Adding McCrary (2008) test for manipulation in the running variable

[pvalenzuelac]

Hi Nikos! I have added the McCrary density test for manipulation in the running variable. I include some tests, and also some comparisons to established packages in R and in Stata for three datasets, including Lee (2008). The results matches. I added a small example in the README, plus the plots for the comparisons, and a test of time.
The package seems to perform well in relatively small samples. However, when I increased the sample size to one million, the Julia implementation is ~4 times slower than the other two. I still need to figure this out and improve the speed here. Let me know if you have any comment.

[nignatiadis]

Hi Pablo! Happy holidays!

Thanks a lot for contributing this code! I will take a more careful look later to figure out the slowdown (it should not happen with Julia)!

I have a few initial remarks:

• Since your changes, Evan's PR is in the repo, so you need to resolve the conflicts.
• I like the timings etc. you added, but think they should be removed from the README (the README should be short and perhaps contain just a quick example explaining how to use the McCrary functionality). Once we have a better documentation system in place for this package, we can find a better place for it!
• The interface right now does not look very "Julian" and is closer to how one would write a package in R or other languages. Of course this package is still in very early stages, so it's not clear what the best interface is. To make it more unified with other functionality in this package, perhaps you could define a McCraryTest type ( that e.g. contains the bandwidth as a field) , a fit method for it that returns a FittedMcCraryTest. See for example the code for local linear regression. Then you could define plotting functionality for the FittedMcCraryTest with Plot recipes (https://docs.juliaplots.org/latest/recipes/) instead of loading Plots.jl which is a very heavy dependency.

I would be happy to talk more about any of these points or provide guidance!

[pvalenzuelac]

Hi Nikos! Happy holidays too! Sorry for the delay in my response. I was out of town for the holidays and just come back. I will start working on your comments. Thank you for them :) I will let you know if I have any issue.

[codecov-io]

Codecov Report

Merging #15 (167e75f) into master (7405152) will increase coverage by 0.06%. The diff coverage is 63.69%.

@@            Coverage Diff             @@
##           master      #15      +/-   ##
==========================================
+ Coverage   61.78%   61.84%   +0.06%     
==========================================
  Files           7        8       +1     
  Lines         348      477     +129     
==========================================
+ Hits          215      295      +80     
- Misses        133      182      +49     

Impacted Files	Coverage Δ
src/RegressionDiscontinuity.jl	100.00% <ø> (ø)
src/density_test.jl	61.36% <61.36%> (ø)
src/running_variable.jl	40.60% <85.71%> (+0.16%)	:arrow_up:

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[pvalenzuelac]

Hi Nikos! I hope this message finds you well. I added the points you made to the code. I created a McCraryTest type, with the default values to be those calculated by McCrary (2008). The fit(McCraryTest(), data::RunningVariable) returns FittedMcCraryTest.
Let me know if you have more comments! Best

[nignatiadis]

Thanks a lot @pvalenzuelac for contributing this and I apologize for the delay in getting back to you. The functionality looks great to me and I am going to merge it as soon as tests finish! I think some of my last remarks really pertain to the package more generally so I will try to think about how to resolve them from a broader perspective.

One last remark about the tests: they occasionally fail, because they are random (e.g. testing if a null p-value is >0.05 will fail 5% of the time :), that's why I commented these tests out for now). A fix is to 1) test the outcome over multiple replicates (to check for the statistical behavior of the p-values) and 2) to set a random simulation seed, say by writing:

using Random
Random.seed!(1)