A Metropolis-Hastings Robbins-Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The…

Item factor analysis (IFA), already well established in educational measurement, is increasingly applied to psychological measurement in research settings. However, high-dimensional confirmatory IFA remains a numerical challenge. The current research extends the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm, initially proposed for…

Motivated by Gibbons et al.'s (Appl. Psychol. Meas. 31:4-19, "2007") full-information maximum marginal likelihood item bifactor analysis for polytomous data, and Rijmen, Vansteelandt, and De Boeck's (Psychometrika 73:167-182, "2008") work on constructing computationally efficient estimation algorithms for latent variable…

We apply the Supplemented EM algorithm (Meng & Rubin, 1991) to address a chronic problem with the "two-stage" fitting of covariance structure models in the presence of ignorable missing data: the lack of an asymptotically chi-square distributed goodness-of-fit statistic. We show that the Supplemented EM algorithm provides a…