Assessing the dimensionality of a set of test items

This study compared four methods of determining the dimensionality of a set of test items: linear factor analysis, nonlinear factor analysis, residual analysis, and a method developed by Bejar (1980). Five artifi-cial test datasets (for 40 items and 1,500 examinees) were generated to be consistent with the three-parame-ter logistic model and the assumption of either a one-or a two-dimensional latent space. Two variables were manipulated: (1) the correlation between the traits (r =.10 or r =.60) and (2) the percent of test items measuring each trait (50 % measuring each trait, or 75 % measuring the first trait and 25 % measuring the second trait). While linear factor analysis in all instances over-estimated the number of underlying dimensions in th