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2afc Analysis Essay

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Analysis: Shaky Patriots beaten up, fall to No

Jeff Howe Sunday, January 03, 2016

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Credit: Matt Stone

(Miami Gardens, FL, 01/03/16) New England Patriots offensive tackle Cameron Fleming looks down at quarterback Tom Brady after he went down hard during the second quarter of the NFL game against the Miami Dolphins at Sun Life Stadium on January 03, 2016. Staff photo by Matt Stone

Credit: Associated Press

New England Patriots quarterback Tom Brady (12) sits in the sidelines during the first half of an NFL football game against the Miami Dolphins, Sunday, Jan. 3, 2016 in Miami Gardens, Fla. (AP Photo/Lynne Sladky)

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MIAMI GARDENS, Fla. — The Dolphins beat the Patriots, 20-10, today at Sun Life Stadium, so the Pats' regular season has ended with four losses in their last six games.

The Patriots (12-4) will have to settle for the No. 2 seed in the AFC, as the Broncos took the top spot with their win over the Chargers. Here's how it all went down.

1. Tom Brady survived a second-quarter injury scare when Ndamukong Suh rolled onto the quarterback’s right ankle after an incompletion. Brady hobbled to the sideline and received a brief amount of medical attention before the trainers left him alone, and Brady resumed studying play sheets with Josh McDaniels. But Brady still reached down for the ankle a couple times, so he tried to walk it off before sitting on the defensive bench to get re-taped by trainer Jim Whalen. Brady resumed throwing after that and took the field without missing a snap on the next possession.

2. The Patriots were extremely conservative on offense. They ran the ball on eight of nine plays in the first quarter, including all six plays of their second possession, but it didn’t exactly get them anywhere with just 21 rushing yards and no points. Their running backs finished the first half with 20 carries for 63 yards, and Brady was 4-of-5 for 20 yards as the Pats fell behind, 10-3. It was the fewest first-half passes Brady had ever thrown in his career. Steven Jackson had 10 carries for 28 yards, and Brandon Bolden chipped in with eight runs for 31 yards. The Patriots showed very little willingness to put Brady in harm's way on a consistent basis.

3. The Dolphins weren't exactly an offensive machine, but they took advantage of their two best opportunities. Greg Jennings lost Leonard Johnson down the left sideline for a 31-yard gain to the Pats’ 15-yard line with 52 seconds remaining in the first half, and DeVante Parker got through Johnson's zone to beat Devin McCourty to the corner of the end zone for a 15-yard touchdown and a 10-3 lead. And in the fourth quarter, Parker outjumped Logan Ryan for a 46-yard catch down the right sideline to the Pats' 6. Two plays later, Jordan Cameron beat McCourty through a screen for a 2-yard touchdown and 17-10 advantage.

4. Once the Patriots decided to open it up in the second half, Brady was harassed too frequently. It started in the third quarter with Olivier Vernon’s cheap shot into Brady’s back, which drew a roughing penalty, but Vernon hit Brady twice more on the drive. Then in the fourth, when the Pats took over down, 17-10, Brady was sacked twice in three plays. With an undermanned roster and an apparently short playbook in the first half, the Patriots couldn't turn it on when necessary. Their only touchdown drive was keyed by James White's 68-yard reception on third-and-4, which set up Jackson's 2-yard scoring plunge to open the third quarter.

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Consequences of an improper link function in N alternative forced choice procedures (e

Background: In some cognitive psychology research areas N-alternative forced choice tasks are common. The most common of these is a two alternative forced choice (2AFC). This usually takes the form of participants being given a stimulus and asked to make one of two judgement, e.g. the target stimuli is present/absent, the stimulus on the left is the same/different than the the one on the right, etc. Designs in which the experimental data is from a 2AFC but there is only one data point per subject are rare, but do exist, e.g. some eye-witness identification research. Since the dependent variable (correct/incorrect) is binary, these experiments are reasonable places to use logistic regression.

