Multistructure Statistical Model Applied To Factor Analysis

A general statistical model for the multivariate analysis of mean and covariance structures is described. Various models, such as those of Bock and Bargmann; Joreskog; and Wiley, Schmidt and Bramble, are special cases. One specialization of the general model produces a class of factor analytic models. The simplest case represents an alternative conceptualization of the multiple-factor model developed by Thurstone. In contrast to the traditional model, the new model has common-factor loadings that are invariant with respect to variable scaling and unique variances that must be positive. A special feature of the model is that it does not allow the confounding of principal components analysis and factor analysis. Matrix calculus is used to develop statistical aspects of the model. Parameters are estimated by the maximum likelihood method with Newton-Raphson iterations.