What is the relationship between the model used for imputation and the model used for analysis?
An imputation model should be chosen to be (at least approximately) compatible with the analyses to be performed on the imputed datasets. The imputation model should be rich enough to preserve the associations or relationships among variables that will be the focus of later investigation. For example, suppose that a variable Y is imputed under a normal model that includes the variable X1. After imputation, the analyst then uses linear regression to predict Y from X1 and another variable X2 which was not in the imputation model. The estimated coefficient for X2 from this regression would tend to be biased toward zero, because Y has been imputed without regard for its possible relationship with X2. In general, any association that may prove important in subsequent analyses should be present in the imputation model. The converse of this rule, however, is not necessary. If Y has been imputed under a model that includes X2, there is no need to include X2 in future analyses involving Y unles