My question is this: since chance performance is 50% in a 2AFC trial, is it still reasonable to use the standard logistic link function? Specifically, the logistic function has a minimum value approaching 0% correct, but in practice participants in a 2AFC should be correct at least 50% of the time due to chance. I imagine the following case in which it may present a problem: an independent variable is assessing the difficulty of the discrimination (e.g. difficulty 1, easy - 5, hard; please note this is introduced in ordinal terms only for ease of comprehension - for the sake of this discussion consider this variable as being interval) - participants got 50% correct at 5 and 4, 75% correct at 3, 85% correct at 2, and 99% correct at 1. Would using a standard logistic link function cause us to underestimate the slope? [I think so, but please correct me if I'm wrong, see below]

Edit: Those who have answered my question so far have expressed that the way in which I set up the problem was unclear. I'm providing the sample below to help clear things up.

In the above image the orange horizontal line marks 50% correct responses. The jagged black line represents the data supplied to the estimation equation (note the values for 4 and 5 disappear behind the orange 50% marker). The blue line is the equation produced by a standard logistic link. Note that it estimates below 50% accuracy when discrimination is most difficult (5). The cyan line is the standard logistic link with a quadratic term. The green line is a non-standard link that takes into account that the data comes from a 2AFC experiment where performance is very unlikely to fall below 50%. Note that the AIC for a model fit using a non-standard link function is superior to the standard logistic link function. Also note that the slope for the standard equation is less than the slope for the standard equation with the quadratic term (which more accurately reflects the real data). Thus, using a logistic function blindly on 2AFC data does (at least) appear to underestimate the slope.

Is there a problem with my demonstration that means that I am not seeing what I think I am seeing? If I'm correct, then what other consequences (if any) are there of using the generic logistic function with 2AFC data [presumably extensible to NAFC cases]?

asked Aug 8 '10 at 18:10

My question is this: since chance performance is 50% in a 2AFC trial, is it still reasonable to use the standard logistic link function?

Think of it this way: suppose you fit a logistic regression where your $y$ variable takes value 1 if subject i has flue, 0 otherwise.

So long as neither $y_i=1$ nor $y_i=0$ are rare events, then flue incidence (i.e. $n^<-1>\sum_^ny_i$) is not relevant, it will be absorbed by the intercept of your model.

but in practice participants in a 2AFC should be correct 50% of the time due to chance

if this statement is true and all your exogenous variables have been de-meaned, then, you can expect your estimated constant to be $logit^<-1>(0.5)\approx0.05$

I'm not sure I understand your answer. I think you are saying I do not need to specify a link function because the intercept of my model will adjust based on the data and effectively account for the fact that at high difficulties people will not be able to perform the task. Is that correct? If so, how does this prevent a flattening of the slope estimate due to the same values at difficulties 4 and 5? I may need a less technical explanation (if possible). – rpierce Aug 8 '10 at 18:40

I'm not sure I understand your answer. Is that correct? yes The limitation with the logit is one of symmetry; going back to your example, you force the slope between 4 and 5 to be the same as the slope between 1 and 2. If symmetry is a problem, you might want to try a complementary log-log link (not implemented in LMER). – user603 Aug 8 '10 at 20:09

I don't see how the question in your example is sensible. The slope of the values is the slope of the values. Using a logistic link function then you get the slope of the logit of the values. There's no under or overestimating.

The more interesting case in your (our) field is that of interactions in accuracy. You might want to read Dixon (2008) as one of the more recent papers on this problem. It also addresses many of your fundamental concerns.

In general, in cognitive and perceptual psychology a logit link function is better than any other standard link. If you want to know the true effects of your independent variables, (i.e. whether they interact or are additive, whether they are linear or curvilinear) then you would need to know better the true underlying model. Since you probably don't know that logistic regression is probably better than almost anything else and vastly better than just analyzing meaned accuracy scores.

The primary consequence of doing this is contradicting other findings where mean accuracy scores were put into an ANOVA or regression.

Now that you've added some data it looks like you're trying to model a floor effect that you shouldn't be. At some point the task becomes impossible. It looks like that already happened at your level 4 difficulty. Modelling level 5 is useless. What if you had a level 6 or 7 difficulty?

It looks like a logistic will fit points 1-4 pretty well.

