Full-information item factor analysis

Abstract

A method of item factor analysis based on Thurstone’s multiple-factor model and implemented by marginal maximum likelihood estimation and the EM algorithm is described. Statistical significance of successive factors added to the model is tested by the likelihood ratio criterion. Provisions for effects of guessing on multiple-choice items, and for omitted and not-reached items, are included. Bayes constraints on the factor loadings are found to be necessary to suppress Heywood cases. Numerous applications to simulated and real data are presented to substantiate the accuracy and practical utility of the method. Index terms: Armed Services Vocational Aptitude Battery, Beta prior, E M algorithm, Item factor analysis, TESTFACT, Tetrachoric correlation.