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.

On Components, Latent Variables, PLS and Simple Methods: Reactions to Rigdon's Rethinking of PLS

“…Whether in classical unidimensional or multidimensional formats, and various response functions, these methods describe the probabilities of endorsement of binary or ordinal items or response categories in terms of parameters as well as latent variable trait scores. This is an interesting and active field, especially in the multidimensional context (e.g., An & Bentler, 2011, 2012; Cai, 2010; Cai, Yang, & Hansen, 2011; Reckase, 2009; J. Wu & Bentler, 2012, 2013).…”