Results matching “R”

I'm speaking Monday 14 April at 4:30 on weakly informative prior distributions and models with interactions. I'll try to make things accessible to a general audience of people who might not know much about statistics in general or Bayesian methods in particular.

Richard Florida links to this article by Ruy Teixeira and Alan Abramowitz:

Dramatic shifts have taken place in the American class structure since the World War II era. Consider education levels. Incredible as it may seem today, in 1940 three-quarters of adults 25 and over were high school dropouts (or never made it as far as high school), and just 5 percent had a four-year college degree or higher. . . . by 2007, it was down to only 14 percent. . . . In 1940, only about 32 percent of employed US workers held white collar jobs (professional, managerial, clerical, sales). By 2006, that proportion had almost doubled to 60 percent . . . we [Teixeira and Abramowitz] discuss these shifts in the class structure and analyze their political implications, primarily by focusing on the decline of the white working class.

Yu-Sung made some graphs (to appear in our book) that extend earlier estimates of Brooks and Manza show some of the trends in voting over the past fifty years:

Professionals (doctors, lawyers, and so forth) and routine white collar workers (clerks, etc.) used to support the Republicans more than the national average, but over the past half-century they have gradually moved through the center and now strongly support the Democrats. Business owners have moved in the opposite direction, from close to the national average to being staunch Republicans; and skilled and unskilled workers have moved from strong Democratic support to near the middle.

These shifts are consistent with the oft-noted cultural differences between Red and Blue America. Doctors, nurses, lawyers, teachers, and office workers seem today like prototypical liberal Democrats, while businessmen and hardhats seem like good representatives of the Republican party. The dividing points were different 50 years ago. The Republicans still have the support of most of the high-income voters, but these are conservatives of a different sort. As E. J. Dionne noted in analyzing poll data from 2004, the Democrats' strength among well-educated voters is strongest among those with household incomes under $75,000---"the incomes of teachers, social workers, nurses, and skilled technicians, not of Hollywood stars, bestselling authors, or television producers, let alone corporate executives."

We tried to take our analysis further by regressing on income within occupation groups, but we didn't find anything exciting; there wasn't much evidence of different rich/poor voting gaps in different occupation categories. The Teixeira and Abramowitz article adds something to this picture because they talk about how the relative sizes of these different groups are changing.

John Shonder points me to this article on the work of Brett Pelham, who's been featured here before. The news article states,

In studies involving Internet telephone directories, Social Security death index records and clinical experiments, Brett Pelham, a social psychologist, and colleagues have found in the past six years that Johnsons are more likely to wed Johnsons, women named Virginia are more likely to live in (and move to) Virginia, and people whose surname is Lane tend to have addresses that include the word “lane,” not “street.”

They didn't mention my favorite, which is that there are almost twice as many dentists named Dennis in the United States, compared to what you would expect based on the number of dentists and Dennises alone.

Nooooooooooo...............

I want to correct one misconception that was aired in the Times article. As with many such things, it turns on conditional probability. The article states,

In studies that make believers in free will squirm, Dr. Pelham’s team asserts that names and the letters in them are surprisingly influential in people’s lives. . . . Skeptics of the name-letter effect question how strong the affinity really is between a person’s name and his or her destiny. 'I’m willing to believe that such patterns exist,' said Stanton Wortham, a professor of education and anthropology at the University of Pennsylvania. 'But I’m not willing to grant that those sorts of patterns are going to explain or drive a substantial amount of behavior.'"

OK, first off, free will has nothing to do with it. Everybody agrees that your party identification and, for that matter, your religious affiliation, are highly correlated with your parents'; does this mean you don't have a chance to alter these things? Free will requires the ability to alter things; it doesn't require complete statistical independence of preconditions and outcomes. Just a moment's thought, blah blah blah.

On to the second point. The pattern of names and occupations (for example) can be clear and still represent a small effect. Just for example, there were 482 dentists in the United States named Dennis, as compared to only 260 that would be expected simply from the frequencies of Dennises and dentists in the population. On the other hand, the 222 "extra" Dennis dentists are only a very small fraction of the 620,000 Dennises in the country; this name pattern thus is striking but represents a small total effect. Some quick calculations suggest that approximately 1% of Americans' career choices are influenced by the sound of their first name.

P.S. I agree that stories about names are amusing.

Leo Kahane, David Paton, and Rob Simmons have an interesting discussion in Vox EU on how to study effects of abortion on crime rates. They write:

The hypothesis that the legalisation of abortion contributed to a dramatic fall in crime rates in the United States, originally proposed by John Donohue and Steven Levitt in an article in 2001 and popularised by Levitt’s best selling book Freakonomics, has been the subject of close scrutiny by other academics. . . .

For the US (as noted by D&L), crime starts to fall about 18 years after the legalisation of abortion, consistent with abortion being a causal influence. In contrast, property crime in England and Wales starts to fall about 23 years after the first full year of abortion (1969), too late to be consistent with a causal effect. Violent crime does not decrease at all over the period. . . .

A natural way of distinguishing these explanations is to examine whether crime fell more (or increased less) amongst those young enough to have been affected by abortion legalisation compared to those born before the legislation. Figure 2 shows the pattern of conviction rates for those aged 10-15, 16-20 and 21 plus in England and Wales. The trends are not supportive of a link between abortion and crime. . . . Given all this, it seems highly unlikely that the legalisation of abortion can, as D&L hypothesised, explain the dramatic drop in crime observed in the US in the 1990s. However, we cannot necessarily conclude from this that abortion has no impact on crime. . . .

A potential explanation of this apparent conundrum arises from considering what actually happened to children who would not have been born had abortion been legal at the time of their conception. Some such children would have been brought up in adverse circumstances (either by the birth parent or by being taken into the care of the state) and may consequently have been at a higher risk of committing crime. On the other hand, other children conceived in similarly adverse circumstances would have been given up for adoption and then brought up in relatively stable and affluent circumstances. Put another way, prior to the legalisation of abortion, unwanted babies did not necessarily become unwanted children. . . .

Figure 3 illustrates trends in rates of infant adoptions and children taken into state care in England and Wales between 1960 and 1980. The rate of children in care barely changes after abortion legalisation in 1968, whilst there appears to be a dramatic effect on adoptions. . . .

Kahane, David Paton, and Rob Simmons conclude with a speculation and a research suggestion:

It seems that the legalisation of abortion contributed to a structural shift in society from a situation in which it was normal to put “unwanted” infants up for adoption to one in which adoption was actively discouraged. Once this structural change occurred, it is plausible that, say, a subsequent marginal tightening of the abortion law will have two effects. Children conceived in adverse circumstances are (marginally) more likely to be born rather than aborted but are then more likely to be brought up in those same adverse consequences rather than being put up for adoption. If true, we will observe a negative link between abortion rates and subsequent crime rates.

Although speculative, this hypothesis is consistent with observed trends in adoptions and with the analyses of the abortion-crime link in both the US and the UK. The hypothesis suggests a natural way forward for researchers interested in the social impact of abortion. Rather than trying to identify a causal link from abortion to indirect outcomes such as crime which are only observed many years later, it may be more fruitful to try to tease out the size and direction of the impact of abortion on contemporaneous and direct indicators such as the rates of children taken into care.

I don't know anything about this and so can't comment on the substance, but I like the idea of trying to look at intermediate outcomes. This is an important general point in statistics; see, for example, this famous example.

P.S. The graphs are great, but I have a few suggestions . . .

1. Label the lines directly rather than use a legend. The lines on the first graph are particularly difficult to identify: three of the symbols are nearly identical at this resolution, and the labels on the legend are not in order of the lines.

2. I'm not thrilled with normalizing the series (as was done in the first two graphs). To start with, you lose the information of which countries are higher and which are lower; second, it creates a misleading picture of divergence. For the first graph, I think the way to go is to make two separate plots, one for violent crimes and one for property crimes.

3. Think a bit harder about the numbers on the axes. On the first graph, the y-axis numbers start at 100,000 even though they've been normalized at 100. That can't be right. Labeling the x-axis every two years doesn't help; do every 10 years instead. The second graph doesn't actually say what a "conviction rate" is. But I expect that it makes sense to send the y-axis all the way down to zero. Again, x-axis every 10 yrs would be fine (and also make it easier to compare to the scale of the top graph). Finally, the third graph y-axis should be 0, 10, 20 (or maybe 0, 5, 10, 15), and the y-axis is particularly hard to read.

