| Indeterminacy, as a psychometric issue, first obtained prominence in the context of the factor analysis model. Piaggio (1931), Guttman (1955), and others, gave results that proved that random factor analysis models are fundamentally indeterminate, while Steiger and Schonemann (1978) gave a comprehensive history of the issue. Many researchers have noted the similarity between item response models for dichotomous variables, and factor analysis models for continuous variables. The present work demonstrates the structural equivalence of certain random item response models for dichotomous variables and certain random factor analysis models. As a result of these structural equivalences, item response models also are seen to be indeterminate. Unidimensional models alone are considered, since the indeterminacy issue applies equally to multidimensional models. Measures to assess the degree of indeterminacy in a given item response solution are derived, and determinacy in the limit is discussed. Finally, the interpretation of the mathematical results on indeterminacy are shown to rest on a proper characterization of the notion of a latent variable. |
