  Monotone missing data is a common problem in data analysis. However,
imputation combined with dimensionality reduction can be computationally
expensive, especially with the increasing size of datasets. To address this
issue, we propose a Blockwise principal component analysis Imputation (BPI)
framework for dimensionality reduction and imputation of monotone missing data.
The framework conducts Principal Component Analysis (PCA) on the observed part
of each monotone block of the data and then imputes on merging the obtained
principal components using a chosen imputation technique. BPI can work with
various imputation techniques and can significantly reduce imputation time
compared to conducting dimensionality reduction after imputation. This makes it
a practical and efficient approach for large datasets with monotone missing
data. Our experiments validate the improvement in speed. In addition, our
experiments also show that while applying MICE imputation directly on missing
data may not yield convergence, applying BPI with MICE for the data may lead to
convergence.