And, you should be looking at residuals to assess fit, not just the curves overlaid.

answered Aug 8 '10 at 21:57

The example is a case where a single predictor linear equation, though rationally sound given the dataset, will provide a suboptimal solution to the problem. If in the example case you fit a quadratic as well you'd likely get an improved model fit would you not? The improved model fit wouldn't be a consequence of some underlying real quadratic effect of the IV, just that you'd hit a measurement floor. – rpierce Aug 8 '10 at 22:06

I'll take a look at Dixon - thanks for the reference - it looks right up my alley. The alternative link I was imagining was an explicitly 2AFC link, e.g. mafc.logit(2) in the psyphy package of R. – rpierce Aug 8 '10 at 22:14

As to your first comment, I see that you have a good answer about how to look at the residuals from another posted question but you still don't have why. AIC, log-likelihood, etc. all tell you how good you fit is but they don't tell you the nature of the fit. it's like comparing SD and histograms for looking at variability. They both tell you about variability. – John Aug 9 '10 at 12:22

How To Fix DirectAccess Error 0x2AFC

How To Fix DirectAccess Error 0x2AFC Symptoms of Error 0x2AFC
  • "Error 0x2AFC" appears and crashes the active program window.
  • Your PC frequently crashes with Error 0x2AFC when running the same program.
  • “Direct Access Error 0X2Afc” is displayed.
  • Windows runs sluggishly and responds slowly to mouse or keyboard input.
  • Your computer periodically “freezes” for a few seconds at a time.

These 0x2AFC error messages can appear during program installation, while a Microsoft Corporation-related software program (eg. DirectAccess) is running, during Windows startup or shutdown, or even during the installation of the Windows operating system. Keeping track of when and where your 0x2AFC error occurs is a critical piece of information in troubleshooting the problem.

Causes of Error 0x2AFC
  • Corrupt download or incomplete installation of DirectAccess software.
  • Corruption in Windows registry from a recent DirectAccess-related software change (install or uninstall).
  • Virus or malware infection that has corrupted Windows system files or DirectAccess-related program files.
  • Another program maliciously or mistakenly deleted DirectAccess-related files.

Runtime Errors such as “Error 0x2AFC” can be caused by a variety of factors, so it is important that you troubleshoot each of the possible causes to prevent it from recurring.

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How To Fix DirectAccess Error 0x2AFC

Below is a list of troubleshooting steps to resolve your Error 0x2AFC problems. These troubleshooting steps get progressively more difficult and time consuming, so we strongly recommend attempting them in ascending order to avoid unnecessary time and effort.

Please Note: Click the [ ] image to expand the troubleshooting instructions for each step below. You can also click the [ ] image to hide the instructions as you proceed through each step.

Step 1: Repair Registry Entries Associated with Error 0x2AFC

Manually editing the Windows registry to remove invalid Error 0x2AFC keys is not recommended unless you are PC service professional. Incorrectly editing your registry can stop your PC from functioning and create irreversible damage to your operating system. In fact, one misplaced comma can prevent your PC from booting entirely!

Because of this risk, we highly recommend using a trusted registry cleaner such as WinThruster (Developed by Microsoft Gold Certified Partner) to scan and repair any Error 0x2AFC-related registry problems. Using a registry cleaner automates the process of finding invalid registry entries, missing file references (like the one causing your 0x2AFC error), and broken links within the registry. A backup is automatically created before each scan, with the ability to undo any changes in a single click, protecting you against the possibility of PC damage. The best part is that repairing registry errors can also dramatically improve system speed and performance.

Caution: Unless you an advanced PC user, we DO NOT recommend editing the Windows registry manually. Using Registry Editor incorrectly can cause serious problems that may require you to reinstall Windows. We do not guarantee that problems resulting from the incorrect use of Registry Editor can be solved. Use Registry Editor at your own risk.

