st: ICE: Combining proportions using Rubin's rules via mim

[Leslie Phillips <leslie.phillips@gmail.com>]

Dear all,
I am using Patrick Royston's ICE to multiply impute data that will be
used to calculate proportions.  I have calculated my proportions on
the m imputed datasets which ICE appends into one dataset.  I now want
to combine my proportions using Rubin's rule.  It is my first
experience with MICE/ICE and I am a basic to less-than-basic Stata
user so I am stumbling through this a bit but my read of it is that
the overall estimate is the average of the individual estimates (in my
case proportions).  It seems ICE will do this for me as follows:
1) I use ice to carry out m imputations
2) I calculate my proportion ("myprop") in the appended dataset which
calculates m proportions for each _mi
3) Here's where it gets tricky for me, is it correct to use the mim
combine command as below to get the appropriately combined proportions
and a standard error that accounts for both the within and between
imputation variance a la Rubin?  And if so, I should just repeat this
for each _mi?

mim, cat(combine)  est(_b[myprop]) se(_se[myprop]) : mean myprop if _mi==1

Applying Rubin's rules, using statsby for analysis:

-> statsby est = (_b[myprop]) se = (_se[myprop]),  by(_mj) nodots
clear : mean  myprop if _mi==1

     command:  mean myprop if _mi==1
         est:  _b[myprop]
          se:  _se[myprop]
          by:  _mj


Combined estimate  |       Mean     Std. Err.      [95% Conf. Interval]    FMI
-------------------+----------------------------------------------------------
 _b[myprop]             |   .7146546     .0178508        .637849
.7914602      .

Any guidance is warmly welcomed,
Leslie

leslie.phillips@gmail.com
University of Washington, Seattle

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