But the main thing is point 1 above. This should be standard, I think. Given all the effort put into doing this research, why not make the graphs readable too? To me, having cryptic graphs is like writing a paper full of run-on sentences and non-sequitors.

Let me conclude by saying that the paper looks really interesting; I wouldn't have spent the time commenting on the graphs if I didn't think they were potentially saying something important.

Michail Fragkias writes,

The advice is interesting but I don't really have much to say about it--in particular, I have no sense if it's good advice for people interviewing for jobs in statistics. My real question, though, is how much are these pieces of advice are zero-sum and how much of them would create overall improvements.

Just for analogy, if I give people advice about how to make cleaner powerpoint presentations, that's positive-sum (better communication for all); if I tell people a secret way to put their proposals at the top of the pile for a granting agency, that's zero-sum; if I give people the advice of not posting preliminary results so they don't get scooped, that's negative-sum.

Now let me play this game with Dan's advice:

Chris Wiggins points me to this column by John Tierney reporting research by Keith Chen on cognitive dissonance--that well-known phenomenon whereby we change our preferences to match our pre-existing decisions (for example, not wanting to hear bad news about one's preferred presidential candidate). Chen wrote a paper claiming that cognitive dissonance is not nearly as important as everyone thought it was. For Tierney's column, Chen writes,

All of the studies I [Chen] talk about take as their basic model a famous and incredibly influential experiment by Jack Brehm in 1956; the first study, in fact, which psychologists took to demonstrate cognitive dissonance. In Brehm’s study and its modern variants, subjects are first asked to rate or rank a bunch of goods based on how much they like them. Then, subjects are offered a choice between two of the goods they just rated, and are told they can take the good they choose home with them as payment for the study. They are then asked to re-rate all of the original goods; cognitive dissonance theory suggests that people would have a better opinion of the good they choose after choosing it than before.

So, for example, subjects may first be asked to rank 15 goods from 1 to 15, with 1 being the best and 15 being the worst. Then, a subject would be asked to choose between two goods they initially ranked similarly, say the goods they ranked 7 and 9. After making this choice, psychologists have looked at whether, if asked to rank these goods again, the chosen good rises in rank, and if the rejected good falls. This seems like a perfectly reasonable thing to look at; but there’s a big problem in how this has been done.

The problem is, when you ask subjects to choose between goods they ranked 7 and 9 (call these goods A and B), many subjects choose good B, (the good they initially ranked lower). Typically about one-quarter to one-third of subjects do this. Now, why people do this isn’t entirely clear, but one thought is that it indicates that asking subjects to rank goods from best to worst isn’t a perfect measure of how they feel. Some of them might not take the task that seriously; some might get confused by all the choices. So while they’ll initially rank B below A in the list of items, when they actually focus just on those two items they realize they actually prefer B to A.

The real problem, though, is what psychology studies did with subjects who “switched” — that is, those who chose the good they initially said they liked less. What many studies did (following the original Brehm study) is to exclude from the study those subjects who choose good B. Is this a problem that can bias their findings? Yes, if we think that the subjects being excluded from study are systematically different from those who aren’t. Specifically, when we drop subjects who choose good B over good A, we may be systematically dropping subjects who like good B (more than good A). Ignoring this possibility is like ignoring Monty’s choice and what it tells us about where the car is likely to be. By throwing out subjects, a study “stacks the deck” of remaining subjects with people who like good A more than they like good B. In fact, all remaining subjects have signaled they feel that way, twice. Maybe it shouldn’t be a surprise then, when asked to re-rank these items, the rank of good A rises; it originally ranked 7 from a larger group, then those who on second thought didn’t like it so much, were dropped.

Many studies that examine “spreading” look at how much A goes up and B goes down only for those people who chose A (as just described). Others look at whether the chosen good (A if you choose A and B if you choose B) went up and the non-chosen went down for everyone. This is also problematic for exactly the same reason; we shouldn’t be surprised that people like the things they choose, and the experiment needs to take that into account before it can correctly claim that dissonance is occurring.

This is interesting. I'm certainly sympathetic to the argument that preferences don't exist, independently of the settings in which they are chosen. (See here and here.) On the other hand, the desire to avoid cognitive dissonance seems real to me. I'd like to see how this work fits into the general literature on the topic. (Also, I'm not quite sure why Tierney calls this "social psychology." Isn't it "cognitive psychology"? I'm sure there's something I'm missing here.

Greg Ward writes,

The conference consisted of two panels discussing various aspects of the working life of statisticians. The statisticians on the first panel were all currently working in academia, while the statisticians on the second panel were all working in industry.

Matthew Atkinson, Ryan Enos, and Seth Hill sent along this paper:

Recent research finds that inferences from candidate faces predict aggregate vote margins. Many have concluded this to mean that voters choose the candidate with the better face. We implement a survey with participant evaluations of over 167,000 candidate face pairings. Through regression analysis using individual- and district-level vote data we find that the face-vote correlation is explained by a relationship between candidate faces, incumbency, and district partisanship. We argue that the face-vote correlation is not just the product of simple voter reactions to faces, but also of party and candidate behavior that affects which candidates compete in which contests.

This is great stuff. They're talking about a 2005 article by Alexander Todorov, Anesu Mandisodza, Amir Goren, and Crystal Hall which found that people thought the faces of winning congressional candidates looked more "competent" than faces of losing candidates. I wrote about this about a year ago and expressed skepticism about the interpretation of those findings . . .

After reading our article, "Voting as a rational decision," Mark Thoma asked,

If helping other people makes me happy, why would caring about other people be contrary to my own self-interest? This is essentially a question about the meaning of the term selfish. I [Mark] assume selfishness means maximizing my utility, which may or may not include the happiness of other people as an argument.

My reply:

The challenge in all such arguments is to avoid circularity. If selfishness means maximizing utility, and we always maximize utility (by definition, otherwise it isn't our utility, right?), then we're always selfish. But then that's like, if everything in the world is the color red, would we have a word for "red" at all? I'm using selfish in the more usual sense of giving instrumental benefits. For example, if I cut in front of someone in line, I'm being selfish. If I don't do it (because I get pleasure from being a nice guy and pain from being a jerk), then that's other-directed. I'm sacrificing something (my own time) in order to help others. Just because something is enjoyable it doesn't have to be selfish, I think.

To put it another way, if "selfish" means utility-maximization, which by definition is always being done (possibly to the extent of being second-order rational by rationally deciding not to spend the time to exactly optimize our utility function), then everything is selfish. Then let's define a new term, "selfish2," to represent behavior that benefits ourselves instrumentally without concern for the happiness of others. Then our point is that rationality is not the same as selfish2.

Also, some of his commenters questioned whether a single vote could be decisive, what with recounts etc. The answer is, yes, it can, because there is ultimately some threshold (even if unobservable) as to whether the recount occurs. And even if this threshold is itself probabilistic, the probabilities can be added. We demonstrate this mathematically in the Appendix to the 2004 Gelman, Katz, and Bafumi article in the British Journal of Political Science; see page 674 here.

P.S. Mark has further remarks here. Those are his comments on my comments on his comments on my article which, when you come down to it, was basically a comment on some of the political science literature. That should be enough, I think.

Charlie Williams asks if I have any comment on this. I'll refer you to Brendan Nyhan's discussion here. Brendan seems to have done everything that I was thinking of doing here.

Henry Farrell writes:

Via Cosma Shalizi, this is a nice tool for mapping the relationship between donations from energy companies and politicians in Presidential, House and Senatorial elections. . . . Why is it that there appears to be so little literature out there on this kind of network? Is it the difficulty of establishing causal relationships (although surely this would invalidate whole swathes of US political science if this standard were applied rigorously)? Is it difficulties in gathering the relevant data (Cosma notes that gathering it and cleaning it up is surprisingly hard)? The perceived publication practices of major US journals? I'm genuinely puzzled as to the reason why there's this gap in the literature. Both comparativists (Jerry Easter) and international relations scholars (Charli Carpenter) have published well regarded articles in the major journals of their field on the importance of networks in domestic and international settings. So why not Americanist political scientists?

