. The main reason is that the time series structure is interesting and important in its own right. We are interested in individual and contextual effects and unexplained variation at the individual and group levels, just as we are interested in autocorrelation, periodicity, long-range dependence, and so forth.

See chapters 1 and 11 of ARM for more discussion of motivations for multilevel modeling.

James Morone writes in the New York Times:

[President Obama] seems eager to put aside small political differences and to restore a culture of cooperation in Washington. But it's going to be a long, hard effort because, well, that golden bipartisan era never existed.

The popular myth of getting past politics, in its modern form, dates back to the 1880s, when reformers known as Mugwumps challenged the corrupt bosses, powerful parties and political machines. . . . And while the Mugwumps eventually achieved a lot of their reforms, their larger aspiration -- nonpartisan politics -- always slipped out of reach.

Morone then gives some examples, but I don't think they make his case so well. For example, he wrotes:

Yet modern Mugwumps keep searching for a nonpartisan golden age to emulate. They point, for example, to the early years of the cold war when foreign policy consensus repudiated isolationism and engaged the world. That elite consensus never reached as far as Congress, where the House Un-American Activities Committee was hunting Joe McCarthy's slippery list of Reds and traitors.

But NATO passed with bipartisan support. Beyond this, the 1950s and early 1960s were a relatively nonpartisan era by many measures.

Later, Morone writes:

Ronald Reagan's fierce attachment to three verities -- markets are good, government is bad, communism is evil -- also meant little reaching out to the other side. His every move reverberated with the cold war philosophy he described so simply: "We win and they lose."

But when Reagan was president, the House of Representatives was controlled by the Democratic party. So his programs had to have some bipartisan support.

Summary

I'm not saying that partisanship doesn't work, or that Obama shouldn't be partisan---or, for that matter, that congressional Republicans should be less partisan themselves. I'm just pointing out that, in some of these historical examples purporting to show partisanship, the actual story isn't so simple.

"In Pain and Joy of Envy, the Brain May Play a Role"

May play a role??? I guess the jury is still out on whether the seat of envy is actually in the liver. . . .

This level of scientific illiteracy disturbs me. I'm not knocking the news article or the scientific study being described there, just the headline, which is in a class by itself.

Carl Bialik writes:

There hasn't been a single 7-3 finish in the NFL since the league adopted the two-point conversion rule in 1994 . . . "Football scores are funny," Driner wrote me [Bialik] in an email. "Did you know that teams win more often when they score 13 points than when they score 14? It's a cause-effect thing. In order to get 13, you (usually) need two field goals. And teams don't kick field goals if they're down by 20 points. So teams lose 35-14 more often than they lose 35-13. That's why scoring 13 is better correlated with winning than scoring 14 is.

And, most amazingly,

An NFL game hasn't finished with a score of 7-0 in over a quarter-century.

More boringly, the most common final score is 20-17.

I just received an email from "info@googlelotto.com" with subject line, "Your email just won £500,000 British Pounds in our anniversary promo." This email went into my inbox; it did not get caught by the spam filter.

What I wanna know is, if "Your email just won £500,000 British Pounds in our anniversary promo" isn't spam, what is???

Chris Masse writes:

The reality check is that the social utility of the prediction markets is marginal. The added accuracy is minute, and, anyway, doesn't fill up the gap betweeen expectations and omniscience (which is how people judge forecasters). In our view, the social utility of the prediction markets lays in efficiency, not in accuracy. In complicated situations, the prediction markets integrate facts and expertise much faster than the mass media do. It is their velocity that we should put to work.

Interesting. This relates to other technology-based ways of aggregating information, such as using cell phone traffic to track epidemics.

Jeff Jenkins writes:

Here's Lindley. I suspect I'd agree with Lindley on just about any issue of statistical theory and practice. I've read some of Lindley's old articles and contributions to discussions and, even when he seemed like something of an extremist at the time, in retrospect he always seems to be correct. That said, I disagree with him on Taleb. I think the difference is that Lindley was evaluating The Black Swan based on its statistical content, whereas I liked the book because it was full of ideas and stories that sparked thoughts in my mind (and, I think, in the minds of many readers).

Also, I disagree with Lindley 100% about Karl Popper. Even though, again, I think Lindley and I are extremely close on issues of statistical practice and theory.

