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Abstract
A broad framework for examining the class of unidimensional and multidimensional models for item responses is provided by nonlinear factor analysis, with a classification of models as strictly linear, linear in their coefficients, or strictly nonlinear. These groups of models are compared and constrasted with respect to the associated problems of estimation, testing fit, and scoring an examinee. The invariance of item parameters is related to the congruence of common factors in linear theory.
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