Graham is right. In multiple imputation, interactions should be imputed as
though they are additional variables, not constructed by multiplying imputed
values. The same is true if you have x and x^2 in a model. The x^2 term
should be imputed just like any other variable, not constructed by squaring
the imputed values of x. While this principle may seem counterintuitive, it
is easily demonstrated by simulation that the more "natural" way to do it
produces biased estimates.
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Paul D. Allison
Department of Sociology
University of Pennsylvania
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