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naraburns  nihil supernum  1yr ago (text post)   31959 thread views

Culture War Roundup for the week of December 5, 2022

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I thought maybe BMI was confounded by age, but it turns out age isn't a good predictor of monthly income. Here's a linear fit with age and log(monthly income)


                 coef    std err          t      P>|t|      [0.025      0.975]

------------------------------------------------------------------------------

age           -0.0025      0.010     -0.260      0.795      -0.022       0.017

bias           8.2223      0.292     28.195      0.000       7.648       8.797

(n=223)

And here it is with bmi and age


                 coef    std err          t      P>|t|      [0.025      0.975]

------------------------------------------------------------------------------

age            0.0034      0.009      0.370      0.712      -0.015       0.022

bmi           -0.0636      0.013     -4.978      0.000      -0.089      -0.038

bias           9.5392      0.383     24.899      0.000       8.784      10.294

Then I thought maybe older women are working more hours, but the regression on log-hourly income (rather than monthly income) is similar:


                 coef    std err          t      P>|t|      [0.025      0.975]

------------------------------------------------------------------------------

age            0.0024      0.006      0.416      0.678      -0.009       0.014

bmi           -0.0275      0.008     -3.414      0.001      -0.043      -0.012

bias           6.3876      0.241     26.454      0.000       5.912       6.863

Edit: here is the data in a form more friendly to a python programmer https://pastebin.com/aZqGTbG5

Technical question: why are you using log(monthly income)?

There are a lot of ways of deriving and thinking about linear regression, so I'm not sure I can give the One True Explanation. I'll give a couple though:

The practical answer is "whenever there are order-of-magnitude differences, it's a good idea to take the log".

The intuitive answer is that if we're assuming y is a linear function of x, so a fixed change in x should yield (roughly) a fixed change in y. This isn't really sensible if y covers several orders of magnitude but x does not.

Another answer is that it doesn't really make intuitive sense to use L2 loss when your labels vary by orders of magnitude. If I'm predicting the income of a poor person and a rich person, it should probably matter whether I'm $10/hour off on my predictions for the poor person or the rich person. Taking the log of our labels implicitly converts our loss function from (y - yhat)^2 to log(y/yhat)^2 which matches the intuition that a $10 mistake for somebody who makes $1000/hour matters less than it does for somebody who makes $10/hour.

Another answer is that if you're going to assume Y = a R + b S + c T then the most sensible distribution for these variables is Gaussian, since the sum of Gaussians is Gaussian. From this philosophy, it's sensible to do some preprocessing on our variables to make them Gaussian. Academia often makes the assumption that income is log-normal, so taking the log of income makes sense. And if we look at the histogram of our data, it indeed looks much more Gaussian after the log transform.

Thanks for the thorough explanation.

I've recently become interested in measuring things, so finding related domains that I'm ignorant about is pretty helpful to keep following the thread.

I was wondering if BMI was also interacting with social class.

These are escorts. Part of their whole schtick is being able to consistently ape a upper social class. Aside from some kind of outlier, we should assume that they're all able to do so, and that includes semi-permanent characteristics like conforming to beauty standards, or they would not be working as escorts.

: here is the data in a form more friendly to a python programme

Just pd.read_csv(<filename.csv>) it.

I personally think copying and pasting data into your python file (takes maybe 5 seconds?) is more convenient than downloading the file, copying the file path into your text editor, and then (the real pain point) learning how pandas handles "sheets" (I expect I'm not alone in not knowing how to do that).

As a data scientist, I'm cringing at the thought of anyone doing that (but that's more of my problem than yours), but no point in being elitist about a twitter survey. A good 95% of the time, I work with datasets so large that you would have to be a madman to even think about manually copy-pasting data in, on top of all the other reasons you don't manually copy paste in data. But I would do it the hard way just because.

Moreover, you don't really need to download the data. the read_csv() function can parse web hosted files, and if its more complicated, you can use the requests module, and if its still a pain, there are packages to read google sheet data. As for pandas parsing sheets, it's a keyword argument into the read_<filetype> function. In the case of google sheets, you can specify it in the API endpoint.

Pandas is a powerful library.

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