The assessment of dimensionality of data is important to item response theory (IRT) modelling and other multidimensional data analysis techniques. The fact that the parameters from the factor analysis formulation for dichotomous data can be expressed in terms of the parameters in the multidimensional IRT model suggests that the assessment of the dimensionality of the latent trait space can also be approached from the factor analytical viewpoint. Some problems connected with the assessment of the dimensionality of the latent space are discussed, and the conclusions are supported by simulated results for sample sizes of 250 and 500 on a 15-item test. Five tables contain data from the simulation; and 48 graphs illustrate eigenvalues and plotted mean residuals. A 46-item list of references is included. (Author/SLD)