On Tue, 20 Sep 2005, Laurenceau, Jean-Philippe wrote:
Dear Impute list--I was hoping that I could get your thoughts on the
following two questions related to multiple imputation (MI).
1) Do you know of any way to combine R-squared from a multiple
regression using MI? I don't know what the SE would be to combine
and test using Rubin's rules. Would one have to do a multiparameter
inference testing whether all the regression coefficients
simultaneously differ from zero?
Because the standard combining rules rely on asymptotic normality, and
R-squared is a proportion of variance, asymptotic normality will be better
approximated with a transformation, like log (R-squared). Then the
standard rules can be used with the corresponding asymptotic variance for
it. It would probably be more accurate, and more work to do the standard
multivariate version, or the LRT version of Meng&Rubin
2) I have noticed from MI practice that the degrees of freedom (df)
after combination following MI can be quite different (often much
larger) than the sample N.
The standard combining rules assume N -> big, i.e., asymptotics.
I can see from the formula for df that it
depends on a few things, such as the rate of missing information, the
number of imputations, etc. In order to report dfs in a manuscript I
am working on that uses MI, a colleague of mine recommended looking
into the use of adjusted df from a paper in the 90s by Bernard and
Rubin (correct?) rather than df based on the sample size. Would you
agree with this suggestion?
Yup.
Would you suggest an alternative
approach? I tried to find the Bernard and Rubin paper, but I have
been unsuccessful.
Biometrika, 1999, p.944.
Thank you for your time and your thoughts on these issues. J-P
Jean-Philippe Laurenceau, Ph.D.
Department of Psychology
University of Delaware
218 Wolf Hall
Newark, DE 19716-2577
Voice: (302) 831-2309
Fax: (302) 831-3645
[EMAIL PROTECTED]
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Donald B. Rubin
John L. Loeb Professor of Statistics
Department of Statistics
1 Oxford Street
Harvard University
Cambridge MA 02138
Tel: 617-495-5498 Fax: 617-496-8057
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