Nesting Monte Carlo EM for high-dimensional item factor analysis

Abstract

The item factor analysis model for investigating multidimensional latent spaces has proved to be useful. Parameter estimation in this model requires computationally demanding high-dimensional integrations. While several approaches to approximate such integrations have been proposed, they suffer various computational difficulties. This paper proposes a Nesting Monte Carlo Expectation-Maximization (MCEM) algorithm for item factor analysis with binary data. Simulation studies and a real data example suggest that the Nesting MCEM approach can significantly improve computational efficiency while also enjoying the good properties of stable convergence and easy implementation.

Keywords:

• full information item factor analysis
• Monte Carlo EM
• nesting EM

Acknowledgements

We would like to express our appreciation to the editors and reviewers for their helpful critiques and suggestions. This research was supported by grants 5K05DA000017-33 and 5P01DA001070-37 from the National Institute on Drug Abuse to P. M. Bentler, who acknowledges a financial interest in EQS and its distributor, Multivariate Software.