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# Re: st: calculating effect sizes when using svy command

 From Steven Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: calculating effect sizes when using svy command Date Wed, 8 Dec 2010 12:23:02 -0500

```Dawne Vogt:

```
You should not expect the p-values from -pcorr- with aweights to come close to those from -svy: reg-. Using analysis weights is a mathematical trick to get -pcorr- to compute the proper weighted correlations, but the trick does not extend to estimating the standard errors. For that reason, Bill Sribney suggested in the FAQ that the p- value for the (simple) correlation come from the original survey regression, not from -correlate-. Note that the t-statistic from the full -svy: reg-- is the same as that for -svy: reg- of the partialed residuals.
```
```
You can get another approximate partial correlation starting from the t statistic, as you originally did: Instead of using the survey sample size n in the formula, substitute n' = n/DEFF. DEFF is the design effect and can be computed by running "estat effects" after the original regression; n' is the SRS size that would have produced the same value of t.
```

Steve
Steven J. Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783

On Dec 8, 2010, at 10:54 AM, Vogt, Dawne wrote:

```
Thanks to everyone who weighed in on this issue. I figured out how to compute the weighted partial correlations with aweights. I noticed, however, that the p values associated with these weighted partial correlations are different than the p values associated with the t values that are presented in the svyreg output. I understand that the relationship between partial rs and t values only hold for ordinary least squares, but I am having trouble reconciling cases where the p values associated with the t for a particular predictor is not significant (p <.05) but the p value associated with the partial r for the same variable is significant. I'm not sure what to make of it. Do people have thoughts or suggestions?
```

-----Original Message-----
```
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu ] On Behalf Of Steven Samuels
```Sent: Wednesday, December 08, 2010 8:56 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: calculating effect sizes when using svy command

--
The simplest way of computing the weighted partial correlation is to
use -pcorr- with aweights, as suggested by Bill Sribney's FAQ. In the
example, repeated below, the difference is R-square from regression of
residuals = 0.259; partial correlation-squared from -pcorr- = 0.288.

Steve

**************************CODE BEGINS**************************
sysuse auto, clear
svyset rep78 [pw=trunk]

/* Compute partial correlation of mpg and weight, controlling for turn
*/
svy: reg mpg weight turn

svy: reg mpg turn
predict r_mt, resid

svy: reg weight turn
predict r_wt, resid

svy: reg r_mt r_wt   //R-squared is partial r-square
pcorr mpg weight turn [aw=trunk]

***************************CODE ENDS***************************

On Dec 7, 2010, at 5:39 PM, Steven Samuels wrote:

Well, I got the details wrong, but the example right.

If the multiple regression is:
svy: reg y x z

svy: reg y z,  with residual r_yz
svy: reg x z, with residual  r_xz

Thecorrelation of r_yz and r_xz is the partial correlation r_yx.z So
the goal is to estimate the correlation of r_yz and r_xz with one of
the methods in the post, including

svy: reg r_yz r_xz

Sorry for the confusion.

Steve
sjsamuels@gmail.com

On Dec 7, 2010, at 5:03 PM, Steven Samuels wrote:

--

What Dawne  called "correlation" is actually the partial correlation
of y and x, controlling for other covariates z (r_yx.z).  The  partial
correlation in OLS can be estimated by  t^2/(df_error + t^2), but that
is not true for survey regression. However it can be estimated in a
three step process: -svy regress- y on x, with residual r_yx ;   y on
the z's with residual r_yz. Then compute the  correlation of r_yx and
r_yz by means of 1) Nick's program 2) the methods in Bill Sribney's
FAQ; or 3) by running -svy: reg r_yx r_yz- and taking the R-squared
reported by that command. The p-value issue discussed by Bill doesn't
arise for Dawn, because she takes the p-value from the original
regression.  See below for an example.

Steve

**************************CODE BEGINS**************************
sysuse auto, clear
svyset rep78 [pw=trunk]

/* Compute partial correlation of mpg and weight, controlling for turn
*/
svy: reg mpg weight turn

svy: reg mpg turn
predict r_mt, resid

svy: reg weight turn
predict r_wt, resid

svy: reg r_mt r_wt   //R-squared is partial r-square
***************************CODE ENDS***************************

On Dec 7, 2010, at 4:18 PM, Nick Winter wrote:

Re: svy and (bivariate) correlation, this FAQ talks about how to do
the equivalent of the nonexistent -svy: correlate-:

http://www.stata.com/support/faqs/stat/survey.html

The short version is that the point estimate is -correlate- with
aweights, and the p-value as you discuss below.

My -corr_svy- from SSC implements this approach, though it is a Stata
version 7 program so it does not take advantage of Stata's current,
more extensive -svy- features.

-Nick Winter

On 12/7/2010 4:11 PM, Vogt, Dawne wrote:
```
```Thanks. So it sounds like I can take the square root of the R
squared value to get the correlation coefficient for a regression
with 1 predictor. But how do I get effect size indicators
(preferably in the form of correlation coefficients) for each
predictor in a regression with multiple predictors?

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu
] On Behalf Of Steven Samuels
Sent: Tuesday, December 07, 2010 4:00 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: calculating effect sizes when using svy command

--
-
I should have added:  The  relation of (partial) r-squares to t-
statistics holds only for ordinary least squares, not for the
estimation formulas of survey regression. So, neither of your
calculated r's is correct.

Steve

On Dec 7, 2010, at 3:31 PM, Vogt, Dawne wrote:

I have two questions related to calculating effect sizes using svyreg
(pweights):

First, when doing unweighted regressions in SPSS, I like to provide
effect sizes for each predictor by calculating a correlation
coefficient value (r) from the t values provided in the output. I like
using r because it is easy for most people to interpret. Can I do the
same using svyreg output?

My second question is related to the first. Since there is no
correlation option under the svy commands, I have been computing
regressions of Y on X and X and Y and using the largest p value of the
two sets of results, as recommended elsewhere. I've having trouble
figuring out how to convert the results provided in the output to a
correlation coefficient though.  I noticed that the r value I get by
taking the square root of the R squared is different from my own hand
calculation of r derived from the t value provided in the regression
output [sqrt of (t squared divided by t squared + df). I'm not sure
which r is correct (or if either of them are correct).

Thanks in advance for any guidance others may be able to offer.

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```
```
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```