st: ice command question about interactions

[Alan Acock <acock@mac.com>]

John Graham, who has done a lot of work with Schafer, published a  
chapter, "Missing Data Analysis: Making it Work in the Real World" in  
the 2009 Annual Review of Psychology 60:549-576. He compares a wide  
variety of software and I was surprised that he never mentions Stata.  
Some of what he says, however, is inconsistent with how I've been  
utilizing the ice command. Here is a key example.

ice allows us to passively estimate an interaction term by estimating  
the main effects and then multiplying these together so the  
interaction of X&Y will be the imputed X times the imputed Y. This  
seems necessary to preserve the interpretation of the interaction.

Graham says we need to include the interaction term. "The problem with  
excluding such variables from the imputation model is that all  
imputation is done under the assumption that the correlation is r = 0  
between the omitted variable and all other variables in the  
imputation." This is the same argument that Graham makes for imputing  
the dependent variable in the imputation (a sensible thing to do).

I understand the importance of including the dependent variable when  
doing multiple imputations, and see how Graham could apply this to the  
interaction term, but it makes no sense to me to have an interaction  
of X and Y not equal X*Y.

What do those of you with more experience on missing values than I  
have think about this?
Alan Acock


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