One more thought upon additional reflection. Another way to express the data
such that it contains the same information is to create k* (k-1) binary
variables, each of which rank the data as "is object A preferred to object B".
These would all be dichotomous. This is the old-school numerical way of
running an ordered probit model--constructing all these variables and then
allowing each to have a unique intercept term. Some of these dichotomous
variables would be missing if either A or B were missing in your data, that is,
you don't know if A or B is higher ranked. With the data in this format,
everything would be congenial to the multivariate normal assumptions of Amelia
and the standard multiple imputation model. You could run the Amelia algorithm
on this data. Sometimes you would end up with imputations of all these k*(k-1)
new variables that were not transitive, which would be a violation of what we
know to be true. Matt Blackwell has written a rejection sampler for Amelia
that is described in the Amelia manual. You could rejection sample all
imputations that violate transitivity. This would be a model that would be
very reasonable given k=5 ranked data and reasonably immediately implementable
with the current library.
James Honaker
On Wed, Jun 23, 2010 03:12 PM "JAMES HONAKER" <tercer(a)psu.edu> wrote:
Donald,
A paper you might want to look at is:
Lim, Lordo and Wolfe. 1999. "A screening analysis for incomplete ranking
data" The Statistician
http://www.jstor.org/stable/2680899
If you have an interesting application or want to discuss ideas feel free to
contact me off list as it's a question I've been thinking about and delving
into lately.
James Honaker.
On Wed, Jun 23, 2010 02:24 PM Matt Blackwell <blackwel(a)fas.harvard.edu> wrote:
Hi Donald,
Amelia does not have the ability to do logical checks of the sort you
describe. One approach you could try is treating the rank of each item
as an ordinal variable. Of course, this will not preserve the logical
consistency within a unit. Depending on your analysis model this might
or might not be hugely important.
I hope that helps.
Cheers,
matt.
On Tue, Jun 22, 2010 at 7:19 PM, Donald Braman <dbraman(a)law.gwu.edu> wrote:
I need to impute a ranking of 5 items. Any
advice on how to go about it?
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