VIF for selected variables

[Parul Gupta]

I want to estimate the variance inflation factor after OLS regression. My model has a lot of fixed effects, and I want the VIF only for the key variables of interest. Is there a way to do this?

[Carlo Lazzaro]

Parul:
you can calcuate the VIF you're interested in by hand following the formula reported in the -regress postestimation- entry, Stata .pdf manual:

. sysuse auto.dta
(1978 automobile data)

. regress price trunk weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.80
       Model |   186872936         2  93436468.2   Prob > F        =    0.0000
    Residual |   448192460        71  6312569.86   R-squared       =    0.2943
-------------+----------------------------------   Adj R-squared   =    0.2744
       Total |   635065396        73  8699525.97   Root MSE        =    2512.5

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       trunk |  -60.03885   92.85726    -0.65   0.520     -245.191    125.1133
      weight |   2.266182   .5110542     4.43   0.000     1.247169    3.285195
       _cons |   148.5533   1203.406     0.12   0.902     -2250.97    2548.077
------------------------------------------------------------------------------

. estat vif

    Variable |       VIF       1/VIF  
-------------+----------------------
       trunk |      1.82    0.548139
      weight |      1.82    0.548139
-------------+----------------------
    Mean VIF |      1.82

. help regress

. regress trunk weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     59.35
       Model |  603.514706         1  603.514706   Prob > F        =    0.0000
    Residual |  732.106916        72  10.1681516   R-squared       =    0.4519
-------------+----------------------------------   Adj R-squared   =    0.4442
       Total |  1335.62162        73  18.2961866   Root MSE        =    3.1888

------------------------------------------------------------------------------
       trunk | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |   .0036996   .0004802     7.70   0.000     .0027423    .0046569
       _cons |   2.586002   1.496605     1.73   0.088    -.3974248    5.569429
------------------------------------------------------------------------------

. di 1/(1-0.4519)
1.8244846

[Parul Gupta]

Thank you Carlo. Should I use pwcorr if I have more than two variables?

[Carlo Lazzaro]

Parul:
no, you have to repeat the previous approach changing the dependent variable:

. sysuse auto.dta
(1978 automobile data)

. regress price trunk weight mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =      9.92
       Model |   189420421         3  63140140.2   Prob > F        =    0.0000
    Residual |   445644976        70  6366356.79   R-squared       =    0.2983
-------------+----------------------------------   Adj R-squared   =    0.2682
       Total |   635065396        73  8699525.97   Root MSE        =    2523.2

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       trunk |  -65.32347   93.62548    -0.70   0.488    -252.0536    121.4067
      weight |   1.955753   .7100895     2.75   0.007     .5395243    3.371982
         mpg |  -54.91704   86.81541    -0.63   0.529    -228.0649    118.2308
       _cons |   2328.163   3651.422     0.64   0.526    -4954.368    9610.694
------------------------------------------------------------------------------

. estat vif

    Variable |       VIF       1/VIF  
-------------+----------------------
      weight |      3.49    0.286341
         mpg |      2.89    0.345694
       trunk |      1.84    0.543775
-------------+----------------------
    Mean VIF |      2.74

. regress trunk mpg weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     29.78
       Model |  609.343683         2  304.671841   Prob > F        =    0.0000
    Residual |  726.277939        71  10.2292667   R-squared       =    0.4562
-------------+----------------------------------   Adj R-squared   =    0.4409
       Total |  1335.62162        73  18.2961866   Root MSE        =    3.1983

------------------------------------------------------------------------------
       trunk | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -.0827393   .1096069    -0.75   0.453    -.3012892    .1358106
      weight |   .0032024   .0008159     3.92   0.000     .0015755    .0048293
       _cons |   5.849263   4.576131     1.28   0.205    -3.275284    14.97381
------------------------------------------------------------------------------

. di 1/(1-0.4562)
1.8389114

. regress mpg trunk weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     67.19
       Model |  1598.76953         2  799.384767   Prob > F        =    0.0000
    Residual |  844.689926        71  11.8970412   R-squared       =    0.6543
-------------+----------------------------------   Adj R-squared   =    0.6446
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.4492

------------------------------------------------------------------------------
         mpg | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       trunk |   -.096229   .1274771    -0.75   0.453    -.3504112    .1579531
      weight |  -.0056527   .0007016    -8.06   0.000    -.0070516   -.0042537
       _cons |   39.68913    1.65207    24.02   0.000       36.395    42.98327
------------------------------------------------------------------------------

. di 1/(1-.6543)
2.8926815

. regress weight mpg trunk

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     88.48
       Model |  31468208.8         2  15734104.4   Prob > F        =    0.0000
    Residual |  12625969.6        71  177830.557   R-squared       =    0.7137
-------------+----------------------------------   Adj R-squared   =    0.7056
       Total |  44094178.4        73  604029.841   Root MSE        =     421.7

------------------------------------------------------------------------------
      weight | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |   -84.4932   10.48699    -8.06   0.000    -105.4037   -63.58274
       trunk |   55.67266   14.18442     3.92   0.000     27.38973    83.95559
       _cons |   4053.061   375.5729    10.79   0.000      3304.19    4801.932
------------------------------------------------------------------------------

. di 1/(1-0.7137)
3.4928397

.

[Parul Gupta]

Thank you!