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

[Estrella Gomez <estrellastata@gmail.com>]

Hi

We would like to include downloads as dependent variable, but the
problem is that we don't have this information, so that's why we use
rank as a proxy for downloads (or sales). Distance is supposed to
capture not only the physical effect but mainly the cultural distance
between countries.
How should I implement this log link in Stata?

Thank you very much,
Estrella

2014-04-23 15:29 GMT+02:00 Austin Nichols <austinnichols@gmail.com>:
> 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
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