Solutions for the indeterminate common factor of a group of variables satisfying the single common factor model are not unique. This paper examines a number of thereoms concerning that problem and draws conclusions from them for factor analysis in general. (Author/JKS)

Nonlinear common factor models with polynomial regression functions, including interaction terms, are fitted by simultaneously estimating the factor loadings and common factor scores, using maximum likelihood and least squares methods. A Monte Carlo study gives support to a conjecture about the form of the distribution of the likelihood ratio…

Two major and two minor principles are shown to serve to generate a large number of multivariate models, including canonical analysis, factor analysis, and latent trait test theory. The statistical underpinnings of the theory are discussed. (Author/JKS)