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Note: In OLS regrerssion the way that to obtain the VIF and tolerance is to use the estat vif after the regress command.
use http://www.ats.ucla.edu/stat/stata/notes/hsb2, clear
generate rw = read*write
svyset [pw=socst], strata(ses)
pweight: socst
VCE: linearized
Strata 1: ses
SU 1:
FPC 1:
svy: regress read write rw
(running regress on estimation sample)
Survey: Linear regression
Number of strata = 3 Number of obs = 200
Number of PSUs = 200 Population size = 10481
Design df = 197
F( 2, 196) = 2732.78
Prob > F = 0.0000
R-squared = 0.9789
------------------------------------------------------------------------------
| Linearized
read | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
write | -.850208 .0265923 -31.97 0.000 -.9026501 -.7977658
rw | .0174374 .0002659 65.57 0.000 .0169129 .0179618
_cons | 48.0699 .9949204 48.32 0.000 46.10784 50.03196
------------------------------------------------------------------------------
display "tolerance = " 1-e(r2) " VIF = " 1/(1-e(r2))
tolerance = .02105442 VIF = 47.495965
svy: regress write read rw
(running regress on estimation sample)
Survey: Linear regression
Number of strata = 3 Number of obs = 200
Number of PSUs = 200 Population size = 10481
Design df = 197
F( 2, 196) = 1795.43
Prob > F = 0.0000
R-squared = 0.9677
------------------------------------------------------------------------------
| Linearized
write | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | -1.026298 .0301498 -34.04 0.000 -1.085756 -.9668401
rw | .0189835 .000346 54.87 0.000 .0183012 .0196657
_cons | 53.00732 .9279013 57.13 0.000 51.17742 54.83721
------------------------------------------------------------------------------
display "tolerance = " 1-e(r2) " VIF = " 1/(1-e(r2))
tolerance = .03233581 VIF = 30.925463
svy: regress rw write read
(running regress on estimation sample)
Survey: Linear regression
Number of strata = 3 Number of obs = 200
Number of PSUs = 200 Population size = 10481
Design df = 197
F( 2, 196) = 5429.51
Prob > F = 0.0000
R-squared = 0.9917
------------------------------------------------------------------------------
| Linearized
rw | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
write | 50.02573 .9657679 51.80 0.000 48.12116 51.9303
read | 55.46852 .8909744 62.26 0.000 53.71145 57.22559
_cons | -2724.5 55.57823 -49.02 0.000 -2834.104 -2614.895
------------------------------------------------------------------------------
display "tolerance = " 1-e(r2) " VIF = " 1/(1-e(r2))
tolerance = .00831673 VIF = 120.23951
Note that we used each of the predictor variables, in turn, as the response variable
for a survey regression. Tolerance is defined as 1-R2 and VIF as
1/tolerance. VIF values greater than 10 may warrant further examination.
In this example, all of the VIFs were problematic but the variable rw
stands out with a VIF of 120.24.
This same approach can be used with survey logit (svy: logit) or any of the
survey estimation procedures.
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