ABSTRACT
A distinction is made between models that are linear in both their coefficients and the latent traits, models that are linear in their coefficients but not in the latent traits, and models that are nonlinear in both. Exploratory devices for distinguishing between alternative models, linear in their coefficients, for data with a given covariance structure, are described. General theory is given for the fitting of a prescribed nonlinear hypothesis, linear or nonlinear in its coefficients, by least squares or maximum likelihood-ratio criteria.
