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# Re: st: Propensity score matching and multiple imputation

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: Propensity score matching and multiple imputation Date Thu, 17 May 2012 10:03:24 -0400

```Yes, show us numbers, including the number of imputed observations. I would note that
the analysis without MI will have a smaller sample size than that for the MI analysis because observations with missing data are excluded. Therefore basing your expectation on the pre-MI standard error can be misleading.

Steve
sjsamuels@gmail.com

2012, at 8:07 AM, Brendan Halpin wrote:

On Thu, May 17 2012, Michela Coppola wrote:

> Now the combined standard error using the Rubin's rule is smaller than
> the standard errors in each of the 5 implicates! I expected bigger
> standard errors not smaller ones (as the variability introduced through
> the imputation is now taken into account).
>
>
>
> How is it that possible (I checked several times the formulas, so I'm
> sure that there are no errors when combining in excel the standard
> errors)?

If I understand the relevant formula correctly (see e.g., p237 of
Patrick Royston's 2004 Stata Journal article) the variance of the
imputation is the average of the variance of the imputed data sets (the
"within" part), plus the "between" part, which is strictly non-negative.

I suspect Excel is not doing what you think it is doing. And given
the nature of Excel, it is a little hard for you to show us what it is
doing.

Show us the figures, perhaps?

Brendan
--
Brendan Halpin,   Department of Sociology,   University of Limerick,   Ireland
Tel: w +353-61-213147  f +353-61-202569  h +353-61-338562;  Room F1-009 x 3147
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```