In addition to Paul von Hippel I would say that in future research you 
might be using the covariate in some (unforeseen) analysis of the 
imputed data. Iit has been shown that in order to obtain
a proper estimate of the relationship between variables suffering from 
missing values and
another (complete) relevant variable, this variable should be entered in 
the  imputation
model; the strength of the relationship will be underestimated if such a 
variable is left out
(see, e.g., Little, 1992, Schafer, 1997, pp. 140-143, or Schafer & 
Olsen, 1998). Therefore,
to get an unbiased estimate of this relationship in subsequent analysis, 
the covariate should be included in the
imputation model.

Little, R. J. A.(1992). Regression with missing X's: A review. Journal 
of the American
Statistical Association, 87, 1227{1237.

Schafer, J. L.(1997). Analysis of incomplete multivariate data. London: 
Chapman and
Hall.

Schafer, J. L., & Olsen, M. K.(1998). Multiple imputation for 
multivariate missing data
problems: A data analyst's perspective. Multivariate Behavioral 
Research, 33,
545{571.

Niels Smits
Research Methodology, 
Statistics and Data-analysis
Faculty of Psychology and Education
Free University Amsterdam
Van der Boechorststraat 1
1081 BT Amsterdam
The Netherlands
Tel:   +31 (0)20 5988713
Secr:  +31 (0)20 5988757
Fax:   +31 (0)20 5988758 




Paul von Hippel wrote:

> My understanding is that you can get bias from having too few 
> variables but not from having too many.
>
>
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