New Admissions Calculator for T14+1

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srt2021

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Re: New Admissions Calculator for T14+1

Postby srt2021 » Thu Jan 04, 2018 10:02 pm

I worked with an SVM on the Penn data since it looked like the weirdest data. It boosted the accuracy from about 61 to 64% and variance explained from 43 to 54%, and it did start to address those odd outliers that icechicken's pointed out (e.g., for the same data linked to, the RD person is at 27% admissions and ED person is at 86%). Now, it isn't exactly what the data shows, but tighter fits are hard since, as icechicken's pointed out, there just isn't all that much good data on ED applicants. Looking at the data visualization, what is clear is that, beyond those outliers, it's pretty darn challenging to distinguish between admits and waitlisted applicants (see below). That and early decision throw a real wrench in things. This might just be the best we get for schools like Penn.

The highlighted points are as follows:
SVM Prediction: Accept, Actual: Accept: https://ibb.co/eBvpWb
SVM Prediction: Accept, Actual: Waitlist: https://ibb.co/jRV1cG
SVM Prediction: Waitlist, Actual: Accept: https://ibb.co/mugUWb
SVM Prediction: Waitlist, Actual: Waitlist: https://ibb.co/m3x3rb
The red cluster is ED applicants, green is URMs, and blue is everyone else.

I may try to update the calculator to get something based on the SVM up for various schools, but I'm not sure how much I can time I'll have with exams coming up.

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pupper

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Re: New Admissions Calculator for T14+1

Postby pupper » Thu Jan 04, 2018 10:57 pm

srt2021 wrote:Do you remember which schools they might have been?


If I recall correctly, Duke and WUSTL were particularly easy to predict with decision trees.

srt2021 wrote:This might just be the best we get for schools like Penn.


I'm glad the SVM worked well for you. Even if this the best it gets, I think predictors like this are still much more helpful than what is currently available!

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TripleM

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Re: New Admissions Calculator for T14+1

Postby TripleM » Thu Jan 04, 2018 11:34 pm

Can you give a Cliff's notes version of how we should understand the third chart? I understand the concept of variance at a caveman level but this seems to be a more nuanced idea. I understand that you probably on't be able to completely catch me up, but can you give me some broad strokes on how I should see the numbers on that chart? Thanks for doing the whole project, by the way. I've found it really useful and interesting.

icechicken

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Re: New Admissions Calculator for T14+1

Postby icechicken » Fri Jan 05, 2018 12:16 pm

TripleM wrote:Can you give a Cliff's notes version of how we should understand the third chart? I understand the concept of variance at a caveman level but this seems to be a more nuanced idea. I understand that you probably on't be able to completely catch me up, but can you give me some broad strokes on how I should see the numbers on that chart? Thanks for doing the whole project, by the way. I've found it really useful and interesting.


I'm not great with stats, but like to think of the fraction of variance unexplained as how much "randomness" is left over once you've applied your model.

Let's take an extreme example. I'm trying to predict admissions outcomes at Yale. Since most people who apply to YLS get rejected, my model is: if you apply, you're going to get rejected. Yale has an acceptance rate of 8.39%, so, for any given applicant, my model picks out the right answer (what Chart 3 refers to as "retrodictive accuracy") over 90% of the time! But, obviously, that's a crappy model, because it fails to predict any of the outliers who do get admitted. The percentage of variance explained (i.e., predicted by the model) is 0%.

I can make a new model: If your LSAT score is 175 or higher, you'll get admitted, and, if it's 174 or lower, you'll get rejected. This one probably produces incorrect results more often than the "everyone gets rejected" model, but it at least explains some of the variance in outcomes.

OP's model is more sophisticated still, but it's inherently limited because it only considers a handful of inputs (LSAT, GPA, URM status) when in reality there's a lot more going on (softs, writing ability, the whims of individual faculty readers). So it's only able to explain 33% of the variance in outcomes. The trends in the chart mostly conform to received wisdom about how T13 schools differ: Yale is harder to predict based on one's numerical profile alone, while Harvard/Columbia/NYU/Duke are much easier.



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