And here's Robert. I like his connection of "black swans" to "model shift." This fits in well to my three stages of Bayesian Data Analysis (model building, model fitting, model checking), with model checking being the all-important but often neglected ugly sister. (As I've discussed many times, you rarely see graphical model checks in a published paper, because either (a) the model didn't fit, in which case, at worst you'd be too embarrassed to admit it, or at best you'd fix the model and there'd be nothing to report, of (b) the model fits ok, in which case the model check is probably only worth a sentence or two.)

From a philosophical point of view, I think the most important point of confusion about Bayesian inference is the idea that it's about computing the probability that a model is true. In all the areas I've ever worked on, the model is never true. But what you can do is find out that certain important aspects of the data are highly unlikely to be captured by the fitted model, which can facilitate a "model shift" moment. This sort of falsification is why I believe Popper's philosophy of science to be a good fit to Bayesian data analysis.

Also, I agree with Christian's characterization of Black-Scholes etc. as not "n accurate representation of reality, but rather a gentleman's agreement between traders that served to agree on prices." The way I put it was that these graduate programs in "financial mathematics / financial engineering" served a useful function by screening for students who were mathematically able and willing to work hard. It's too bad they couldn't have been learning statistics instead, but, for better or worse, competence in statistics is easier to fake than competence in math.

Christian also has an interesting conclusion:

Encouraging a total mistrust of anything scientific or academic is not helping in solving issues, but most surely pushes people in the arms of charlatans with ready answers.

I wonder what Taleb would say about this. Possibly he'd reply that it's better to have citizens to think critically than to be awed by their financial advisors.

In response to the comments here, I say:

I have never ever seen an example where I've felt a boxplot was appropriate. I'm open to being convinced, but I don't think you'll be able to convince me. Bring on the examples!

The earliest postwar suburbs are sixty years old. Ideas for what to do with them, from Ellen Dunham-Jones and June Williamson.

"Perpetually Statistically Curious" writes:

Say you have two variables, Y1 and Y2, whose correlation depends on the value of a third dichotomous variable, X. Now say you take the absolute value of the difference between Y1 and Y2, and regress that absolute difference on the dichotomous (indicator) variable, X. My sense is that the expected value of the coefficient for the variable X in the regression would be related in a deterministic way with the gap between the correlations between Y1 and Y2 at the different values of X. But how?

This comes up in research on identical and fraternal twins, where the chief research interest is in the degree of similarity on some trait between identical twins relative to similarity on some trait between fraternal twins.

In the spirit of Bullwinkle, I think that all blog entries should be required to have two titles. . . .

Anyway, Seth linked to this amusing note by Preston McAfee.

P.S. In a comment to my earlier entry, somebody linked to McAfee's free introductory economics textbook. I started reading it, and it seems great so far. Maybe if I'd read a book like this thirty years ago I would've become an economist. Or maybe not, I dunno. It's not like my statistics textbooks were so delightful; I just liked the subject. And I've never read a poli sci textbook in my life.

John and I gave our presentation on statistical graphics today, and then coincidentally I found this monograph by Rafe Donahue (link from Helen DeWitt). I started skimming and it looks pretty good so far. He uses horizontal jittering instead of the horrible boxplot, and that makes me happy already. On the other hand--since I'm being superficial here--I'm not a fan of the marginal-notes style of referencing. I always feel that this style draws undue attention to what are ultimately the least important parts of the book.

More seriously, Donahue's monograph looks interesting, and I'll have to read it more carefully. I've been looking for something on graphics that goes beyond the nuts and bolts of how to make a particular graph and considers what should actually be plotted and why.

On a theoretical level, I wonder how his ideas connect to my ideas of exploratory data analysis and statistical modeling (see here and here). I think the connections are there (as in Donahue's principle #28, 43, 52, and 86: "The data display is the model."

Actually, many of his principles are things that I tell people also. Just today I discussed how you have to tell the viewer what the plot is (Donahue's principle #23).

P.S. A minor point: Donahue's principle #53 is, "Plot cause versus effect." Doesn't he mean, "Plot effect versus cause"? Usually we say y vs. x, not x vs. y. Or else I'm missing something here.

