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.