In trying to answer this question, I think it's important to separate two aspects of the above research: network analysis as a general statistical/social-science research method as applied to Americna politics, and the analysis of political contributions in particular.

In social science as a whole, networks have become very trendy--and I pretty much think that's a good trend. There are some roadblocks in applying these ideas to the study of public opinion and voting, however, since we're talking about a network of 250 million adults where the average person knows only 750 other Americans. You can get this sort of data from surveys but it's hard to know what to make of it. Tian Zheng, Tom DiPrete, Julien Teitler, and I have been involved in a research project estimating the segregation of Democrats and Republicans in social networks, and we collected data specially for our study. Still, the analysis is difficult, just at the technical level of building a statistical model for what we've got. It's no surprise that a lot more work has been done on networks in Congress. This isn't the part of American politics that I study but it counts, right? But, getting back to public opinion and voting: networks are clearly important but they're hard to study given the inherent sparseness of the data.

Moving to research on political contribution networks, I wonder if one reason you don't hear much about it is that this sort of work is politically marginalized, as it's associated with left-wing critiques of the political system, rather than more traditional representations of American politics as being generally representative of public opinion. For example, I don't know that Thomas Ferguson has formally used network analysis, but he and his collaborators have done lots of work tracking down campaign contributions (and I'm not talking about Vin Scully here). I agree with Henry that political donations would be a natural place for network analysis, since many of the major contributors have clear enough links that sparseness is less of an issue.

James Annan writes,

I wonder if you would consider commenting on Marty Weitzman's "Dismal Theorem", which purports to show that all estimates of what he calls a "scaling parameter" (climate sensitivity is one example) must be long-tailed, in the sense of having a pdf that decays as an inverse polynomial and not faster. The conclusion he draws is that using a standard risk-averse loss function gives an infinite expected loss, and always will for any amount of observational evidence.

I looked up Weitzman and found this paper, "On Modeling and Interpreting the Economics of Catastrophic Climate Change," which discusses his "dismal theorem." I couldn't bring myself to put in the effort to understand exactly what he was saying, but I caught something about posterior distributions having fat tails. That's true--this is a point made in many Bayesian statistics texts, including ours (chapter 3) and many that came before us (for example, Box and Tiao). With any finite sample, it's hard to rule out the hypothesis of a huge underlying variance. (Fundamentally, the reason is that, if the underlying distribution truly does have fat tails, it's possible for them to be hidden in any reasonable sample. It's that Black Swan thing all over again.) I think that Weitzman is making some deeper technical point, and I'm sure I'm disappointing Annan by not having more to say on this . . .

More

Richard Morey points us to this article. We posted Yair's take on the polling problems here.

But what really amused, or upset, me, was what I encountered when following the link on that page which read, "Smarter poll could call the closest races." That headline set off some warning bells--the closest races are the ones that can't be forecasted! I followed the link to an article that I couldn't read without a subscription, so I found it through our library and tracked down the original research article, "A new approach to estimating the probability of winning the presidency," by Edward Kaplan and Arnold Barnett, professors of management at Yale and MIT. The article appeared in 2003 in the journal Operations Research and is pretty misinformed. It's bad in so many ways, and the also, annoyingly, call their method Bayesian. Huge amounts of detail on essentially trivial algebra and a complete misunderstanding of elections. The sad thing is, there are excellent quantitative political scientists at both Yale and MIT--if these guys had just walked over a few buildings and asked for help, they could've been spared this embarrassment. Seeing this stuff just makes me want to barf: it's just not that hard to do something reasonable, and I hate the way they put in all this algebra for what are straightforward simulations of a probability distribution. (But ya gotta give the publicity office of Yale or MIT credit for getting this mentioned in the popular press.)

I hope the paper that Kari and I are writing will clear things up.

P.S. I have nothing against these guys personally. It's the kind of thing that can happen when you come into a field from the outside and don't know who are the right people to talk to. I'm sure if I tried to write a paper about business management, it would be equally silly.

Juli pointed me to this article about statistician Patrick Ball:

Since 1988, Ball has been "hacking code" – writing software – to unlock secrets from numbers. He taught himself computer programming so he could get a job that would cover expenses not included in his undergraduate scholarship to Columbia University. . . . He took a leave of absence and went to El Salvador with the Peace Brigades . . . Ball wrote software that allowed the commission to aggregate and analyze the human rights records of officers in the El Salvadoran Army. The results forced a quarter of the military leadership to retire. . . . Kosovo attracted international concern when hundreds of thousands of ethnic Albanian refugees fled to Albania. Amid what seemed little more than chaos, Ball saw dozens of data sources that, could point to the cause of the crisis: "Everything is data to us. A pile of scrungy paper from the border guards – 690 pages – that's data." He combined those scrungy papers, one for nearly every family that crossed the border, with crossing records kept by several international organizations; later, he brought in data from 11 sources on civilian deaths in the province. He analyzed the two separately, using one method for patterns of migration and another for mortality. . . .

Boris sent along this. I can't comment on the examples used there, but I agree with the general point that it's good to use more data. To get back to algorithms, what I'd say is that one important feature of a good algorithm is that it allows you to use more data. Traditional statistical methods based in independent, identically distributed observations can have difficulty incorporating diverse data, whereas more modern methods have more ways in which data can be input.

Seth is skeptical of skepticism in evaluating scientific research. He starts by pointing out that it can be foolish to ignore data, just because they don't come from a randomized experiment. The "gold standard" of double-blind experimentation has become an official currency, and Seth is arguing for some bimetallism. To continue with this ridiculous analogy, a little bit of inflation is a good thing: some liquidity in scientific research is needed in order to keep the entire enterprise moving smoothly.

As Gresham has taught us, if observational studies are outlawed, then only outlaws will do observational studies.

I think Seth goes too far, though, and that brings up an interesting question.

Clarification: Somebody pointed out that, when people come here from a web search, they won't realize that it's an April Fool's joke. See here for my article in Bayesian analysis that expands on the blog entry below, along with discussion by four statisticians and a rejoinder by myself that responds to the criticisms that I raised.

Below is the original blog entry.

Bayesian inference is a coherent mathematical theory but I wouldn't trust it in scientific applications. Subjective prior distributions don't inspire confidence, and there's no good objective principle for choosing a noninformative prior (even if that concept were mathematically defined, which it's not). Where do prior distributions come from, anyway? I don't trust them and I see no reason to recommend that other people do, just so that I can have the warm feeling of philosophical coherence.

Bayesian theory requires a great deal of thought about the given situation to apply sensibly, and recommending that scientists use Bayes' theorem is like giving the neighborhood kids the key to your F-16. I'd rather start with tried and true methods, and then generalizing using something I can trust, like statistical theory and minimax principles, that don't depend on your subjective beliefs. Especially when the priors I see in practice are typically just convenient conjugate forms. What a coincidence that, of all the infinite variety of priors that could be chosen, it always seems like the normal, gamma, beta, etc., that turn out to be the right choice?

To restate these concerns mathematically: I like unbiased estimates and I like confidence intervals that really have their advertised confidence coverage. I know that these aren't always going to be possible, but I think the right way forward is to get as close to these goals as possible and to develop robust methods that work with minimal assumptions. The Bayesian approach--to give up even trying to approximate unbiasedness and to instead rely on stronger and stronger assumptions--that seems like the wrong way to go.

In the old days, Bayesian methods at least had the virtue of being mathematically clean. Nowadays, they all seem to be computed using Markov chain Monte Carlo, which means that, not only can you not realistically evaluate the statistical properties of the method, you can't even be sure it's converged, just adding one more item to the list of unverifiable assumptions.

People tend to believe results that support their preconceptions and disbelieve results that surprise them. Bayesian methods encourage this undisciplined mode of thinking. I'm sure that many individual Bayesian statisticians and are acting in good faith, but they're providing encouragement to sloppy and unethical scientists everywhere. And, probably worse, Bayesian techniques motivate even the best-intentioned researchers to get stuck in the rut of prior beliefs.

Bayesianism assumes: (a) Either a weak or uniform prior, in which case why bother?, (b) Or a strong prior, in which case why collect new data?, (c) Or more realistically, something in between, in which case Bayesianism always seems to duck the issue.

