lnvar after suset with reg

[Jasmine Xu]

Hello everyone,

I am trying to understand -lnvar- in the output of -suest- with -reg-.

The following is an example from the manual:

. use https://www.stata-press.com/data/r18/income

. regress inc edu exp male

      Source |       SS           df       MS      Number of obs   =       277
-------------+----------------------------------   F(3, 273)       =     42.34
       Model |  2058.44672         3  686.148908   Prob > F        =    0.0000
    Residual |  4424.05183       273  16.2053181   R-squared       =    0.3175
-------------+----------------------------------   Adj R-squared   =    0.3100
       Total |  6482.49855       276  23.4873136   Root MSE        =    4.0256

------------------------------------------------------------------------------
         inc | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         edu |   2.213707    .243247     9.10   0.000     1.734828    2.692585
         exp |    1.47293    .231044     6.38   0.000     1.018076    1.927785
        male |   .5381153   .4949466     1.09   0.278     -.436282    1.512513
       _cons |   1.255497   .3115808     4.03   0.000      .642091    1.868904
------------------------------------------------------------------------------

. est store Inc

. probit promo edu exp male, nolog

Probit regression                                       Number of obs =    277
                                                        LR chi2(3)    =  49.76
                                                        Prob > chi2   = 0.0000
Log likelihood = -158.43888                             Pseudo R2     = 0.1357

------------------------------------------------------------------------------
       promo | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         edu |   .4593002   .0898537     5.11   0.000     .2831901    .6354102
         exp |   .3593023   .0805774     4.46   0.000     .2013735    .5172312
        male |   .2079983   .1656413     1.26   0.209    -.1166527    .5326494
       _cons |   -.464622   .1088166    -4.27   0.000    -.6778985   -.2513454
------------------------------------------------------------------------------

. est store Promo

. suest Inc Promo, vce(cluster famid)

Simultaneous results for Inc, Promo                        Number of obs = 277

                                (Std. err. adjusted for 135 clusters in famid)
------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Inc_mean     |
         edu |   2.213707   .2483907     8.91   0.000      1.72687    2.700543
         exp |    1.47293   .1890583     7.79   0.000     1.102383    1.843478
        male |   .5381153   .4979227     1.08   0.280    -.4377952    1.514026
       _cons |   1.255497   .3374977     3.72   0.000      .594014    1.916981
-------------+----------------------------------------------------------------
Inc_lnvar    |
       _cons |   2.785339    .079597    34.99   0.000     2.629332    2.941347
-------------+----------------------------------------------------------------
Promo_promo  |
         edu |   .4593002   .0886982     5.18   0.000     .2854549    .6331454
         exp |   .3593023    .079772     4.50   0.000     .2029522    .5156525
        male |   .2079983   .1691053     1.23   0.219    -.1234419    .5394386
       _cons |   -.464622   .1042169    -4.46   0.000    -.6688833   -.2603607
------------------------------------------------------------------------------

From the help file:

regress does not include its ancillary parameter, the residual variance, in its coefficient vector and (co)variance matrix. Moreover, while the score option is allowed with predict after regress, a score variable is generated for the mean but not for the variance parameter. suest contains special code that assigns the equation name mean to the coefficients for the mean, adds the equation lnvar for the log variance, and computes the appropriate score variables.

Does it mean lnvar is the residual variance?
I understand lnvar is not important when comparing coefficients across models, but I am just wondering what lnvar means, and whether it is useful in some way.

Thanks.

[Joseph Coveney]

Does it mean lnvar is the residual variance?

Not quite; it means that it's the natural logarithm of the residual variance.

. . . I am just wondering what lnvar means, and whether it is useful in some way.

Well, for example, when both models are linear regression, you can examine it for evidence of heteroscedasiticity, either just eyeballing it or with a formal test (a Wald test). Run the code below to see it in action for this purpose, along with a couple of alternatives that use a slightly different test statistic (a likelihood-ratio test instead of a Wald test), but allow a similar conclusion to be drawn.

version 18.0

clear *

quietly sysuse auto

// Use in examining residual variance
quietly regress headroom if !foreign
estimates store Domestic
quietly regress headroom if foreign
estimates store Foreign

suest Domestic Foreign
* Wald test of equality of residual variance for headroom between foreign and domestic manufacturers
test [Domestic_lnvar]_cons = [Foreign_lnvar]_cons

// Alternative #1 (examine the LR test in the footnote)
hetreg headroom i.foreign, het(i.foreign) nolog

// Alternative #2 (same:  examine the LR test in the footnote)
mixed headroom i.foreign, residuals(independent, by(foreign)) nolog

exit

I guess that it's accepted that logarithmic transformation renders the distribution of the residual variance symmetric enough to report standard errors, confidence bounds and Wald test statistics.