-----Original Message-----
From: Frank E Harrell Jr [mailto:[EMAIL PROTECTED]
Sent: Wednesday, January 02, 2008 11:48 AM
To: David Judkins
Cc: Alan Zaslavsky; impute@lists.utsouthwestern.edu;
[EMAIL PROTECTED]
Subject: Re: [Impute] Rounding option on PROC MI and choosing a final MI
dataset
David Judkins wrote:
Raquel,
Your problem is typical of the class of problems that I have been
working on for about 15 years now. You can look up my imputation
papers
in the CIS. None of the currently available (free or marketed)
software solutions known to me are designed to preserve the structure
of
general multivariate data. The ones that build models of multivariate
relationships are mostly designed for either normal or binary data.
Programs designed for general data are usually designed to impute a
single variable at a time and generally fail to preserve multivariate
structure. If you have the luxury of a large programming budget, you
could program the algorithms that some of us here at Westat have
developed and published.
David,
In theory you are correct, but I think your note slightly misses the
point. It is amazing how well the chained equations approach of MICE
and my aregImpute function work, given they were not designed to
preserve the multivariate structure. And they make fewer assumptions.
I am particularly dubious about any methods that assume linearity and
multivariate normality.
aregImpute uses Fisher's optimum scoring algorithm to impute nominal
variables. If predictive mean matching is used with aregImpute (a more
nonparametric approach not available with your multivariate approach),
the distribution of imputed categories is quite sensible.
Frank Harrell
As Alan replied, however, given that all your individual item rates
are
low, perhaps one of the available solutions would work reasonably well
for you.
It sounds as if you don't have any skip patterns. If so, you could
just
impute the mode for each variable. A second solution that is only a
little more complicated would be to independently impute each variable
by a simple hotdeck. Either way, you end up with 100% complete
vectors.
You don't have to do any rounding. All variables have permissible
values. You will have better marginal distributions with independent
hotdecks than you get by imputing modes.
But neither solution protects multivariate structure. Here is a bit
more complicated solution that tries to do that but is still fairly
simple:
Pick a single variable as the most important for your analyses. Call
it
Y. Let S be the maximum set of variables with zero item nonresponse.
Build the best model for Y in terms of S that you can. (Doesn't have
to
be a linear model.) Output predicted values of Y for the whole
sample.
Call them Ypred. Let O be the maximum set of cases with zero
nonresponse on all variables. Find the nearest neighbor in O for each
case with one or more missing values. So then you have a donor case
and
a recipient case. Let X1i,...,Xpi be the set of variables on
recipient
case i with missing values. Let X1j,...,Xpj be the corresponding set
of
variables on the donor case. Impute Xki=Xkj for k=1,...,p.
To the extent that the variables in S are good predictors of Y and to
the extent that the other variables are related to Y, you should get
slightly better preservation of covariances than with independent
hotdecks. There are many variants on this theme. You will still
have
some fading of multivariate structure, however. And you will
under-estimate post-imputation variances.
For combining hotdecks with multiple imputation, see the exciting new
papers by Siddique and Belin and by Little, Yosef, Cain, Nan, and
Harlow, both in the first issue of volume 27 of Statistics in
Medicine.
--Dave
-----Original Message-----
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Alan
Zaslavsky
Sent: Wednesday, January 02, 2008 10:07 AM
To: impute@lists.utsouthwestern.edu; [EMAIL PROTECTED]
Subject: [Impute] Rounding option on PROC MI and choosing a final MI
dataset
From: "Raquel Hampton" <[EMAIL PROTECTED]>
Subject: [Impute] Rounding option on PROC MI and choosing a final MI
dataset
My first question is: there is a round option for PROC MI, but I read
in
an article (Horton, N.J., Lipsitz, S.P., & Parzen, M. (2003). A
potential for bias when rounding in multiple imputation. The American
Statistician 57(4), 229-232) that using the round option for
categorical
data (the items have nominal responses, ranging from 1 to 5) produces
bias estimates, though logical. So what can be done? I only have
access
to SAS and STATA, but I am not very familar with STATA. Will this
not
be such a problem since the proportion of missing for each individual
item is small?
Do you really mean nominal (unordered categories, like French, German,
English, or chocolate, vanilla, strawberry) or ordinal (like poor,
fair,
good, excellent)? If nominal, you won't get anything sensible by
fitting
a normal model and rounding. If ordinal and well distributed across
the
categories, the bias of using rounded data will be less than with the
binomial data primarily considered by the Horton et al. article.
You might also consider whether it is necessary to round at all --
depends on how the data will be used in further analyses.
With only a couple of percent missing on each item, all of the issues
about imputation become less crucial, although as noted in a previous
response you should definitely run the proper MI analysis to verify
that
the between-imputation contribution to variance is small. In practice
any modeling exercise is a compromise involving putting more effort
into
the important aspects of the modeling and in this case this might not
require doing the most methodologically advanced things with the
imputation.
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