Nowadays people use a lot of empirical Bayes methods. I applaud the Bayesians' newfound commitment to empiricism but am skeptical of this particular approach, which always seems to rely on an assumption of "exchangeability." I do a lot of work in political science, where people are embracing Bayesian statistics as the latest methodological fad. Well, let me tell you something. The 50 states aren't exchangeable. I've lived in a few of them and visited nearly all the others, and calling them exchangeable is just silly. Calling it a hierarchical or a multilevel model doesn't change things--it's an additional level of modeling that I'd rather not do. Call me old-fashioned, but I'd rather let the data speak without applying a probability distribution to something like the 50 states which are neither random nor a sample.

Also, don't these empirical Bayes methods use the data twice? If you're going to be Bayesian, then be Bayesian: it seems like a cop-out and contradictory to the Bayesian philosophy to estimate the prior from the data. If you want to do hierarchical modeling, I prefer a method such as generalized estimating equations that makes minimal assumptions.

And don't even get me started on what Bayesians say about data collection. The mathematics of Bayesian decision theory lead inexorably to the idea that random sampling and random treatment allocation are inefficient, that the best designs are deterministic. I have no quarrel with the mathematics here--the mistake lies deeper in the philosophical foundations, the idea that the goal of statistics is to make an optimal decision. A Bayes estimator is a statistical estimator that minimizes the average risk, but when we do statistics, we're not trying to "minimize the average risk," we're trying to do estimation and hypothesis testing. If the Bayesian philosophy of axiomatic reasoning implies that we shouldn't be doing random sampling, then that's a strike against the theory right there. Bayesians also believe in the irrelevance of stopping times--that, if you stop an experiment based on the data, it doesn't change your inference. Unfortunately for the Bayesian theory, the p-value _does_ change when you alter the stopping rule, and no amount of philosophical reasoning will get you around that point.

I can't keep track of what all those Bayesians are doing nowadays--unfortunately, all sorts of people are being seduced by the promises of automatic inference through the "magic of MCMC"--but I wish they would all just stop already and get back to doing statistics the way it should be done, back in the old days when a p-value stood for something, when a confidence interval meant what it said, and statistical bias was something to eliminate, not something to embrace.

I recently read Dan Ariely's book Predictably Irrational and wrote down my comments as I read. After the jump, you can read these thoughts.

Jowei Chen sent along this paper:

In the aftermath of the summer 2004 Florida hurricane season, the Federal Emergency Management Agency (FEMA) distributed $1.2 billion in disaster aid to Florida residents. This research presents two empirical findings that collectively suggest the Bush administration engaged in vote buying behavior. First, by tracking the geographic location of each aid recipient, the data reveal that FEMA treated applicants from Republican neighborhoods much more favorably than those from Democratic or moderate neighborhoods, even conditioning on hurricane severity, home value, and demographic factors. Second, I compare precinct-level vote counts from the post-hurricane (November 2004) and pre-hurricane (November 2002) elections to measure the effect of FEMA aid on Bush's vote share. Using a two-stage least squares estimator, this analysis reveals that core Republican voters are easily swayed by FEMA aid - $16,800 buys one additional vote for Bush - while Democrats and moderates are not. Collectively, these results suggest the Bush administration maximized its 2004 vote share by concentrating FEMA disaster aid among core Republicans.

This is interesting. In many aspects of politics, it seems clear that politicians reward their supporters, but political scientists sometimes really resist this idea, arguing on logical grounds that candidates should be focusing their efforts on the median voter. It's interesting to see some clear evidence where supporters are getting rewarded--and it's also good to see someone getting down and dirty with the data, rather than just reanalyzing the same old datasets over and over (which is what I usually do...). Sure, it's ultimately an n=1 study, but I imagine it will add something useful to the literature on government spending

Also, my little thoughts:

This looks interesting. Yi Li writes of a panel discussion at the Harvard biostatistics department. My own thoughts are below; first here's Li's description. There's some good stuff:

Seth rants about institutional review boards (IRBs). I have no problem with that; I rant about IRBs all the time. (And when IRBs should be doing something, they don't seem to be around.) But I don't know that Seth is being fair to blame "literature professors" for the problem. I've been on some NIH panels where some pretty ridiculous human subjects concerns were raised. And these were scientists on the panels, not literature professors.

I followed the link from commenter Lemmus and encountered this list of resources on Bayesian reasoning. These were all fine, but they didn't look like the Bayesian statistics that I am familiar with. (For example, the wikipedia link defines "A Bayes estimator is a statistical estimator that minimizes the average risk." Which doesn't have anything to do with anything that I do!) And the examples are all discrete--which makes sense, that's a good way to start--but I think it gives a misleading perspective of Bayesian data analysis as a statistical method.

So I thought I'd post Chapter 1 from Bayesian Data Analysis so people could see a practicing statistician's perspective. (Here's the table of contents and front matter of the book, to place it in context.)

"Bayesian reasoning" and "Bayesian data analysis" have (almost) the same name, but they're different things.

P.S. The distinction arises in other fields too. For example, a book on "thinking like a lawyer" will be different than a book on the practice of law, a book on "the engineering way of life" might not be very descriptive of what engineers actually do, and so forth.

P.P.S. If you're coming from statistics or econometrics, and you want to see how Bayesian inference generalizes classical least squares and maximum likelihood, then Chapter 18 from my book with Jennifer may be the best place to start.

Kjetil Halvorsen sends along this article by Irene Pepperberg:

I've begun to rethink the way we teach students to engage in scientific research.

Ken Lee writes:

Here.

Dear Prof. Andrew Gelman,

There is a great video on YouTube which shows a project representing numbers of people by grains of rice. You can see the contrast of one person (in this case, Tony Blair - clearly, this is a UK project) to the number of people on one continent, to the number of people in one country, etc. Though simple, it's interesting to actually see someone do this.

Link:
http://www.youtube.com/watch?v=iDWcuBygAUw

Chris Zorn sends along this. A rare paper about graphics that offers data as well as opinion!

Kaiser writes,

Jacob Felson writes,

In a 2002 article in the Journal of Economic Perspectives, economists Samuel Bowles and Herbert Gintis attempt to decompose the correlation in income between parents and children into genetic and environmental components. In addition, the authors attempt to calculate the extent to which the intergenerational correlation in income is due to inherited IQ. But unlike most data analyses, they do not use any particular data. Instead, the authors collect estimates of effect sizes from a variety of meta-analyses and attempt to estimate ballpark estimates for parameters in a theoretical path analysis. I am wondering -- is this "meta-meta-analysis" appropriate? Can one conduct path analyses and evaluate relative magnitudes of correlations taken from a variety of studies?

My reply: I haven't read the paper, but I'm skeptical of path analysis in general, and the meta-meta-analysis setting doesn't help any!

Boliang writes,

Mike Maltz writes,

Writing about four-leaf clovers, Steven Levitt says, "I’ve been looking my whole life and never found one." This reminds me that when I was a kid, my sister Susie and I used to find them in the backyard all the time. We'd also occasionally find siamese dandelions (one stalk, two heads) that we'd put on our older sister's bed to freak her out. Much later, Susie told me that our land was on some sort of former waste dump and so we (along with the clovers and dandelions) were probably being poisoned.

The New York version of this story: several years ago I was standing on the subway platform, and I offhandedly said to my companion, Hey, let's look for rats. We looked, and, indeed, there was a rat. I mean, I knew that there were rats in the subway--I've occasionally even seen them on the platform--but I didn't know they could be summoned at will in this way.

Aleks writes:

From here, see this. It could be used as a foundation to latch additional analysis functionality on top of it.

Here are some examples of interactive statistics on the web. But few things compare to the venerable b-course.

I posted here about a data-processing mistake that I made recently (and luckily noticed). From a more general statistical perspective, the interesting thing is that I noticed the error because the mistaken case looked wrong. Checking funny-looking data points and correcting them if necessary can be viewed as a Bayesian procedure--but it's well known (well, maybe not well enough known) that Bayesian point estimates can have systematic errors. This is a point made by Tom Louis in the context of estimating ensembles of parameters and by Phil Price and myself in our paper on why all maps of parameter estimates are misleading. Being Bayesian (or approximately Bayesian) is fine but it doesn't solve all problems!

