A Hybrid EM Algorithm for Linear Two-Way Interactions with Missing Data

TL;DR

This paper introduces a hybrid EM algorithm for product-term regression models with missing data, combining analytical and numerical solutions to improve estimation accuracy and efficiency.

Contribution

The paper presents a novel hybrid EM algorithm that analytically solves most cases, reducing reliance on numerical integration in missing data problems.

Findings

Higher estimation accuracy compared to full numerical methods

Analytical solutions are feasible for most missing data patterns

Effective on both simulated and real datasets

Abstract

We study an EM algorithm for estimating product-term regression models with missing data. The study of such problems in the likelihood tradition has thus far been restricted to an EM algorithm method using full numerical integration. However, under most missing data patterns, we show that this problem can be solved analytically, and numerical approximations are only needed under specific conditions. Thus we propose a hybrid EM algorithm, which uses analytic solutions when available and approximate solutions only when needed. The theoretical framework of our algorithm is described herein, along with two numerical experiments using both simulated and real data. We show that our algorithm confers higher accuracy to the estimation process, relative to the existing full numerical integration method. We conclude with a discussion of applications, extensions, and topics of further research.