Missing Data Imputation in Balanced Construction for Incomplete Block Designs

Abstract

Observational data with massive sample sizes are often distributed on many local machines. From an experimental design perspective, investigators often desire to identify the effect of new treatments (even ML algorithms) on many blocks of experimental data. With time requirements or budget constraints, assigning all treatments to each block is not always feasible. This creates incomplete responses with respect to a randomized complete block design (RCBD). These incomplete responses are missing by design. However, whether they can be estimated with missing imputation methods is not well understood. Thus, it is challenging to correctly identify the treatment effects with missing data. To this end, this paper provides a method for imputation and analysis of the responses with missing data. The proposed method consists of three steps: Reconstruction, Imputation, and ‘Complete’-data Analysis (RICA). The incomplete responses are imputed with the expectation-maximization (EM) algorithm. The RCBD model is then fitted by the resulting dataset. The identifiability result suggests that the missing may be nonignorable for each block, but the whole data of an incomplete design are missing by design when the design is balanced. Theoretical results on relative efficiency also inform us when the missingness should be imputed for incomplete designs with the role of balanced variance. Applications on real-world data verify the efficacy of this method.

Keywords

• distributed data
• expectation-maximization
• incomplete block design
• missing by design
• machine learning