A method of item factor analysis is described, which is based on Thurstone's multiple-factor model and implemented by marginal maximum likelihood estimation and the EM algorithm. Also assessed are the statistical significance of successive factors added to the model, provisions for guessing and omitted items, and Bayes constraints. (TJH)

Combining Rasch and latent class models is presented as a way to overcome deficiencies and retain the positive features of both. An estimation algorithm is outlined, providing conditional maximum likelihood estimates of item parameters for each class. The model is illustrated with simulated data and real data (n=869 adults). (SLD)

This study examined the application of the marginal maximum likelihood-EM algorithm to the parameter estimation problems of the normal ogive and logistic polytomous response models for Likert-type items. A rating scale model, based on F. Samejima's (1969) graded response model, was developed. (TJH)

Type I error rates of F. M. Lord's chi square test for differential item functioning were investigated using Monte Carlo simulations with marginal maximum likelihood estimation and marginal Bayesian estimation algorithms. Lord's chi square did not provide useful Type I error control for the three-parameter logistic model at these sample sizes.…

A probabilistic item response theory (IRT) model is developed for pair-comparison design in which the unfolding principle governing the choice process uses a discriminant process analogous to Thurstone's Law of Comparative Judgment. A simulation study demonstrates the feasibility of estimation, and two examples illustrate the implications for…