To manually repair your Windows registry, first you need to create a backup by exporting a portion of the registry related to Error 0x2AFC (eg. DirectAccess):

  1. Click the Start button.
  2. Type "command " in the search box. DO NOT hit ENTER yet!
  3. While holding CTRL-Shift on your keyboard, hit ENTER .
  4. You will be prompted with a permission dialog box.
  5. Click Yes .
  6. A black box will open with a blinking cursor.
  7. Type "regedit " and hit ENTER .
  8. In the Registry Editor, select the Error 0x2AFC-related key (eg. DirectAccess) you want to back up.
  9. From the File menu, choose Export .
  10. In the Save In list, select the folder where you want to save the DirectAccess backup key.
  11. In the File Name box, type a name for your backup file, such as "DirectAccess Backup".
  12. In the Export Range box, be sure that "Selected branch " is selected.
  13. Click Save .
  14. The file is then saved with a .reg file extension .
  15. You now have a backup of your DirectAccess-related registry entry.

The next steps in manually editing your registry will not be discussed in this article due to the high risk of damaging your system. If you would like to learn more about manual registry editing, please see the links below.

We do not claim any responsibility for the results of the actions taken from the content linked below - complete these tasks at your own risk.

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Lunch with the FT: Noam Chomsky

Lunch with the FT: Noam Chomsky

There is a time capsule near the lifts of the Stata Center at the Massachusetts Institute of Technology. It contains items from Building 20, home to fundamental wartime advances in physics, and where, in 1955, a 27-year-old began to transform humanity’s understanding of language. The original ramshackle facility is no more. But the linguist is still here, strolling past in a mustard-coloured puffer jacket.

“Professor Chomsky,” I call out. The 84-year-old greets me and we walk through the new Frank Gehry-designed building, all airy and angular. Students smile and wave and give up more space than Chomsky’s steady gait requires. MIT is in part a monument to his ideas, I suggest. His theories of grammar, which argue that language is innate, have revolutionised modern psychology, computing and cognitive science.

“One of the things about this field is that there’s not a lot you can do with it,” he deadpans, as we pass sleep-deprived coders. (Another example of Chomsky humour: he calls his assistant’s dog, “Cat”.) We step out into the bitter Cambridge day, towards the restaurant. He once came close to joining UC Berkeley, he admits, but California is too hot for him. “I like the cold weather. It means you get work done.”

I tell him I felt the same way when I studied at Harvard. “[Its] faculty doesn’t like me much,” he says. This is not true of the staff of Chomsky’s chosen lunch spot. The Black Sheep welcomes him like the regular he is. A chipper waiter shows us to a table in the corner of the cosy bistro. Perhaps the restaurant’s name is apt, I say. “Not at MIT [but] I don’t have much contact with the main academic world.”

However, Chomsky’s distance from the mainstream is not down to his academic work. Referring to him as a linguist is a bit like calling Arnold Schwarz­enegger a bodybuilder. Chomsky is arguably the world’s most prominent political activist. To his opponents, he is a crank who sees evil as made in America. To his supporters, he is a brave truth-teller and unrelenting huma­nist; a latter-day Bertrand Russell.

I am about to ask the professor about Hugo Chávez. who died the night before our lunch, but a waitress arrives and asks for our order. Chomsky chooses the clam chowder, and a salad with pecans, blue cheese, apples and a lot of adjectives. I go for tomato soup and a salmon salad. The professor asks for a cup of coffee and since we are about to discuss the late Venezuelan leader, I ask for a cup, too.

In 2006, Chávez recommended Chomsky’s Hegemony or Survival: America’s Quest for Global Dominance to the UN General Assembly. “It’s a mixed story,” Chomsky says of Chávez’s legacy. He points to reduced poverty and increased literacy. “On the other hand there are plenty of problems,” such as violence and police corruption; he also mentions western hostility – in particular an attempted coup in 2002 supported by the US. America’s behaviour towards Caracas is obviously important in any assessment of Chávez but its appearance is an early signifier of a pattern in a Chomsky conversation: talk for long enough about politics with the professor and the probability of US foreign policy or National Socialism being mentioned approaches one.

I say that he hasn’t referred to Chávez’s human rights record. Some of Chomsky’s critics have accused him of going easy on the faults of autocrats so long as they are enemies of the US. Chomsky denies this vehemently: he spoke out against the consolidation of power by the state broadcaster; he protested the case of María Lourdes Afiuni, a judge who spent more than a year in prison awaiting trial for releasing a government critic. “And I do a million cases like that one.”

