A Simplex Fitting Approach to Dimensionality Assessment of Binary Data Matrices

Abstract

A Monte Carlo investigation of simplex fitting as a method of determining the dimensionality of binary data matrices was carried out. The simplex is an index of dimensionality having considerable appeal on a priori grounds. The study was carried out to explore the adequacy of simplex fitting for estimating dimensionality of binary item pools. To achieve this objective, an examination was made of the fit of correlation matrices with known factor structure to a correlation matrix representing a perfect simplex. Results indicated that the simplex fitting method is a viable approach to dimensionality assessment under certain situations. However, simplex fitting breaks down under extreme values of two important parameters. At less extreme levels of these parameters, the simplex fitting method is more effective than are the usual factor analytic dimensionality criteria. Results are discussed within the realm of considering the tenability of the goal of strict unidimensionality and the consequences of failure to assess correctly the dimensionality of a data matrix. The importance of attempting to measure major or dominant factors is also described. Finally, the need for examining whether current methods fail under similar conditions and suggestions for future research involving simplex fitting are discussed.