Michael I. Lichter <[email protected]>
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
[email protected]
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