5 ms·

OK, I think I'm missing something. To quote the article: > And no, you can not get around this problem by doing a multivariate regression of speed on gas pedal

by eykanal 14y ago

OK, I think I'm missing something. To quote the article: > And no, you can not get around this problem by doing a multivariate regression of speed on gas pedal and hill. That's because gas pedal and hill will be perfectly colinear. This is one of the reasons why you check for multicollinearity [1] when performing multivariate linear regressions; aside from introducing significant instability into the model, if your predictors are correlated, then you're essentially measuring the same thing twice. The stated problem is actually a good example as to why you should avoid having highly correlated predictors in a multivariate model; by blindly pursuing the regression despite the inputs being correlated, we miss out on the fact that there is a relationship present (i.e., the dependent variable (speed) is actually a factor of both of the independent variables (pedal height and hill slope)). [1]: http://en.wikipedia.org/wiki/Multicollinearity http://en.wikipedia.org/wiki/Multicollinearity

Irregardless 14y ago
Sounds like the nail in the coffin on this topic. It always sucks when you accuse an entire profession of overlooking a fundamental principle, only to find out you've committed the same error in a more egregious fashion.
cynicalkane 14y ago
You aren't missing anything. The author's article isn't about the optimal ways to do statistics, it's a criticism of the informal economic discussion that dominates policy, blogs, and pop-economics--and, according to the post, an unfortunate number of actual econ papers--that says things like "economic plan X doesn't work because there hasn't been a change". The criticism generalizes to any statistical methods, though. You always need to think about the underlying model before doing any kind of statistics in any science.
- chimeracoder 14y ago
  Yes, but I wouldn't say that "almost all" economists don't understand the principle (as in the title). I would be more likely to say that "almost all" reporters don't understand basic economics & statistics.
  - babblingdweeb 14y ago
    THIS. The problem lies with reporters lacking the basic econmic and statistical background to either report the news and/or challange others they are interviewing. We are often surrounded by "armchair specialists" who know little about what they are talking about, yet carry large opinions about said topic. I'm all for constructive discourse, but that seems like a rare thing when talking about hot topics.
chimeracoder 14y ago
For anybody who's interested: perfect multicollinearity (which is rare, except in case of human oversight) causes a matrix of less-than-full rank, which essentially means that it's not invertible (the matrix analog of "divide-by-zero" error). More commonly, you'll end up with imperfect multicollinearity, which means that two variables are almost the same, but slightly different. The danger with perfect multicollinearity is that (a) you'll end up with very high variances associated with those predictors, but furthermore (b) the predictor reported as being the 'strongest' may actually not be the strongest. In fact, it may not even be relevant; the model just "happens to be associating most of the variation in the response variable with that predictor. It's a more complicated version of this principle: http://xkcd.com/882/ http://xkcd.com/882/ I mention this because I see people - including people who should know better! - falling into this trap all the time. It's easy to overlook, particularly when you see the results you were expecting.
marris 14y ago
No, that's not the point. The point is that when velocity is constant, there's no indicator that your pedal manipulation is good as opposed to bad. For that to happen, you would need a period of time where you messed up with the pedal, and saw that you messed up. Then you could make an argument like: Hey, when we let hillAngle-pedalAngle [or whatever] drift away from zero, things go bad [velocity will fall]. Now it is true that you can measure collinearity between the hillAngle and the pedalAngle and show that they are correlated... but we sorta knew this already, didn't we? After all, we're setting the pedalAngle based on the hillAngle. We created that functional relationship. There's no need to empirically discover it. Put it another way. Suppose v = w1 * hillAngle + w2 * pedalAngle + v0, and you want to find w1 and w2. If your dataset shows pedalAngle = -hillAngle, then you have v = w1 * (-pedalAngle) + w2 * pedalAngle + v0 = (w2 - w1) * 0 + v0 So you're dataset tells you nothing about w1 and w2.

by eykanal 14y ago

Irregardless 14y ago

Sounds like the nail in the coffin on this topic. It always sucks when you accuse an entire profession of overlooking a fundamental principle, only to find out you've committed the same error in a more egregious fashion.

cynicalkane 14y ago

You aren't missing anything. The author's article isn't about the optimal ways to do statistics, it's a criticism of the informal economic discussion that dominates policy, blogs, and pop-economics--and, according to the post, an unfortunate number of actual econ papers--that says things like "economic plan X doesn't work because there hasn't been a change". The criticism generalizes to any statistical methods, though. You always need to think about the underlying model before doing any kind of statistics in any science.

chimeracoder 14y ago
Yes, but I wouldn't say that "almost all" economists don't understand the principle (as in the title). I would be more likely to say that "almost all" reporters don't understand basic economics & statistics.
- babblingdweeb 14y ago
  THIS. The problem lies with reporters lacking the basic econmic and statistical background to either report the news and/or challange others they are interviewing. We are often surrounded by "armchair specialists" who know little about what they are talking about, yet carry large opinions about said topic. I'm all for constructive discourse, but that seems like a rare thing when talking about hot topics.

chimeracoder 14y ago

For anybody who's interested: perfect multicollinearity (which is rare, except in case of human oversight) causes a matrix of less-than-full rank, which essentially means that it's not invertible (the matrix analog of "divide-by-zero" error). More commonly, you'll end up with imperfect multicollinearity, which means that two variables are almost the same, but slightly different. The danger with perfect multicollinearity is that (a) you'll end up with very high variances associated with those predictors, but furthermore (b) the predictor reported as being the 'strongest' may actually not be the strongest. In fact, it may not even be relevant; the model just "happens to be associating most of the variation in the response variable with that predictor. It's a more complicated version of this principle: http://xkcd.com/882/ http://xkcd.com/882/ I mention this because I see people - including people who should know better! - falling into this trap all the time. It's easy to overlook, particularly when you see the results you were expecting.

marris 14y ago

No, that's not the point. The point is that when velocity is constant, there's no indicator that your pedal manipulation is good as opposed to bad. For that to happen, you would need a period of time where you messed up with the pedal, and saw that you messed up. Then you could make an argument like: Hey, when we let hillAngle-pedalAngle [or whatever] drift away from zero, things go bad [velocity will fall]. Now it is true that you can measure collinearity between the hillAngle and the pedalAngle and show that they are correlated... but we sorta knew this already, didn't we? After all, we're setting the pedalAngle based on the hillAngle. We created that functional relationship. There's no need to empirically discover it. Put it another way. Suppose v = w1 * hillAngle + w2 * pedalAngle + v0, and you want to find w1 and w2. If your dataset shows pedalAngle = -hillAngle, then you have v = w1 * (-pedalAngle) + w2 * pedalAngle + v0 = (w2 - w1) * 0 + v0 So you're dataset tells you nothing about w1 and w2.