# Re: st: two questions about e(V) and e(V_modelbased) after estimation commands

 From jpitblado@stata.com (Jeff Pitblado, StataCorp LP) To statalist@hsphsun2.harvard.edu Subject Re: st: two questions about e(V) and e(V_modelbased) after estimation commands Date Thu, 04 Feb 2010 10:15:06 -0600

```Michael I. Lichter <mlichter@buffalo.edu>

> First, is e(V) really a variance-covariance matrix? According to Stata
> documentation (I'm using Stata 10, but the online docs for Stata 11 look
> similar), e(V) contains a variance-covariance matrix. However, the
> variance components of e(V) appear to be squared standard errors rather
> than variances. E.g.,
>
> . sysuse auto
> (1978 Automobile Data)
> . mean price
>
> Mean estimation                     Number of obs    =      74
>
> --------------------------------------------------------------
>              |       Mean   Std. Err.     [95% Conf. Interval]
> -------------+------------------------------------------------
>        price |   6165.257   342.8719      5481.914      6848.6
> --------------------------------------------------------------
>
> . mat list e(V)
>
> symmetric e(V)[1,1]
>            price
> price  117561.16
>
> . di sqrt( 117561.16)
> 342.87193
>
> Either the "Std. Err." in the -mean- output is really an SD, or the
> variance estimate in e(V) isn't a variance. Right?

It would be clearer if we had documented -e(V)- as the '(co)variance estimates
of the mean estimates' in -[R] mean-.

In fact, many of Stata's postestimation commands, like -test-, require that
-e(V)- contains a matrix of variance and covariance estimates for the point
estimates in -e(b)-.

So, for -mean-, -e(V)- is the matrix of variance and covariance estimates of
the mean estimates in -e(b)-.

Every official Stata estimation command that posts -e(V)- follows this rule,
see -[P] ereturn-.

> Second, what is the difference between e(V) and e(V_modelbased) after
> -svy- commands? It looks like e(V) is the source (or destination) of the
> reported standard errors, and those are purportedly model-based, so both
> matrices are model-based ... but very different. I'm confused, and I
> don't see anything in the survey manual to clear this up.

In -svy- estimation results, -e(V)- contains the design-based variance
estimates; produced using linearization, the jackknife, or BRR.

-e(V_modelbased)- contains the matrix used by linearization.  It is the bread
of the sandwich estimator, see the section titled 'Linearized/robust variance
estimation' in -[SVY] variance estimation- where you'll see that
-e(V_modelbased)- is the 'D' matrix at the bottom of page 161 (Stata 11 manual
reference).

-svy- leaves -e(V_modelbased)- around to help postestimation commands that use
linearization to combine estimation results, such as -suest-.

--Jeff