Four methods for determining the dimensionality of a set of test items were compared: (1) linear factor analysis; (2) residual analysis; (3) nonlinear factor analysis; and (4) Bejar's method. Five artificial test data sets (for 40 items and 1500 examinees) were generated, consistent with the three-parameter logistic model and the assumption of either a one- or a two-dimensional latent space. Two variables were manipulated: the correlation between the traits (either .10 or .60) and the percent of test items measuring each trait (either 50 percent measuring each trait, or 75 percent measuring the first trait and 25 percent measuring the second trait). The results indicated that linear factor analysis in all instances overestimated the number of underlying dimensions in the data. Nonlinear factor analysis, with linear and quadratic terms, led to the correct determination of the item dimensionality in the three data sets where it was used. Both residual analysis and Bejar's method provided disappointing results. The results suggested the need for extreme caution in using linear factor analysis, residual analysis, and the Bejar method, until further investigations confirm their adequacy. Nonlinear factor analysis appeared to be the most promising of the four methods. (Author/GDC)