P.S. I'd like to use the term "bias" here but it has an inappropriate technical meaning in this context so I'm using the phrase "systematic error," which hasn't already been taken.

Zoubin Ghahramani is speaking tomorrow (Wed.):

Machine learning is an interdisciplinary field which seeks to develop both the mathematical foundations and practical applications of systems that learn, reason and act. Machine learning draws from many fields, ranging from Computer Science, to Engineering, Psychology, Neuroscience, and Statistics. Because uncertainty, data, and inference play a fundamental role in the design of systems that learn, statistical methods have recently emerged as one of the key components of the field of machine learning. In particular, Bayesian methods, based on the work of Reverend Thomas Bayes in the 1700s, describe how probabilities can be used to represent the degrees of belief of a rational agent. Bayesian methods work best when they are applied to models that are flexible enough to capture to complexity of real-world data. Recent work on non-parametric Bayesian methods provides this flexibility. I will touch upon key developments in the field, including Gaussian processes, Dirichlet processes, and the Indian buffet process (IBP). Focusing on the IBP, I will describe how this can be used in a number of applications such as collaborative filtering, bioinformatics, cognitive modelling, independent components analysis, and causal discovery. Finally, I will outline the main challenges in the field: how to develop new models, new fast inference algorithms, and compelling applications.

Tyler Cowen links to a calculation by Tom Elia that "of Sen. Obama's 711,000 popular-vote lead, 650,000 -- or more than 90% of the total margin -- comes from Sen. Obama's home state of Illinois, with 429,000 of that lead coming from his home base of Cook County." This is interesting, but it's more a comment on how close the (meaningless) total popular vote count is, than a reflection of something funny going on in Cook County.

Put it another way. Suppose Obama's total margin was only 111,000 votes instead of 711,000. Then his 650,000 vote margin in Illinois would represent a whoppin 580% of the total margin, and Cook County would represent 390% of the total margin! But wait, how can a part be 390% of the whole??

What I'm sayin is, the "90%" and "60%" figures are misleading because, when written as "a percent of the total margin," it's natural to quickly envision them as percentages that are bounded by 100%. There is a total margin of victory that the individual state margins sum to, but some margins are positive and some are negative. If the total happens to be near zero, then the individual pieces can appear to be large fractions of the total, even possibly over 100%.

I'm not saying that Tom Elia made any mistakes, just that, in general, ratios can be tricky when the denominator is the sum of positive and negative parts. In this particular case, the margins were large but not quite over 100%, which somehow gives the comparison more punch than it deserves, I think.

This is pretty embarrassing, but I think it's better to tell all, if for no other reason than to make others aware of the challenges of working with data . . .

Burt Monroe alerts me to this conference at Penn State on May 3. That bald guy looks pretty scary! New faces, indeed. Also, I'll have to find out from Eduardo what he's doing on “The Political Consequences of Malapportionment." It sounds like it might be related to our project on representation and spending in subnational units. (The short story: low-population areas are overrepresented in legislatures around the world--the U.S. Senate is not the only serious offender--and these areas also get more than their share of government spending.) The conference seems like a great idea.

I was looking through the Pew surveys and they are just full of fascinating things. I actually hate to tell youall about this because I think I could just go through this report and pull out one table per day for months and impress you with my political knowledge . . .

Anyway, here's an interesting bit, having to do with how people view businesses in America: Nearly two-thirds of respondents say corporate profits are too high, but, "more than seven in ten agree that 'the strength of this country today is mostly based on the success of American business' – an opinion that has changed very little over the past 20 years."

Everybody loves Citibank

People like business in general (except for those pesky corporate profits) but they love individual businesses, with 95% having a favorable view of Johnson and Johnson (among those willing to give a rating), 94% liking Google, 91% liking Microsoft, . . . I was surprised to find that 70% of the people were willing to rate Citibank, and of those people, 78% had a positive view. I mean, I don't have a view of Citibank one way or another, but it would seem to me to be the kind of company that people wouldn't like.

Professionals vs. working class

Now here's where it gets really interesting. The Pew report broke things down by party identification (Democrat or Republican) and by "those who describe their household as professional or business class; those who call themselves working class; and those who say their family or household is struggling."

Republicans tend to like corporations, with little difference between the views of professional-class and working-class Republicans. For Democrats, though, there's a big gap, with professionals having a generally more negative view, compared to the working class:

A puzzling pattern

There's a pretty consistent pattern across the entire table which I don't fully understand, that goes as follows:

- For some corporations (Halliburton, Walmart, Exxon, McDonald's, Pfizer, Coke), the working-class Democrats are much less supportive than the working-class Republicans. For these corporations, there is almost no difference between professional and working-class Republicans. The only exception is Coke, which was viewed much less favorably by professional-class than working-class Republicans.

- For the others (Citibank, GM, Coors, American Express, Target, Starbucks), working-class Democrats had views that were similar to or more favorable than their Republican counterparts. And for these, there was a consistent pattern of much stronger favorability by professional than working-class Republicans.

I can come up with a story in each individual case but I don't really have a good way of thinking about all these together. (Also, for some reason, the report doesn't give the responses for those who say their families are "struggling." Perhaps the sample sizes were too small.)

One more bit

Respondents were asked how concerned they were about business corporations and government "collecting too much personal information about people like them." In general, Democrats and Independents were more concerned about both.

80% of Democrats and Independents were concerned about business collecting personal information and 65% were concerned about government. Among Republicans, 60% were concerned about business collecting the information and only 40% concerned about government. The survey is from 2007; perhaps Republicans' views about government snooping will change if there is a Democratic administration.

Also, people with higher income and higher education have "less concern about government data collection, while lower income is associated with higher concern. Income and education did not affect opinions about businesses collecting data." The bit about higher status people trusting the government more makes sense and is consistent with other survey results I've seen, but I'm surprised that there isn't a similar pattern regarding concern about businesses. Perhaps there are different patterns among the parties. The data are downloadable from Pew's website so you can go crunch the numbers yourself it you'd like.

Sarah Nequam sends along a link to this paper by Andrew Eggers and Jens Hainmueller:

While the role of money in policymaking is a central question in political economy research, surprisingly little attention has been given to the rents politicians actually derive from politics. We use both matching and a regression discontinuity design to analyze an original dataset on the estates of recently deceased British politicians. We find that serving in Parliament roughly doubled the wealth at death of Conservative MPs but had no discernible effect on the wealth of Labour MPs. We argue that Conservative MPs profited from office in a lax regulatory environment by using their political positions to obtain outside work as directors, consultants, and lobbyists, both while in office and after retirement. Our results are consistent with anecdotal evidence on MPs' outside financial dealings but suggest that the magnitude of Conservatives' financial gains from office was larger than has been appreciated.

I don't really have anything to say about this article in the New York Times, except for a comment on the graph:

In his talk on mental models of the structure of the world, Josh Tenenbaum talked about how people think of animals as being classified in a tree structure, and how this structure might differ from those implied by different scientific models. This kind of thing:

Anyway, as an aside, Tenenbaum pointed out that, although the tree structure seems so natural to us, it doesn't have to be this way. He noted that, traditionally, creatures have been organized into a linear "great chain of being" rather than as a tree structure. Then I realized . . . that's how I think of the animal kingdom. It's how we learned things in 9th grade biology. At the bottom are single-celled animals (amoebas and so forth), then gradually through the invertebrates, then the vertebrates, starting with the fish (with the sharks at the bottom because of their primitive structure), then amphibians, then reptiles (amphs are lower than reps because of being more fish-like and primitive, I think), then birds (higher because they're warm-blooded), then animals, with primates at the top and, well, you know what's the #1 primate . . .

Anyway, only when sitting in Tenenbaum's talk did I realize that I'd swallowed this whole great-chain-of-being formulation without even thinking about it. The assumption is that every invertebrate is lower than every vertebrate, that the most complicated bird is lower than any mammal, that all plants are lower than all animals, etc. It's still hard for me to shake this mode of thinking.

I guess it's a good thing I'm not a biologist. (I did publish in the Journal of Theoretical Biology once, but we all know that knowledge of biology is not necessary to publish in that journal.)

