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From |
Austin Nichols <austinnichols@gmail.com> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
Re: st: Log of the mean vs mean of the log |

Date |
Wed, 23 Apr 2014 09:29:20 -0400 |

Estrella Gomez <estrellastata@gmail.com>: I misread your first post; I thought you meant to include the downloads as an explanatory variable in a gravity model (which seemed an interesting idea, as that might be a proxy for levels of trade that would obtain without respect to distance between countries). The gravity model would then be estimated using -glm- with a log link, not by taking logs and then running a linear regression. See e.g. refs in http://www.stata.com/meeting/boston10/boston10_nichols.pdf If downloads are your depvar, then I can't see how a gravity model is appropriate, since distance in the traditional sense is irrelevant for song downloads. I cannot see why you want ranks at all, but perhaps there was more information at the start of this post that got cut off: On Wed, Apr 23, 2014 at 8:40 AM, Estrella Gomez <estrellastata@gmail.com> wrote: > ranks, that is, the top 300 songs per each country, and I want to use > this (inverted) variable as a proxy for sales (downloads), because I > don't have real downloads. I have already done the analysis at the > song level, but I would also like to aggregate at the country level to > see the total cross border sales per country. That's why I would like > to sum all the ranks, because I understand that the sum of all > (inverted) ranks would be a proxy for total sales from a country to > another. Then I use this as dependent variable in a gravity equation, > which requires the use of logarithms, but I'm not clear if first take > the logarithms of rank and them sum all the logs (by country) or > either if I should first sum all the ranks (by country) and then take > the logarithm of this sum > > Thank you very much, > Estrella > > 2014-04-23 14:05 GMT+02:00 Austin Nichols <austinnichols@gmail.com>: >> Estrella Gomez <estrellastata@gmail.com>: >> >> Neither sounds right to me. You want to take the sum over many songs >> for one country with few downloads, ranking say 200th out of many >> countries on all those songs, and take the log of the sum? Or compute >> the sum of many ln(200) values? What interpretation would this >> variable have--movements up or down in percentage terms in rank of >> downloads is some kind of measure of changes in intrinsic propensity >> to engage in internet trade? I would think you could get much more >> interesting information by preserving the data at the song level, >> because it could inform who are likely to be trading partners, if you >> have country of origin of the song (as least language can play a role, >> if not other cultural factors). Also, numbers of downloads is no doubt >> more informative than rank. If you are committed to using ranks >> instead of numbers, I would think computing ranks from 0 to 1, or >> 1/200 to 1-1/200 for 200 countries, as "percentile" scores, would be >> better than raw rank. For that kind of rank, logit is a more natural >> transformation than log, but I doubt any transformation is required >> here--just keep it on the scale from 0 to 1. >> >> On Wed, Apr 23, 2014 at 4:51 AM, Estrella Gomez <estrellastata@gmail.com> wrote: >>> Hi, >>> >>> I have a variable that is the number of downloads in a country at the >>> song level, so each observation is song & artist & number of downloads >>> & country & rank. I want to aggregate this at the country level and >>> introduce the sum of the ranks as dependent variable in a gravity >>> equation. I have aggregated taking the sum of the ranks and then the >>> logarithm of this sum. My question is: is this correct or should I >>> instead take first the logarithm of the ranks at the song level and >>> then take the sum of this logarithms? I am not very clear on the >>> difference between the sum of the log ranks and the log of the sum of >>> the ranks * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Log of the mean vs mean of the log***From:*Estrella Gomez <estrellastata@gmail.com>

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