Just a few thoughts in response to all the comments:

1. Several people point out that it is the publisher, not the author, who decides the cost of a book. That's right. The author has some input, and for almost all of my books, I've talked with the publisher, before signing any contract, about keeping the price down. We insisted that Bayesian Data Analysis sell for $45, Teaching Statistics sold for $40, and ARM sold for $40 as well. I thought that A Quantitative Tour of the Social Sciences was going to sell for around $25 but now I see on Amazon that it's selling for $33; I don't really know what's up with that. And, as a trade book, Red State, Blue State was always going to be reasonably priced--people aren't generally prepared to pay $40 for a book that they don't feel they need for their work--and, as for the Applied Bayesian Modeling book co-edited with Meng, we never tried to keep the price down, and as a result the publisher charged $100 for it.

2. Ragna is irritated that my Teaching Statistics book is selling for $190 at the local bookstore. This is simply a mistake--they seem to have ordered the hardcover rather than the softcover. Teaching Statistics is a great book but I wouldn't pay $190 for it. Annoyingly enough, if you look up the book on Amazon it sends you to the hardcover. But if you look carefully you can find the softcover for $63 ("list price $70"). I don't know how this happened. It was $40 when it came out.

3. Bayesian Data Analysis now costs $60 on Amazon. But, to be fair, it has been well over a decade since the original $45 version came out. I'd like it to still be $45 but I don't have much influence over this. It's a matter of negotiation.

4. I understand that if the book sells for more, the author probably makes more money. Certainly for technical books. I'd guess that if all my books were doubled in price, they'd sell more than half as well as they sell now (and, conversely, if they were halved in price, I doubt they'd sell at anything like twice their current rate). But my books don't make a lot of money for me (and, as for my book with Deb, we donate all the royalties to charity). What the books do do is make money for the publishers. That's fine, but making money for publishers is not one of my major goals in life.

5. I'll have to look into this open source thing. I'm a traditionalist myself and like hard-copy books. I've seen how students work on the computer: they seem to have the ability to only look at one window at a time, and so I think they need the hard copy of the textbook.

6. Some people were surprised that I didn't already know that these books were expensive. Yes, I know that technical books are expensive (hence my struggle to keep my own books under $40), but . . . an intro stat book? These things don't have a lot of content. $150 seems like a lot. If you pay $70 for Jun Liu's book on statistical computing . . . well, you get Jun Liu's book--that's a pretty good deal! But paying twice as much for something generic--that just seems horrible.

7. In answer to the questions of what my book will be like: I'm not sure! Seeing the $150 books makes me want to quickly write a generic book for $10 or free or whatever, just to do my part to destroy the market for the $150 books, but, no, I'm gonna do something new. I'm still struggling to figure out how it should be structured.

8. In answer to Bob's question: It's my impression that the Ivy League colleges get zillions of applicants, so they have no motivation to break the coalition and charge less for tuition. But, for an intro textbook, it would only take one author to change things, right?

9. I believe that many intro stat books, including Dick DeVeaux's and many others, have strengths. I have my own ideas for how to teach intro statistics, but I'm certainly not trying to claim that the current books are pure crap. And if the choice were DeVeaux's book for $100 or a generic book for $40, I'd probably assign DeVeaux's for $100. I think it would be worth the students' $60 to learn from a better book. But what amazes me is that even completely generic books are selling for well over $100.

10. Yes, I agree with everyone on the basic economic argument that it's the profs who assign the texts but the students (or their parents) who pay. Nonetheless . . . how did they even get the chutzpah to charge $150 in the first place?

11. Sometimes I sort of wish that Jennifer and I had self-published ARM or gone with some zero-margin publisher such as Dover, who do publish new books, by the way, including some great kids' activity booklets for something like $1.50 each. Anyway, if the goal is a $40 book, I think I can go with a regular publisher; after all, Cambridge is selling ARM for $40 and will sell Regression and Other Stories for a bit less, I believe.

12. From some of the resources provided by the commenters, it seems as if free textbooks are out there, and so maybe the current $150 texts are just the last bit of profit-taking before the collapse. I'd love to see time series plots of intro textbook prices in various fields.

13. Regarding the issue of homework questions and test banks: This is a real concern, I agree, or at least it should be a concern. In the courses I've seen, instructors don't actually use these test banks, but maybe that just means we're not getting our money's work.