As part of celebrations to mark the FT’s 125th anniversary this year, Penguin is publishing Lunch with the FT: 52 Classic Interviews. The book, served up with glorious colour cartoons, is available as hardback and ebook www.ft.com/lunchbook

Still, Chomsky thinks about how hard to hit his targets. He admits as much as our soups arrive. “Suppose I criticise Iran. What impact does that have? The only impact it has is in fortifying those who want to carry out policies I don’t agree with, like bombing.” He argues that any criticisms about, say, Chávez, will invariably get into the mainstream media, whereas those he makes about the US will go unreported. This unfair treatment is the dissident’s lot, according to Chomsky. Intellectuals like to think of themselves as iconoclasts, he says. “But you take a look through history and it’s the exact opposite. The respected intellectuals are those who conform and serve power interests.”

In 1967 the New York Review of Books published “The Responsibilities of Intellectuals”. a dazzling essay by the then 38-year-old Chomsky. In it he denounced the subservience to power of the Washington intellectual elite. Today he still concentrates his ire on the US on the grounds that it has the most power and he is an American citizen. This makes sense, I say, but doesn’t his position in another community, the anti-war left, mean he also has a duty to call out wrongdoing by its figureheads?

“Maybe some, small percentage should be concerned with that community. But nowhere near the [percentage concerned with the] responsibility for [American] state power and mass media.”

Chomsky has said that, if judged against the principles set out at the Nuremberg Trials, every postwar US leader would be found guilty of war crimes. I ask for his views on Barack Obama. What of the president who opposed the Iraq war? “He’s carrying out a global assassination campaign.” Here is vintage Chomsky, a provocative idea in a matter-of-fact tone, daring the interlocutor to respond. I take the bait, and ask him to explain. “Suppose that some German, Nazi official had been carrying out a global assassination campaign in the west, that would have qualified at Nuremberg.”

Although we are both still slurping soup, the waitress brings us our main courses. This seems like a cue to take a break from war crimes. In an effort to spur reflection I ask whether he feels he has lived up to the standards he set out in his essay in the NYRB all those years ago? “Not really,” he says. “There are a lot of things I should have done more.” He says he began resisting western involvement in Vietnam a decade too late and “that’s only one case”. He wishes he could do more: in eastern Congo, Sri Lanka and on climate change. for instance.

Almost everything, even personal reflections, it seems, comes back to politics. Chomsky has evidently taken to heart Marx’s dictum about the role of the philosopher (“philosophers have only interpreted the world. The point, however, is to change it”). But does he wish he spent more time doing pure research? “What actually goes is not academia, it’s personal life.” He spends six or seven hours a day answering emails, which leaves little time for hobbies.

“The one thing I’ve found all the way through is to keep time for family.” He has three children, five grandchildren, all of whom are now adults, and a great-grandson who occasionally plays with the restaurant’s toy fire engines. Carol Chomsky, his wife and a fellow linguist, died in 2008. “Since then I’ve dived into work.” I ask whether this was a deliberate, escapist decision. After a rare pause, he says: “Well, John Milton pointed out that the mind is a strange place, so who knows?”

I take the hint and ask about the food. “It’s always good here. I’m not a great gourmet but this is the one place I ever go to.” Like MIT, it is familiar and friendly. “I even get a free drink when I come in the evening.” His tipple is a gin and tonic. Isn’t that an awfully colonial cocktail? “Well, British colonial,” he says, pointing to himself, “I’m a good American.”

Just then, a woman who was seated at the next table comes over, says, “Thank you, so much,” and walks away. Chomsky’s reaction is calm; his bold features don’t flinch under his impressive white mop of hair. “I don’t know who she is,” he says. I tell him he is a celebrity. “It’s a small place.”

The food here is very different from the helpings served by Chomsky’s mother, an immigrant from Belarus, to Noam and his Ukranian-born father, in their home in Philadelphia. Chomsky remembers it fondly, though “by today’s standards, everyone would say it is poison: east European greasy meat, sour cream.”