Yan Jiao writes,

I have a question about multilevel models and expect you to offer me some help.

Dave Judkins wrote:

From the American Association for Public Opinion Research.

See here. He's offering a copy of Tufte's "The visual display of quantitative information." My own favorite among Tufte's books is his second book, "Envisioning information," which, to my taste, has more in the way of practical tips and less in the way of ranting. (Don't get me wrong, I like all of Tufte's books; I'm just giving you my preferences. His first book was fun to read, but his second book changed how I do statistics.)

I was sorry to see Steven Levitt repeating the claim about driving a car being good for the environment. I wrote about this last week when it appeared in the other New York Times column of John Tierney, but perhaps it's worth repeating:

Here's the paper (with Jennifer and Masanao), and here's the abstract:

The problem of multiple comparisons can disappear when viewed from a Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. These address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low group-level variation, which is where multiple comparisons are a particular concern.

Multilevel models perform partial pooling (shifting estimates toward each other), whereas classical procedures typically keep the centers of intervals stationary, adjusting for multiple comparisons by making the intervals wider (or, equivalently, adjusting the p-values corresponding to intervals of fixed width). Multilevel estimates make comparisons more conservative, in the sense that intervals for comparisons are less likely to include zero; as a result, those comparisons that are made with confidence are more likely to be valid.

Check out Figures 4 and 6; it's pretty cool stuff. You really see the efficiency gain. We had several more examples but no room in the paper for all of them. Also, here's the presentation.

Dave Garbutt writes,

I don't know if you saw this recent report in New scientist about Paxil. It is bad because it alleges suicide attempts were included from washout were included for placebo & excluded from treatment. If you read the pdf they link to - on page seven there is a dire graphic of duration until suicide attempts where age is the Y axis & time is the X. With no indication of nos at risk. A better analysis?

I have no thoughts on this but it looked interesting enough to post. Well, I don't like that the cited graph uses nearly identical symbols for the two different categories. More to the point, if this is true, it's pretty scary. There seems to be a real conflict of interest here (and in similar trials). Maybe it would be better if they approved more drugs but then had an outside agency monitor them.

Michael Spagat has written this paper criticizing the study of Iraq mortality by Burnham, Lafta, Doocy, and Roberts:

I [Spagat] consider the second Lancet survey of mortality in Iraq published in 2006. I give evidence of ethical violations against the survey's respondents including endangerment, privacy breaches and shortcomings in obtaining informed consent. Violations to minimal disclosure standards include non-disclosure of the survey's questionnaire, data-entry form, data matching anonymized interviewer IDs with households and sample design. I present evidence suggesting data fabrication and falsification that falls into nine broad categories: 1) non-disclosure of key information; 2) implausible data on non-response rates and security-related failures to visit selected clusters; 3) evidence suggesting that the survey's figure for violent deaths was extrapolated from two earlier surveys; 4) presence of a number of known risk factors for interviewer fabrication listed in a joint document of American Association for Public Opinion Research and the American Statistical Association; 5) a claimed field-work regime that seems impossible without field workers crossing ethical boundaries; 6) large discrepancies with other data sources on the total number of violent deaths and their distribution in time and space; 7) two particular clusters that appears to contain fabricated data; 8) irregular patterns suggestive of fabrication in claimed confirmations of violent deaths through death certificates and 9) persistent mishandling of other evidence on mortality in Iraq presented so as to suggest greater support for the survey's findings from other evidence than is actually the case.

I haven't read Spagat's paper and so am offering no evaluation of my own (see here for some comments form a year or so ago), but the discussions of ethics and survey practice are fascinating. Social data always seem much cleaner when you don't think too hard about how they were collected! May I say it again: a great example for your classes...

P.S. As a minor point, I still am irritated at the habit of referring to a scientific publication by the name of the journal where it was published ("the Lancet study").

P.P.S. A reporter called me about this stuff a couple months ago, but I'm embarrassed to say that I offered nothing conclusive, beyond the statement that these studies are hard to do, and for some reason it's often hard to get information from survey organizations about what goes on within primary sampling units. (We had to work hard even to get this information from these simple telephone polls in the U.S.)

Possible statistics-related art includes pretty mathematical functions, interesting data displays, patterns of migrating birds, complicated high-tech signals, playful pointillist paintings made out of little 4's and 7's, . . .

More information here.

Rachel sent me this link. I don't know what sort of novelist would have a blog about statistics, but since we blog about art and literature, I guess it's only fair. Also she links to Ben Goldacre which is a good sign.

P.S. DeWitt responds here to my question.

John posts some anagrams of Qualy:

La fussy jade laity requited,

Edify equity, readjusts...la-la.

Eyeful stye, radial? Just quaid.

Rad, sad eel, justify equality.

Just quaid, indeed. I couldn't of said it better myself.

Chris Paulse sends in this amusing advice which could be used as an example in teaching decision analysis.

When preparing our GSS survey questions on social and political polarization, one of our questions was, "How many people do you know who have a second home?" This was supposed to help us measure social stratification by wealth--we figured people might know if their friends had a second home, even if they didn't know the values of their friends' assets. But we had a problem--a lot of the positive responses seemed to be coming from people who knew immigrants who had a home back in their original countries. Interesting, but not what we were trying to measure.

Chris sent in this quote from Bill James:

"All research," he says, "begins with ignorance. The ability to focus on what it is that you do not know is critical to doing research. I'm absolutely convinced that none of us understands the world.

"I'm not a person that the world irritates, to quote Bill Buckley, but you turn on the radio and in any debate, you've got people who are convinced they know. Liberals, conservatives, Christians, Muslims, people who think Terry Francona is a genius, those that think he's an idiot. They're all convinced they've got this figured out.

"None of them has it figured out. We do not understand the world; the world is billions of times more complicated than our minds.

"You can make a useful contribution to a discussion if you can figure out specifically what it is you don't understand and try to work on it. If you try to start from the other end - 'I've got the world figured out and I'm going to explain it to everybody' - maybe there are a lot of people who succeed in doing that, but it doesn't work for me."

I agree. As Earl Weaver said, it's what you learn after you know it all that counts.

Jim Hammitt sends along this interesting report comparing different measures of risk when evaluating public health options:

There is long-standing debate whether to count "lives saved" or "life-years saved" when evaluating policies to reduce mortality risk. Historically, the two approaches have been applied in different domains. Environmental and transportation policies have often been evaluated using lives saved, while life-years saved has been the preferred metric in other areas of public health including medicine, vaccination, and disease screening. . . Describing environmental, health, and safety interventions as "saving lives" or "saving life-years" can be misleading. . . . Reducing the risk of dying now increases the risk of dying later, so these lives are not saved forever but life-years are gained. . . .

We discuss some of these issues in our article on home radon risks. Beyond this, I have two comments on Jim Hammitt's paper:

1. I wish he'd talked about Qalys. I just like the sound of that word. Qaly, qaly, qaly. (It's pronounced "Qualy")

2. He talks briefly about "willingness to pay." I've always thought this can be a misleading concept. Sometimes it's really "ability to pay." Give someone a lot more money and he or she becomes more able to pay for things, including risk reduction. True, this induces more willingness to pay, but to me the ability is the driving factor. I think the key is what comparison is being made. If you're considering one person and comparing several risks, then the question is, what are you willing to pay for. But if you are considering several people with different financial situations, then the more relevant question might be, who is able to pay.

Andrew C. Thomas suggests that the method of propensity scores has saved thousands of lives due to its use in medical and public health research. This raises the question of how could we measure/estimate the number of lives (or qalys, or whatever) saved by propensity scores. And then, if that could be done, it would make sense to do it in a context where you could estimate the lives saved by other methods (least squares, logistic regression, Kaplan-Meier curves, etc.) This all seems pretty impossible to me--how would you deal with the double-counting problems, also how do you deal with bad methods that are nonetheless popular. (For example, I hate the Wilcoxon rank test--as discussed in one of our books, I'd rather just rank-transform the data (if that is indeed what you want to do) and then run a regression or whatever. But Wilcoxon's probably saved lots of lives.)

If one more generally wanted to ask how many lives have been saved by statistical methods in total, I'd want to restrict to medical and public health. Otherwise you have difficulties, for example, in counting how many lives were saved or lost due to military research in World War II and so forth.