14. I noticed a remark on cost per page. As an author of a couple reasonebly-priced 600+ page books, I'm sympathetic to this argument . . . but, no, I don't think there's 600 pages worth of material in these intro stat books. My impression is that, at some point, a book being heavy makes it that much harder to use.

The following CUIPS Professional Development Seminar: "How (Not) to Present Quantitative Results," Thursday February 12, 12:30-2:00pm, 707 IAB.

I received a free copy in the mail of an introductory statistics textbook; I guess the publisher wants me to adopt it for my courses. The book isn't bad, actually it's pretty good: it follows the "Moore and McCabe" format, starting with descriptive statistics (up to correlation and regression), then a bit on data collection, then probability, then statistical inference, and at the end chapters on various more advanced topics.

I showed the book to Yu-Sung and he said: Wow, it's pretty fancy. I bet it costs $150. I didn't believe him, but we checked on Amazon and lo! it really does retail for that much. What the . . . ? I asked around and, indeed, it's commonplace for students to pay well over $100 for introductory textbooks.

Well. I'm planning to write an introductory textbook of my own and I'd like to charge $10 for it. Maybe this isn't possible, but I think $40 should be doable. And why would anybody require their students to pay $150 for a statistics book when something better is available at less than 1/3 the price?

This won't be easy, because I'm planning to write an entirely new kind of intro book, starting from scratch. But why hasn't someone written a more conventional book at a cut-rate price? Or maybe they have, and I just haven't heard about it?

It just mystifies me that, in all these different fields, it's considered acceptable to charge $150 for a textbook. I'd think that all you need is one cartel-breaker in each field and all the prices would come tumbling down. But apparently not. I just don't understand.

P.S. More thoughts here.

AT writes:

I've got a count-based data set with a lot of zeroes present. I'm using zero-inflated modeling to capture the shape, and I want to test goodness-of-fit from both ends -- under- and overfitting. I've read your 1996 paper with XL and Hal Stern which recommends a "discrepancy measure" as being a good quantity to calculate with posterior predictive data. The main suggestion there was to use a chi-square statistic, but I'm sure this would be inappropriate in this case given that the zero cases would drive the entire statistic (and breaking the minimum-cell-size rule for the chi-square about 500 times in the process.) I suppose we could correct for this by doing the square-root trick to stabilize variance, but that still doesn't seem like it would resolve the problem with the zeroes. Any thoughts as to how to find a good discrepancy measure to check?

My generic response is that we always want the test summaries to relate to the substantive questions of interest. In this case, I don't have the context but I can make some quick suggestions, such as to create two test summaries: (a) the percentage of zeroes, and (b) some summary of the fit ot the counts when they are not zero.

The so-called minimum cell size rule is irrelevant, since you can compute the reference distribution directly using simulation. And issues such as stabilizing variance are not particularly relevant either, except inasmuch as they allow your test to more accurately capture the aspects of the data that are important for you to fit with your model.

We were discussing the Angrist and Pischke book with Paul Rosenbaum and I mentioned my struggle with instrumental variables: where do they come from, and doesn't it seem awkward when you see someone studying a causal question and looking around for an instrument?

And Paul said: No, it goes the other way. What Angrist and his colleagues do is to find the instrument first, and then they go from there. They might see something in the newspaper or hear something on the radio and think: Hey--there's a natural experiment--it could make a good instrument! And then they go from there.

This sounded fun at first, but I actually prefer this to the usual presentation of instrumental variables. The "find the IV first" approach is cleaner: in this story, all causation flows from the IV, which has various consequences. So if you have a few key researchers such Angrist keeping their ears open, hearing of IV's, then you'll learn some things. This approach also fits in with my fail-safe method of understanding IV's when I get stuck with the usual interpretation.

Sometimes the "lead with the natural experiment" approach can lead to missteps, as illustrated by Angrist and Pischke's overinterpretation of David Lee's work on incumbency in elections. (See here for my summary of Lee's research along with a discussion of why he's estimating the "incumbent party advantage" rather than the advantage of individual incumbency.) But generally it seems like the way to go, much better than the standard approach of starting with a causal goal of interest and then looking around for an IV.

