Suppose I am interested in fitting a linear regression model as follows:
Y = a + b1 * age(continuous) + b2 * sex + b3 * income
This model will be run in both the whole sample and subgroups (defined by age categories including 15–35 years, 36-45 years, and >=46 years).
There are missing values in age, sex, and income, and multiple imputation (e.g., MICE) is used to impute the missing values.
My question is: Besides including all the variables in the analysis model in the imputation model, should the categorised age variable be also included in the imputation model?
I am not a statistician. I read the paper "On the Bias of the Multiple-Imputation Variance Estimator in Survey Sampling". It seems that subgroup variable was referred to as domain.
Thank you in advance for your help!