Eric Mazur is my hero (see also here). But I wonder about this abstract:

A growing number of physics teachers are currently turning to instructional technologies such as wireless handheld response systems—colloquially called clickers. Two possible rationales may explain the growing interest in these devices. The first is the presumption that clickers are more effective instructional instruments. The second rationale is somewhat reminiscent of Martin Davis’ declaration when purchasing the Oakland Athletics: “As men get older, the toys get more expensive.” Although personally motivated by both of these rationales, the effectiveness of clickers over inexpensive low-tech flashcards remains questionable. Thus, the first half of this paper presents findings of a classroom study comparing the differences in student learning between a Peer Instruction group using clickers and a Peer Instruction group using flashcards. Having assessed student learning differences, the second half of the paper describes differences in teaching effectiveness between clickers and flashcards.

Is it really the best choice to keep the answer hidden in this way? Suspense is great, but an abstract should tell you the answer, no?

P.S. I tried took a look at the paper but the link didn't work. If anybody finds out whether clickers worked better, please let me know...

From my paper with Delia:

Party identification and self-defined liberalism/conservatism are increasingly correlated with positions on specific issues. The increases in correlations have been highest for moral issues. Issue positions have also become increasingly correlated with each other--but the increases have been smaller than the increased correlations with party ID and liberal/conservative ideology. Correlations between pairs of issues have increased by about 2% per decade, on average, while correlations of issues with party or ideology have increased by about 5% per decade (again, on average). The data come from the National Election Study.

Our story: voters are sorting themselves into parties and ideologies based on their issue attitudes; having done this sorting, they are aligning themselves slightly with their new allies.

I like John Tierney's New York Times column (for example, here), but sometimes he goes over the top in counterintuitiveness.

Here, for example, Tierney writes about someone who says, "in some circumstances it’s better to drive than to walk. . . . If you walk 1.5 miles, Mr. Goodall calculates, and replace those calories by drinking about a cup of milk, the greenhouse emissions connected with that milk (like methane from the dairy farm and carbon dioxide from the delivery truck) are just about equal to the emissions from a typical car making the same trip. . . . Michael Bluejay, who’s done some number-crunching at BicycleUniverse.info, says that walking is actually worse than driving if you replace the calories with food in the standard American diet and if the car gets more than 24 miles per gallon. . . ."

This is interseting to me because these guys are making a classic statistical error, I think, which is to assume that all else is held constant. This is the error that also leads people to misinterpret regression coefficients causally. (See chapters 9 and 10 of our book for discussion of this point.) In this case, the error is to assume that the walker and the driver will be making the same trip. In general, the driver will take longer trips--that's one of the reasons for having a car, that you can easily take longer trips. Anyway, my point is not to get into a long discussion of transportation pricing, just to point out that this seemingly natural calculation is inappropriate because of its mistaken assumption that you can realistically change one predictor, leaving all the others constant.

As we like to say, it's a great classroom example.

P.S. More here (also see discussion in the comments below).

John Cook puts it well:

There’s only one symbol in statistics, "p". The same variable represents everything. You just get used to it and figure out which p is which from context. It reminds me of George Forman naming all five of his sons George. Here’s an example I [Cook] ran across recently where p represents four different functions in one equation:

p(θ | x) = p(x | θ) p(θ) / p(x)

Usually this is done with no explanation, but in the example above the author explains that he’s denoting entirely different functions with the same symbol in order to avoid the “clumsy notation” that being explicit would require.

Sometimes the overloading of the 16th letter of the English alphabet becomes just too much and statisticians break down and use the Greek counterpart, π (pi). So then to make matters even more confusing to the uninitiated, π can be a variable or a function.

He's right, and I say this as someone who's done my part to spread this notation. We talk in Bayesian Data Analysis about how to use this notation and why it's more rigorous than it might seem as first. I really really don't like the notation where people use f for sampling distributions, pi for priors, and L for likelihoods. To me, that really misses the point. The notation shouldn't depend on the order in which the distributions are specified. They're all probability distributions, that's the point.

Rachel and Tyler write:

The Columbia statistics graduate students are excited to announce a Symposium on Careers for PhD's in Statistics on April 4, 2008. In an effort to broaden our exposure to the various possibilities that our distinguished fields affords, we are inviting leaders from academia and industry for a frank discussion of the careers and lifestyles of statisticians.

Doug Hibbs writes:

Presidential election outcomes are well explained by just two objectively measured fundamental determinants: (1) weighted-average growth of per capita real personal disposable income over the term, and (2) cumulative US military fatalities owing to unprovoked, hostile deployments of American armed forces in foreign conflicts not sanctioned by a formal Congressional declaration of war. At the end of 2007 weighted-average growth of real incomes during Bush’s second term stood at 1.1 percent per annum. If the same performance were sustained for the rest of the term it might barely suffice to keep the Republicans in the White House, other things being equal. However the economy slid into recession at the beginning of the year and per capita real incomes will most likely decline throughout 2008. Moreover, by Election Day cumulative US military fatalities in Iraq will approach 4,500 and this will depress the incumbent vote by more than three-quarters of a percentage point. Given those fundamental conditions the Bread and Peace model predicts a Republican two-party vote share of 46-47% and therefore a comfortable victory for the Democrats in the 2008 presidential election.

Here are the basic data from Hibbs's bread-and-peace model:

or this:

See Hibbs's latest paper for details on his 2008 forecast.

I asked,

I'm writing a book about rich and poor voters in red and blue states, and one thing we've found is that the political differences between so-called red and blue states are much larger among the rich than the poor (or, more precisely, comparing high and low income, since we don't really have measures of "rich" and "poor" in our surveys). Anyway, the point is that the famed Red America / Blue America distinction is among the rich, not the poor.

But, in other ways, it's poorer people who are more localized: lower-income people generally travel less, are more likely to have local accents, and are less likely to know people in other parts of the country.

Well, that's what I think, but I don't really know. Do you happen to know if there have been studies supporting my claim that lower income people are more likely to have local accents?

Mark Liberman replied:

I've often read that "lower income people are more likely to have local accents", as you put it.

For example, Jenny Cheshire and Peter Trudgill, "Dialect and education in the United Kingdom", in Jenny Cheshire, ed., _Dialect and Education_ (1989), starts like this:

In Great Britain and Northern Ireland, as in many other countries, the relationship between social and regional language varieties is such that the greatest degree of regional differentiation is found among lower working-class speakers and the smallest degree at the other end of the social scale, among speakers from the upper middle class.

However, I don't know any research that evaluates this generalization in quantitative terms. (That doesn't mean there isn't any.) And the situation in the United States is probably somewhat different in this respect from the situation in Great Britain, if only because African-American speakers are (I think) less geographically variable in accent than other groups, while also being disproportionately distributed towards the lower end of the S.E.S. scale.

With respect to the more general social-networking questions -- "lower-income people generally travel less, ... and are less likely to know people in other parts of the country" -- again, it seems to me that the historical situation in the U.S. is somewhat different from the British experience. When the draft was in effect, the army to some extent played the role among the poor that elite education playedamong the rich. And there have been large population movements in relatively recent times -- the general migration of farm labor to the cities, and specifically the movement of rural southern blacks; the Okie migration to California, Chicago etc.; the post-WWII migration from the rust belt to the sun belt -- that have involved poorer people at least as much as richer people.

I suspect that it remains true in the U.S. that on average, lower-income people are more likely to have local accents. They are certainly -- pretty much by definition -- more likely to have speech patterns that are perceived as in some way non-standard. But this is not always the same thing. Thus "g-dropping" is other things equal more common for lower-SES speakers -- however, this is true more or less all over the English-speaking world.

Thanks!

P.S. I wanted to call this "Will the real townies please stand up, stand up?" but I was afraid that Mark L. would accuse me of snowcloning.

Thomas Ferguson and Hans-Joachim Voth write:

From Indonesia and Malaysia to Italy, politically connected firms are more valuable than their less fortunate competitors. Yet a key event in the history of the twentieth century has not been examined in terms of the value of political connections—the Nazi rise to power. We systematically assess the value of prior ties with the new regime in 1933. To do so, we [Ferguson and Voth] combine two new data series: A new series of monthly stock prices, collected from official publications of the Berlin stock exchange, and a second series that uses hitherto unused contemporary data sources, in combination with previous scholarship, to pin down ties between big business and the Nazis. . . .

