Nesting Monte Carlo EM for high-dimensional item factor analysis.

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.