Weighted sampling

[paulvonhippel]

I'd like to simulate the results of a poll of n=400 voters from the population of nearly 5 million Illinois voters in 1960. Is there a way to this without writing a population dataset thanearly 5 million rows? It seems to me it should be possible applying some simple command to a 3 line dataset like this (but -sample- won't do it):

candidate votes
Kennedy 2377846
Nixon 2368988
Other 10000

[Ken Chui]

I do not understand where the technical challenge lies (e.g. are you opposing having to generate 5 million cases, or are you not sure how to generate 5 millions cases easily.) I'm going to, actually, generate 5 million cases, and then do a sample. It's just one more line to expand:

* The three original cases:
clear
input str10 candidate votes
Kennedy 2377846
Nixon 2368988
Other 10000
end

expand votes
* Optionally add a "set seed ###" for reproducible outcomes.
sample 400, count

[Leonardo Guizzetti]

A potentially faster solution is to use Ben Jann's gsample. I say potentially because I didn't benchmark times but it felt slow with a sample of 10M records (just to verify sampling proportions). You can also "roll your own" sample program if you prefer a bespoke solution.

set seed 17

input byte candidate long votes
1 2377846
2 2368988
3 10000
end
compress
label define candidate 1 "Kennedy" 2 "Nixon" 3 "Other"
label values candidate candidate
list
tab candidate [fw=votes]

gsample 400 [iw=votes], replace
tab candidate

[Mike Lacy]

This problem might also be framed as "generate a multinomial random variable" in Stata, which was discussed here a few years ago, a conversation in which I participated but had forgotten. The short story is that Stata lacks a multinomial r. v. function, but the obscure built-in -irecode- function can be used to make something like that, as can Mata's -rdiscrete- function. Neither of these offers an easier solution in the current context, but perhaps someone thinking in that direction might find a pointer useful.

[paulvonhippel]

Thanks to all! I agree that -gsample- is the fastest and simplest solution here.