In this spirit, let me again mention my own pet idea for a natural experiment:

The Flynn effect, and the related occasional re-norming of IQ scores, causes jumps in the number of people classified as mentally retarded (conventionally, an IQ of 70, which is two standard deviations below the mean if the mean is scaled at 100). When they rescale the tests, the proportion of people labeled "retarded" jumps up. Seems like a natural experiment that might be a good opportunity to study effects of classifying people in this way on the margin. If the renorming is done differently in different states or countries, this would provide more opportunity for identifying treatment effects.

I think it would be so cool if someone could take this idea and run with it.

I received the following email:

**, Co-Chairman and Co-Chief Executive Officer of **, wants to use the following quote in his upcoming presentation:

"The law of unintended consequences is what happens when a simple system tries to regulate a complex system. The political system is simple, it operates with limited information (rational ignorance), short time horizons, low feedback, and poor and misaligned incentives. Society in contrast is a complex, evolving, high-feedback, incentive-driven system. When a simple system tries to regulate a complex system you often get unintended consequences."

** would like to attribute the quote to the rightful author but is having difficulties in locating its origin. Can you please clarify if this is something that you said, and if so, where and when you said it? If you did not say this, then can you please tell us who was its original author? Thank you in advance for your help.

I replied:

What I wrote about the law of unintended consequences is here and here. The paragraph you give below is from Alex Tabarrok and is given in the first link above.

It's a little scary that the most famous thing I ever wrote was actually written by someone else!

I have got emails occasionally from JAGS users, asking about our new R package: R2jags. Basically, R2jags runs JAGS via R and makes postanalysis easier to be done in R. Taking advantage of the functions provided by JAGS, rjags and R2WinBUGS, R2jags allows users to run BUGS in the same way as they would do it in R2WinBUGS. Nonetheless, R2jags has some powerful features that facilitate the BUGS model fitting:

1. If your model does not converge, update it. If you used to be a R2WinBUGS user, you must feel frustrated that your model does not converge. The best thing you can do is to use your current states of parameters as the starting values for the next MCMC. On the other hand, in R2jags, you just type in the R console:

   fit <- update(fit) 
   

   This will update the model.
2. If you have to shutdown your machine but the model is still not converged.... In R2jags, you can go ahead and save the R workspace and shutdown your machine. When you are ready to run the model again, load the workspace in R and type:

   recompile(fit)
   fit.upd <- update(fit)
   

   This will recompile the model, which means you can update the model again!!

If you want to explore more features of the R2jags, just type ?jags in the R console. The example code contains all the functions in the R2jags.

Installing JAGS and rjags can be tricky in the Mac OS or in the Linux system. I have a blog entry here that shows how this can be done. If you are not a Window user, this post might help you.

I recently reviewed a report that used posterior predictive checks (that is, taking the fitted model and using it to simulate replicated data, which are then compared to the observed dataset). One of the other reviewers wrote (in response to the report, not to me):

The model goodness-of-fit statistics that the authors present on this page are biased, and should be interpreted with at least some caution. They give an over-optimistic evaluation of the fit of the hierarchical Bayes model. This is because the data are used twice: once to fit the model, and once again to assess the fit of the model. In fact, the posterior p-values are not asymptotically uniform, as they should be.

I completely disagree! I've discussed this point before. But the attitude expressed in the above quote is held strongly enough, and commonly enough, that I'm willing to spend some time trying to clear things up.

Let's unpack things.

Nancy Rosenblum posted an article based on her recent book, "On the Side of the Angels: An Appreciation of Parties and Partisanship," which she describes as her "analysis of antipartyism and attempt at rehabilitation." Following up at Cato Unbound is Brink Lindsey, who writes that "under present circumstances at least, partisan zeal ought to be attacked rather than defended."

I'll summarize what Rosenblum and Lindsey have to say and then give my reaction (much of which is based on data from our Red State, Blue State book).

I'm always yammering on about the difference between significant and non-significant, etc. But the other day I heard a talk where somebody made an even more basic error: He showed a pattern that was not statistically significantly different from zero and he said it was zero. I raised my hand and said something like: It's not _really_ zero, right? The data you show are consistent with zero but they're consistent with all sorts of other patterns too. He replied, no, it really is zero: look at the confidence interval.

Grrrrrrr.

I don't see the humor here, but two different people emailed this to me so I think there's some sort of legal requirement that I blog it. . . .

