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

 From "Michael I. Lichter" 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 14:36:03 -0500

```Jeff,

Thank you for clarifying these points.

Michael

```
```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
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```
```
--
Michael I. Lichter, Ph.D. <mlichter@buffalo.edu>
Research Assistant Professor & NRSA Fellow
UB Department of Family Medicine / Primary Care Research Institute
UB Clinical Center, 462 Grider Street, Buffalo, NY 14215
Office: CC 126 / Phone: 716-898-4751 / FAX: 716-898-3536

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```