Factor indeterminacy in generalizability theory

Abstract

Generalizability theory and common factor analysis are based upon the random effects model of the analysis of variance, and both are subject to the factor indeterminacy problem: The unobserved random variables (common factor scores or universe scores) are indeterminate. In the one-facet (repeated measures) design, the extent to which true or universe scores and common factor scores are not uniquely defined is shown to be a function of the dependability (reliability) of the data. The minimum possible correlation between equivalent common factor scores is a lower bound estimate of reliability.