  Variable selection is crucial for sparse modeling in this age of big data.
Missing values are common in data, and make variable selection more
complicated. The approach of multiple imputation (MI) results in multiply
imputed datasets for missing values, and has been widely applied in various
variable selection procedures. However, directly performing variable selection
on the whole MI data or bootstrapped MI data may not be worthy in terms of
computation cost. To fast identify the active variables in the linear
regression model, we propose the adaptive grafting procedure with three pooling
rules on MI data. The proposed methods proceed iteratively, which starts from
finding the active variables based on the complete case subset and then expand
the working data matrix with both the number of active variables and available
observations. A comprehensive simulation study shows the selection accuracy in
different aspects and computational efficiency of the proposed methods. Two
real-life examples illustrate the strength of the proposed methods.
