A Definition for the Common-Factor Analysis Model and the Elimination of Problems of Factor Score Indeterminacy

A factor analysis model consists of a random sequence of variates defined on a probability space and satisfying the usual descriptive equations of the common-factor analysis in which the common-factor scores are dimensionally independent. Necessary and sufficient conditions are given for a model to exist with essentially unique and hence determinate common factor scores. Parallel results are given for the existence of models with nonunique and hence indeterminate scores. It is then próved that two models cannot exist with essentially unique but different scores for the same common factors. The meaning and application of these results are discussed.