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
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>
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