A Computational Note on the Application of the Supplemented EM Algorithm to Item Response Models

TL;DR

This paper introduces Agile-SEM, a refined version of the Supplemented EM algorithm that improves convergence, accuracy, and efficiency in item response model estimation by addressing floating-point limitations.

Contribution

The paper proposes Agile-SEM, a novel refinement of SEM that enhances numerical stability and performance in item response models, with potential for broader EM applications.

Findings

Agile-SEM outperforms original SEM and recent refinements in convergence and accuracy.

Agile-SEM requires fewer tuning parameters and handles floating-point limitations effectively.

Source code for Agile-SEM is publicly available.

Abstract

The EM algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Supplemented EM (SEM; Meng & Rubin, 1991) is one method for obtaining the parameter covariance matrix. SEM is implemented in both open-source (e.g., Chalmers, 2012; Pritikin, Hunter, & Boker, 2015) and commercial (e.g., Cai, Thissen, & du Toit, 2011) item response model estimation software. However, the original formulation of SEM did not adequately account for the limitations of IEEE 754 floating-point. Agile-SEM, a novel refinement of SEM, is proposed and compared against the original algorithm and a recent refinement (Tian, Cai, Thissen, & Xin, 2013) in a variety of item response model simulation studies. By controlling for the numerical noise intensity on a per-parameter basis, Agile-SEM demonstrated the best convergence properties, accuracy, and efficiency while, at the same time, requiring fewer tuning parameters. Complete source code is made freely available. The potential generalization of Agile-SEM to other EM application besides item response models is left as future work.