Drawing on previously unused contemporary sources about management and supervisory board composition and stock returns, we find that one out of seven firms, and a large proportion of the biggest companies, had substantive links with the National Socialist German Workers’ Party. Firms supporting the Nazi movement experienced unusually high returns, outperforming unconnected ones by 5% to 8% between January and March 1933. . . .

By international standards, the value of connections with the Nazi party was unusually high. Comparison with the results of Faccio (2006) suggests that in her sample of 47 countries from around the globe, only Third World countries with poor governance showed similarly high returns. Also, associations with the NSDAP were formed voluntarily, not through family links; also, they were not in place decades before their political value became apparent, as in many Third World countries. One question for future research is how many of these connections turned out to be valuable in the end and through which channels the party rewarded its supporters. Though some businessmen felt that the donations were large, their value was small compared to the rise in stock market value of connected firms. Interestingly, even recently formed affiliations such as those resulting from the fundraising party in Berlin on February 20, 1933, appear to have boosted firms’ fortunes on the stock market. Returns were not arbitraged away by many other firms entering the fray. This suggests that Hitler’s rise to power may have come as a genuine surprise to many, that an ideological distaste for his party kept numerous businessmen from contributing, or that NSDAP representatives deliberately focused their attention on a subgroup of sympathetic business contacts.

Interesting stuff. Certainly not what you usually see in the history books.

David Kane writes,

What is the best way to simulate from a distribution for which you know only the 5th, 50th and 95th percentile along with the mean? In particular, I want to estimate the value for a different percentile (usually around the 40th) and associated confidence interval. I assume that the distribution is "smooth" and unimodal. For background, see here.

(From Kaiser)

P.S. I fixed the mistake in title of blog entry. Anyway, I still think bananas are easier than pears. Although, it's true that you have to take care of bananas so they don't get bruised.

Steven Levitt writes, "I wish that I was teaching intermediate microeconomics this term, because this would be a perfect exam question."

I have mixed feelings about cool exam questions. I used to put effort into making my exams really cool, but a few years ago I decided that it wasn't always clear to the students what they were expected to learn in my classes, so I switched to writing non-clever exams that more directly addressed key points in the course. I expect that the optimal exam depends on how the course is organized. (Also, of course, different exams are good for different students. Presumably clever exams are great for the top students.)

For intro statistics, I wish we used standardized tests so we could have a better sense of what (if anything) the kids are learning during the semester. Also, pre-tests at the beginning of the semester. The whole deal.

After reading Steve Sailer's discussion of unmarried Democrats living in crowded cities and Republicans with large families, we decide that the ultimate predictor of political leanings would be . . . square footage of your residence. It has all the right properties:

- Within any state, people in bigger houses vote more Republican. Check.

- Lower cost-of-living states, where houses are bigger (I assume), are more Republican. Check.

- In crowded coastal states, there is little difference in square footage between the houses of the rich and the poor; in less-crowded, poorer inland states, rich and poor differ more in house size. As a result, the "square footage" model predicts that the rich-poor gap in Republican voting should be larger in poor than in rich states. Check.

I don't know of any datasets that have voting or party ID along with square footage--although, with a large amount of effort it should be possible to put something together using public voter registration information. Also, I can't really see anything useful about the hypothesis (that square footage is an excellent predictor of who you vote for), even if it's true. Nonetheless, the idea amuses me.

P.S. Seeing as I live in a cramped NYC apartment with no understanding of square footage at all, so I'd appreciate others' input on this. (Also, I have no idea how this would work in other countries.)

It seems strange to say that presenting data without explanations is tabloid science. I think of "tabloid-like" as going the other way: theories without data.

From a survey of voters in the 2000 election, the estimated percentage of people they talk politics with who supported Bush for president:

Each respondent was asked to name up to four contacts. On average, each respondent discussed politics with 0.5 family members and 1.4 others. The two plots show separate estimates for the two groups. The top, middle, and bottom lines on each plot show the results for Gore and Bush voters in strongly Republican, battleground, and strongly Democratic states, respectively.

Unsurprisingly, Gore voters were much more likely to know Gore voters and the reverse for Bush voters. The differences between red, blue, and purple states are tiny among family members (about three-quarters of whom share the political affiliation of the survey respondent) but are larger for friends. On average, Bush voters perceived their non-family conversation partners to be more similar to themselves, compared to the perceptions of Gore voters.

(Thanks to Christian Logan for crunching the numbers from the National Election Study.)

Here's the graph that David made showing the Republican share of the two-party vote for president since 1940, for states in the upper third and lower third of per-capita income:

It used to be that rich states voted Republican, now they go for the Democrats (the famous red-blue map). The voting gap between rich and poor states has gradually widened since the early 1980s.

And here's the plot comparing upper and lower income voters:

Rich people are much more Republican than poor people. Differences in voting by income have returned to 1940s levels.

Pulling out the South

We also did separate analyses for southern and non-southern states, since the South is poorer than average and has also moved steadily from the Democrats to the Republicans over the decades. First, a plot showing the difference between rich and poor states over time, overall and in southern and non-southern states:

And now the differences each year between rich and poor voters in the country as a whole and in south and non-south:

Data issues

We used the Republican share of the two-party vote (for the state analysis in 1948, including Thurmond's votes as part of the Democrats'). The state election data are public information and easy to find, for example from David Leip's atlas.

For each election year, we defined rich and poor states in each election year as follows. We first sorted the states by per-capita income using data (from the Census, I think) that Justin Phillips gave us. We then aggregated by population from the top down and the bottom up, to construct a collection of states at the high end whose total population approximated 1/3 of the U.S. population in that year, and similarly for the low end. We rounded down to get rich state and poor state groupings that each had no more than 1/3 the population for that year.

When making the plots for states, we pooled the popular vote within each grouping (rich states and poor states) in each year. For individuals, we took the respondents from the National Election Study (since 1952) and data from Gallup polls prepared for us by Adam Berinsky and Tiffany Washburn (for 1940 and 1944). We don't have individual level data for 1948, since our National Election Study data didn't have state identifiers for respondents in that year.

I'm always worried about using too much jargon when labeling my graphs, but I don't think I'll ever be able to top this title:

"Figure 5-9: Annual Intersextile Ranges in Budget Authority for Domestic Subfunctions, Fiscal Years 1951-2005"

I like the "fiscal years" bit--it's a nice touch.

P.S. The actual content in the graph is interesting and important--as the author (Eric Patashnik) notes in the text, "year-to-year variability [in discretionary government spending on domestic items] declined significantly between the 1950s and the mid-1980s." It's all good stuff, just an amusingly jargon-laden title.

Carp pointed me to this article by Mark Liberman. I'm more sympathetic to David Brooks than Mark is, but I have to say, I thought this was funny:

Alex F. commented here about problems with our Starbucks and Walmart data. Elizabeth Kaplan, who collected the data for me, replied:

Yeah Walmart was a bit of a pain to find the locations for as you can not search just by state on their website, like for Starbucks. In order to find the locations I relied on the yellow page results. Even though I looked through to eliminate double postings for walmarts with the same address, after I looked into it again tonight, it appears the yellow pages dramatically over represented the number of walmarts per state. I have attached the correct data. All of these numbers come from this website (http://www.walmartfacts.com/StateByState/) which I was unable to locate before.

As far as the data for starbucks that should be correct as I got it straight from their website. The one thing is that they don't list all affiliate stores (that is stores not own and operated by the company). There is no reliable source of data on affiliate stores by state, and obviously the yellow pages are not a good source. So the data I sent to you just includes Starbucks owned and operated stores.

Also for population I used the 2006 Census Bureau estimates.

This sort of thing happens all the time to me, so I certainly don't think Elizabeth should feel too bad about this. I'm just glad that Alex noticed and pointed out the problem. Anyway, here are the corrected maps:

and scatterplot:

And also, following Seth's suggestion, the scatterplot on the log scale:

And, following Kaiser's suggestion, a reparameterization showing people per store (rather than stores per million people):