The Effect of Additional Variables on Factor Indeterminacy in Models with a Single Common Factor

Abstract

“Determinate” solutions for the indeterminate common factor of p variables satisfying the single common factor model are not unique. Therefore an infinite sequence of additional variables that conform jointly with the original p variables to the original single common factor model does not determine a unique solution for the indeterminate factor of the p variables (although the solution is unique for the factor of the infinite sequence). Other infinite sequences may be found to determine different solutions for the factor of the original p variables. The paper discusses a number of theorems about the effects of additional variables on factor indeterminacy in a model with a single common factor and draws conclusions from them for factor theory in general.