A SIMPLEX FITTING APPROACH TO DIMENSIONALITY ASSESSMENT OF BINARY DATA MATRICES

A Monte Carlo investigation of simplex fitting as a method of determin ing the dimensionality of binary data matrices was carried out. The si mplex is an index of dimensionality having considerable appeal on a pr iori grounds. The study was carried out to explore the adequacy of sim plex fitting for estimating dimensionality of binary item pools. To ac hieve this objective, an examination was made of the fit of correlatio n matrices with known factor structure to a correlation matrix represe nting a perfect simplex. Results indicated that the simplex fitting me thod is a viable approach to dimensionality assessment under certain s ituations. However, simplex fitting breaks down under extreme values o f two important parameters. At less extreme levels of these parameters , the simplex fitting method is more effective than are the usual fact or analytic dimensionality criteria. Results are discussed within the realm of considering the tenability of the goal of strict unidimension ality and the consequences of failure to assess correctly the dimensio nality of a data matrix. The importance of attempting to measure major or dominant factors is also described. Finally, the need for examinin g whether current methods fail under similar conditions and suggestion s for future research involving simplex fitting are discussed.