Re: st: Computing semipartial correlations

[Richard Williams <Richard.A.Williams.5@nd.edu>]

At 11:54 AM 12/11/2003 -0500, Richard Williams wrote:
> The pcorr routine uses the following formula to compute partial correlations:
>
> t/sqrt(t^2 + N - K -1) where N = Sample size and K = # of X variables
>
> This is not the most intuitive formula in the world, but it works! I would 
> like to modify the program to compute semipartial correlations.  Does 
> anybody know of a similarly straightforward formula that would do 
> this?  pcorr runs a regress command and then uses the saved estimates to 
> do its calculations.  Thanks for any input.
I figured out the answer to my own question, in case anybody else is 
interested.  The formula for a semipartial is, of course,

t * sqrt((1-R^2)/(N-K-1))

(I actually did a proof of this 7 years ago that I had completely forgotten 
about).

To implement this in the pcorr command, you drop this line

*/ %9.4f `s'*sqrt(r(F)/(r(F)+`NmK')) /*

and replace it with

*/ %9.4f `s'*sqrt(r(F)* ((1-e(r2))/`NmK')) /

Also, change the program define line to pcorr2 (or perhaps semicorr) and 
have the program print out Semipartial instead of Partial. I imagine 
somebody who is a little more skilled than I currently am could rewrite the 
routine to print out both the partials and the semipartials.

Given that it is fairly easy to modify pcorr to give both partial and 
semipartial correlations, can I request that Stata do so?  Or, if I 
eventually just do it myself, how would I make a semicorr or a pcorr2 
routine available to the world?  Thanks.



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Richard Williams, Associate Professor
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