Stochastic approximation EM for large-scale exploratory IRT factor analysis.

A stochastic approximation EM algorithm (SAEM) is described for exploratory factor analysis of dichotomous or ordinal variables. The factor structure is obtained from sufficient statistics that are updated during iterations with the Robbins-Monro procedure. Two large-scale simulations are reported that compare accuracy and CPU time of the proposed SAEM algorithm to the Metropolis-Hasting Robbins-Monro procedure and to a generalized least squares analysis of the polychoric correlation matrix. A smaller-scale application to real data is also reported, including a method for obtaining standard errors of rotated factor loadings. A simulation study based on the real data analysis is conducted to study bias and error estimates. The SAEM factor algorithm requires minimal lines of code, no derivatives, and no large-matrix inversion. It is programmed entirely in R.