Traditional Dimensionality Versus Essential Dimensionality

Abstract

This article addresses testing the hypothesis of one versus more than one dominant (essential) dimension in the possible presence of minor dimensions. The method used is Stout's statistical test of essential unidimensionality, which is based on the theory of essential unidimensionality. Differences between the traditional definition of dimensionality provided by item response theory, which counts all dimensions present, and essential dimensionality, which counts only dominant dimensions, are discussed. As Monte Carlo studies demonstrate, Stout's test of essential unidimensionality tends to indicate essential unidimensionality in the presence of one dominant dimension and one or more minor dimensions that have a relatively small influence on item scores. As the influence of the minor dimensions increases, Stout's test is more likely to reject the hypothesis of essential unidimensionality. To assist in interpreting these studies, a rough index of the deviation from essential unidimensionality is proposed.