I had a discussion with Christian Robert about the mystical feelings that seem to be sometimes inspired by Bayesian statistics. Christian began by describing this article that was on the web about constructing Bayes' theorem for simple binomial outcomes with two possible causes as "indeed funny and entertaining (at least at the beginning) but, as a mathematician, I [Christian] do not see how these many pages build more intuition than looking at the mere definition of a conditional probability and at the inversion that is the essence of Bayes' theorem. The author agrees to some level about this . . . there is however a whole crowd on the blogs that seems to see more in Bayes's theorem than a mere probability inversion . . . a focus that actually confuses--to some extent--the theorem [two-line proof, no problem, Bayes' theorem being indeed tautological] with the construction of prior probabilities or densities [a forever-debatable issue]."

I replied that there are several different points of fascination about Bayes:

Yes, I understand that it's frustrating to not be able to drive your expensive SUV at the maximum possible speed attainable by that magnificent machine . . . but, really, how fast do you really expect to be traveling on NYC streets in a snowstorm during rush hour???

Eric Loken writes:

Last week the New York Times published an article on a possible Obama effect on test scores of black test takers. . . . The authors claim that they gave a short academic aptitude type test to black and white test-takers. When they administered the test last summer, they noted a difference between average scores for blacks and whites. However, after (now) President Obama had received his party's nomination and given his acceptance speech, the difference in scores disappeared. The theory is that Obama's rise has had a positive motivating influence on test taking performance.

Eric then gives some background:

Now that we're on the topic of econometrics . . . somebody recommended to me a book by Deirdre McCloskey. I can't remember who gave me this recommendation, but the name did ring a bell, and then I remembered I wrote some other things about her work a couple years ago. See here.

And, because not everyone likes to click through, here it all is again:

I just read the new book, "Mostly Harmless Econometrics: An Empiricist's Companion," by Joshua Angrist and Jorn-Steffen Pischke. It's an excellent book and, I think, well worth your $35. I recommend that all of you buy it.

I also have a few comments.

On the often-interesting judgment and decision making listserv, George Christopoulos wrote:

It seems that in situations similar to the present economic situation economic agents are less willing to take risks and instead they prefer safer options.

Could somebody point to studies that show this negative relationship between depression /recession (or when generally when wealth resources are low) and increased (relative?) risk aversion?

There were a couple of responses on the list, but they seemed to me to miss the point slightly. The respondents referred to econ literature on stock market trading and on wealth and economic decision making, but my impression was that Christopoulos was looking for something more psychological: something like a meta-analysis of studies of uncertainty aversion (I prefer to avoid the term "risk aversion" or even "loss aversion," for reasons I've discussed at length on this blog) over time, to see if subjects in an identical experiment show more uncertainty aversion in bad times than good.

The next step would be to analyze such data to separate out, to the extent possible, effects of individual economic status and national trends. The hypothesis might be that both have effects: that people suffering personal reversals might show more uncertainty aversion, and that, on top of this, everyone might tend to show more uncertainty aversion during economic downturns.

Could be an interesting study, although I doubt that such data are available.

Visualization and Control in Insect Flight

Atilla Bergou, Physics Department, Cornell University

Insects have a 100 million year head-start on us in learning how to fly. Thus, we have a lot to learn from them. Currently, one of the greatest challenges in this study is the accurate measurement, characterization and visualization of the motions of these animals. Recent advances in high-speed videography have allowed us to begin exploiting techniques from computer vision which hold immense promise to resolve these problems. In this talk, I will show our efforts in incorporating ideas from computer vision and physics to study the complex motion of an insect's wing. This motion is due not only to muscular activation but also to fluid, inertial, and elastic forces. Thus, it may be that not all aspects of the wing motion are actively controlled by the insect. We ask whether changes in the wing orientation of flying fruit flies are actuated by insect muscles, or if their wings turn over passively like a falling leaf. By applying a three- dimensional reconstruction technique to high-speed films of freely flying fruit flies, we are able to capture their intricate motion at a level of detail that has previously been impossible. We extract the detailed wing kinematics of flies using a novel motion tracking algorithm, compute the forces acting on the wings and infer whether flapping flight is possible without pitching control.

The talk is 3pm Wed 4 Feb CESPR 414 Sindeband East.

Seems like a good idea to me. This story reminds me of when my course listing mysteriously got removed from the department's website. It took something like two years to get it back up.