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For what it's worth, showing a straight line on a log-log plot isn't really enough to demonstrate existence of a power law. Most papers that test for the exist

For what it's worth, showing a straight line on a log-log plot isn't really enough to demonstrate existence of a power law. Most papers that test for the existence of power laws don't test goodness-of-fit for other distribtions. The lognormal distribution is often just as good a fit to the data. This paper covers a lot of the frequent problems in academic literature that tries to fit power laws: https://arxiv.org/abs/0706.1062 https://arxiv.org/abs/0706.1062

egocodedinsol 8y ago
Yes! And that paper is a fantastic example of making clear criticisms with actionable fixes and the code to perform the comparisons properly. Preferential attachment is such a beautiful theory because it gives power law distributions of node degree. But real world networks seem to have systematic deviations from power law so often one wonders why more work wasn’t done to find schemes that generate, e.g. lognormal distributions. It’s possible that preferential attachment isn’t even a good theory for the underlying principle, it’s just that the underlying principle gives fat tails in degree distribution and power laws give okay fat tails. Sometimes, though, one doesn’t care if it’s a power law per se or just that it has fat tails. In that case why use a power law and not just a better fitting lognormal (or say kernel density estimation)? But power law seems sexy because of its importance in physics (eg scale free, renormalization stuff), so people ran with that when network literature blew up in the mid 2000s.
- soVeryTired 8y ago
  The cynic in me says the econ literature cares much more about elegant theory than how the data fits the theory, so they just go with a low-power test that makes their pet theory credible.
transcranial 8y ago
Here's a recent follow-up paper [1] testing exactly that on many diverse datasets, positing that scale-free (power-law distributed) networks are actually not that common in the real world. Quanta has a nice article about it [2]. [1] https://arxiv.org/abs/1801.03400 https://arxiv.org/abs/1801.03400 [2] https://www.quantamagazine.org/scant-evidence-of-power-laws-found-in-real-world-networks-20180215/ https://www.quantamagazine.org/scant-evidence-of-power-laws-...
jk4930 8y ago
"6. (Mar's Law) Everything is linear if plotted log-log with a fat magic marker." https://spacecraft.ssl.umd.edu/akins_laws.html https://spacecraft.ssl.umd.edu/akins_laws.html

egocodedinsol 8y ago

Yes! And that paper is a fantastic example of making clear criticisms with actionable fixes and the code to perform the comparisons properly. Preferential attachment is such a beautiful theory because it gives power law distributions of node degree. But real world networks seem to have systematic deviations from power law so often one wonders why more work wasn’t done to find schemes that generate, e.g. lognormal distributions. It’s possible that preferential attachment isn’t even a good theory for the underlying principle, it’s just that the underlying principle gives fat tails in degree distribution and power laws give okay fat tails. Sometimes, though, one doesn’t care if it’s a power law per se or just that it has fat tails. In that case why use a power law and not just a better fitting lognormal (or say kernel density estimation)? But power law seems sexy because of its importance in physics (eg scale free, renormalization stuff), so people ran with that when network literature blew up in the mid 2000s.

soVeryTired 8y ago
The cynic in me says the econ literature cares much more about elegant theory than how the data fits the theory, so they just go with a low-power test that makes their pet theory credible.

transcranial 8y ago

Here's a recent follow-up paper [1] testing exactly that on many diverse datasets, positing that scale-free (power-law distributed) networks are actually not that common in the real world. Quanta has a nice article about it [2]. [1] https://arxiv.org/abs/1801.03400 https://arxiv.org/abs/1801.03400 [2] https://www.quantamagazine.org/scant-evidence-of-power-laws-found-in-real-world-networks-20180215/ https://www.quantamagazine.org/scant-evidence-of-power-laws-...

jk4930 8y ago

"6. (Mar's Law) Everything is linear if plotted log-log with a fat magic marker." https://spacecraft.ssl.umd.edu/akins_laws.html https://spacecraft.ssl.umd.edu/akins_laws.html