Hi, Carla-

Although the multiple imputation estimator for coefficients is simply the
average of coefficients across imputed data sets, standard errors cannot be
treated that way.  This is so because beyond the variability associated with
the coefficient estimates in each individual imputed data set (the
"within-imputation" component of variance), additional variability arises when
estimating *across* the different data sets--the "between-imputation" component
of variance.

The formula for calculating standard errors is:

se-MI = √ u-bar-M + ((M+1)/M)*bM),

where:

se-MI is the standard error of a multiply imputed coefficient;

M is the number of imputed data sets;

u-bar-M is mean variance across imputed data sets (1/M * sigma s^^2-I, where
"sigma" is a summation, "s" is the standard error, "^^" means squared, and "I"
indexes imputed data sets);

and b-M is the variance of coefficient estimates around their mean, with an
adjustment factor that reduces b-M in proportion to the number of multiply
imputed data sets (i.e., b-M = ((1/M-1)*sigma(e-I - e-bar-MI)^^2), where e-I is
the coefficient estimate for imputed data set I and e-bar-MI is the mean of
coefficients across imputed data sets).

Sorry for the awkward notation.  You can get a much prettier version of these
equations in pp. 108-109 of:

Raghunathan T.E. (2004). "What do we do with missing data? Some options for
analysis of incomplete data", Annual Review of Public Health, 25, 99-117.


Hope this helps,
David

Quoting carla osorio <[log in to unmask]>:

> Hello,I would like to know what is the best way to calculate and report
> bivariate correlations when multiple imputation (Amelia) is employed.Is it OK
> if I calculate the correlations between the variables of interest in each of
> the imputed datasets and just average them?Also, I have read that it is fine
> to average coeffients over the imputated datasets, but I do not know if
> standard errors can also be treated in that way. thanks.Sincerely,Carla
> Osorio 
>
>
>
>
> **********************************************************
>              Political Methodology E-Mail List
>    Editors: Melanie Goodrich, <[log in to unmask]>
>             Delia Bailey, <[log in to unmask]>
> **********************************************************
>         Send messages to [log in to unmask]
>   To join the list, cancel your subscription, or modify
>            your subscription settings visit:
>
>           http://polmeth.wustl.edu/polmeth.php
>
> **********************************************************
>


------------------------------------
David Crow
Ph.D. Candidate
Department of Government
University of Texas at Austin
------------------------------------

Acueducto 62, Ed. B7, Depto. 202
Col. Huipulco, Del. Tlalpan
México, D.F.  C.P. 14370
M E X I C O

+011 52 (55) 5846-7200

**********************************************************
             Political Methodology E-Mail List
   Editors: Melanie Goodrich, <[log in to unmask]>
            Delia Bailey, <[log in to unmask]>
**********************************************************
        Send messages to [log in to unmask]
  To join the list, cancel your subscription, or modify
           your subscription settings visit:

          http://polmeth.wustl.edu/polmeth.php

**********************************************************