Bounds for the multiple correlation of common factors with the items which comprise those factors are developed. It is then shown that under broad, but not completely general, conditions, the circumstances under which an infinite item domain does or does not perfectly determine selected subsets of its common factors. (Author/JKS)

The practicality of using the EM algorithm for maximum likelihood estimation of item parameters in the marginal distribution is presented. The EM procedure is shown to apply to general item-response models. (Author/JKS)

A two-step weighted least squares estimator for multiple factor analysis of dichotomized variables is discussed. The estimator is based on the first and second order joint probabilities. Asymptotic standard errors and a model test are obtained by applying the Jackknife procedure. (Author)

A new method--similar to Christoffersson's--for the factor analysis of dichotomous variables uses information from the first and second order proportions to fit a multiple factor model. The estimation is considerably simplified. Items from Rotter's locus of control inventory are included. (Author/JKS)

A chain of lower bound inequalities leading to the greatest lower bound to reliability is established for the internal consistency of a composite of unit-weighted scores (such as a test). Algorithms for obtaining various reliability coefficients are presented. (Author/JKS)

An approach for multiple factor analysis of dichotomized variables is presented based on distribution of first and second order joint probabilities of binary scored items. The estimator is based on the generalized least squares principle. Standard errors and a test of the fit of the model is given. (Author/RC)