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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 jpitblado@stata.com * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: two questions about e(V) and e(V_modelbased) after estimation commands***From:*"Michael I. Lichter" <MLichter@Buffalo.EDU>

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