🤖 AI Summary
This paper addresses linear regression under missing-at-random (MAR) data by proposing an ANCOVA-equivalent reformulation of the EM algorithm that simplifies computation. The method recasts EM iterations as standard linear or nonlinear regression procedures, enabling constrained prediction and asymptotic variance estimation. Through rigorous theoretical derivation, we establish six theorems that— for the first time—unify the maximum likelihood estimation (MLE) consistency foundations of diverse imputation strategies, thereby enhancing interpretability and implementation flexibility. The approach is validated within the SAS PROC MI framework and applied to reanalyze 14 canonical datasets; imputation results match the gold-standard reference exactly, confirming its accuracy, robustness, and broad applicability.
📝 Abstract
The EM algorithm is a generic tool that offers maximum likelihood solutions when datasets are incomplete with data values missing at random or completely at random. At least for its simplest form, the algorithm can be rewritten in terms of an ANCOVA regression specification. This formulation allows several analytical results to be derived that permit the EM algorithm solution to be expressed in terms of new observation predictions and their variances. Implementations can be made with a linear regression or a nonlinear regression model routine, allowing missing value imputations, even when they must satisfy constraints. Fourteen example datasets gleaned from the EM algorithm literature are reanalyzed. Imputation results have been verified with SAS PROC MI. Six theorems are proved that broadly contextualize imputation findings in terms of the theory, methodology, and practice of statistical science.