April 30, 1997

Dear EMCOV User:

Now that Joe Schafer's Norm program is available for Windows, I will
be supporting that program.  EMCOV is still available, but unless you
have a very special application, or are still running Windows 3.1 or
DOS, I would suggest you make the switch.  What follows is a very
simplistic tutorial for running Norm for Windows.  You can do a lot
more with Norm, but this will at least get you started.  If you have
questions, feel free to email me.  If I can't help, I will forward
your question to Joe.

Thanks for your support of the EMCOV program.  I hope you enjoy this
new software as much as I have.

John Graham
jwg4@psu.edu

*********************************************************************
Downloading Norm for Windows 95/NT, and setting it up in Windows 95 or NT
*********************************************************************

On the World Wide Web, go to address:

http://methcenter.psu.edu

Click on "software for missing data estimation"

Click on "norm"

Click on "multiple imputation" next to "Download Here"

Go to the bottom of that screen, and click on 
    "Stand-alone Win32 applications" next to "New!"



**********************************************************************
Simplified steps for running the Joe Schafer's Norm for Windows (v1.00)
**********************************************************************

    1.  click on the Norm icon.

************
Data Stuff
************

    2a.  click on "file", and find your input dataset.  It is easiest
if your data elements are separated by a space, and if each record is
on a separate line, but these are not absolute requirements if you
know the program.  Every missing value should be represented by the
same missing value indicator (e.g., -9).

   2b.  The program will guess at the number of variables and cases.
If you set up your data as shown above, the guess should be correct.
If the numbers are not correct, you should change them.

   2c.  The program will guess at your missing data indicator
(actually, this version always guesses -9).  If -9 is not correct,
enter the correct missing data indicator.

   2d.  The program accepts the data, and shows it to you in a data
window.  When you are satisfied that things look right, you can close
or minimize the data window.

   2e.  click on "run".  Click on "summarize the data".  This gives
you a summary of the missing data patterns, etc.  Close or minimize
the data summary window when you are satisfied with it.  It is stored
if you need it later.

**************************************
Initial Estimation with EM Algorithm
**************************************

   4a.  click on "run".  Click on "EM Algorithm".

   4b.  Make sure the default window is correct (it should be).

   4c.  You can usually accept all the defaults.  Click on the
"computing" tab if you want to change the defaults (e.g., raising the
maximum number of iterations).

   4d.  I generally just accept all the defaults here.  Click on "run"

   4e.  When EM is finished, you will see an EM window.  You should
record the number of iterations it took EM to converge.  The
information is also in this window.

*****************************************************************
Data Augmentation and Multiple Imputation (the real fun begins!)
*****************************************************************

   5.a.  Click on "run" again.  Click on "Data Augmentation"

   5.b.  I usually accept all the defaults on the first main screen.

   5.c.  Click on the "imputation" tab.  Click on the space marked
"impute at every kth iteration".  Change the value of k= to be twice
the number of iterations it took EM to converge.

   5d.  Click on the "computing" tab.  Change the value in the "number
of iterations" box to be 5 * k (if you want 5 imputations) or 10 * k
(if you want 10 iterations).

   5e.  Click on "run" and watch the fun.

Norm will automatically generate a proper imputed dataset every kth
iteration until it is done.  If your original dataset was "orig.dat",
the imputed datasets will be "orig1.imp", "orig2.imp", and so on.

********************
Analyzing your data.
********************

   I am assuming here you have decided to create 5 imputed datasets.

   6.  Analyze each of the 5 imputed datasets with whatever
complete-data analysis you are accustomed to using. (e.g., SAS PROC
REG).  Treat each of these datasets as if you had no missing data.

   6b.  Store the results from each of the 5 datasets in a separate
file like this (each dataset has just the two columns of numbers--no
labels).  You would have a separate row for each parameter of interest
to you.

           parameter est.    standard error
              .422751          .07721
              .621001          .07618
              .090011          .05412

   6c.  Make sure you have a separate dataset containing the results
from each imputed dataset.  That is, if you have 5 imputations, you
should have five output datasets.  I usually call them something like
"imp1.dat", "imp2.dat", and so on.

   Check the "Norm Utilities" web page for some programs we have written
   that make this part of the process a little easier.


***********************
Combining the Results
***********************

   7a. Rubin (1987) and Schafer (1997) have described how to put the
information together to allow you to draw the proper statistical
inferences.  Norm does a very nice job of doing all the work for you.

   7b.  Click on "Analyze" and click on "MI Inference".  Make sure
your default directory contains your datasets.

   7c.  Click on each dataset to select it (or click again to deselect
a dataset).

   7d.  Click on "go"

   7e.  You can usually accept all the defaults on the next window.
Click on "run".

   7f.  The next window shows the results of multiple imputation.
This is what you report in your article!

Good luck.

John Graham