I ask about his upbringing – did the political drive come before the academic imagination? “Yes, from childhood.” Before he was a teenager he was writing for the school newspaper about the spread of fascism in Europe. “It was pretty scary. My parents would put Hitler’s Nuremberg rally speeches on the radio. I couldn’t understand a word.”

His story reminds me, I say, of the start of Philip Roth’s The Plot Against America. which imagines the repercussions for a Jewish family of a Charles Lindbergh victory in the presidential election of 1940. “It was pretty close to that,” Chomsky says. Which brings me to another criticism of Chomsky, voiced by those such as the late British-born journalist Christopher Hitchens – that opposing the war in Iraq, which began almost exactly 10 years ago. represented the appeasement of a modern-day fascist, Saddam Hussein. “Of course not. If you think he was in the same ballpark as Hitler then you have got to condemn Reagan and Bush number one because they pretty strongly supported him.”

The professor launches into the case for the prosecution. Readers of his book 9/11: Was There an Alternative? will be familiar with his style of argument: to contrast an event perpetrated by an enemy of the US, such as al-Qaeda on September 11, 2001, with an event involving the US, such as the overthrow of President Salvador Allende in Chile on September 11, 1973.

“Just do a simple thought experiment about what we call September 11. Imagine that the plane that was downed in Pennsylvania hit its target, which was probably the White House. And suppose it had killed the president, set off a military coup, which had been planned, which overthrew the government, murdered a couple of thousand people, tortured tens of thousands, and established an international terrorist centre that was helping install neo-Nazi governments throughout the region, carrying out assassinations. It would have been a lot worse than 9/11. Indisputable. And the fact that we can’t see it is a comment on western society and culture.”

The field of comparative massacre makes me feel rather uneasy: the professor’s example implies there is a moral equivalence, I say, between the US and al-Qaeda, and it underplays the responsibility of General Pinochet for the years of oppression that took place after the coup.

“When I compare the two, it isn’t in terms of responsibility, it was in terms of the nature of the atrocity,” he says. “Separate to that comes the question of responsibility. There was no American who sent the planes to kill the [Chilean] president but the US did what it could do to implement the coup.”

We are already running over our scheduled time for lunch. Chomsky has a student waiting, so I skip a few planned questions and ask the one that has been most puzzling in my effort to understand his work. What, if any, is the connection between his academic research and his activism? There seems to be a missing link, I say.

“It has to do with: ‘what is the fundamental core of human nature?’ ” Early Enlightenment thinkers wrote about how it is creative character that separates humans from the rest of the organic world. This character is manifested most clearly in language. Later intellectuals extended this idea to the social sphere. “So, if there is anything that restricts a person’s natural need to carry out creative work under their own direction, that is illegitimate.”

As we get up from the table I ask whether he will always be creatively working. “While I’m upright: there’s a lot to do.”

Does he think about death? “I used to when I was a child. I thought it was terrifying but I got over that stage.”

I explain to Chomsky that the FT picks up the bill. “Brenda Anderson took care of your cheque,” says the waitress. The name isn’t familiar and I suggest to Chomsky that this is probably breaking some kind of rule. “It’s a wonderful place,” he says, unsurprisingly unworried about rule-breaking. He leaves the restaurant before I can find Ms Anderson, who it later turns out is the general manager. “Well, you can go back and give them a big tip. They’re nice people.”

On the way back to the new MIT building, Chomsky points out that his office now looks out on to the Koch building, named after the billionaire brothers and Tea Party supporters. “They’re a lethal force,” he says. What about the Lockheed Martin classroom, I ask, which we pass in the foyer. “I’ve managed to avoid it so far.” He explains that when he joined MIT it was nearly 100 per cent Pentagon-funded “but our lab was also one of the main centres for the anti-war resistance movement”.

We reach the time capsule. What do you think a future historian will write about you, I ask. “I think he’ll have more important topics to write about,” Chomsky says, before warmly greeting the student and apologising for his lateness.

Professor Noam Chomsky will be delivering the 2013 Edward W Said London Lecture, programmed by AM Qattan Foundation/The Mosaic Rooms, on March 18 at 7pm; www.mosaicrooms.org

John McDermott is the FT’s executive comment editor

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