Factor-analytic research is common in the study of constructs and measures in psychological assessment. Latent factors can represent traits as continuous underlying dimensions or as discrete categories. When examining the distributions of estimated scores on latent factors, one would expect unimodal distributions for dimensional data and bimodal or multimodal distributions for categorical data. Unfortunately, identifying modes is subjective, and the operationalization of counting local maxima has not performed very well. Rather than locating and counting modes, the authors propose performing parallel analyses of categorical and dimensional comparison data and calculating an index of the relative fit of these competing structural models. In an extensive Monte Carlo study, the authors replicated prior results for mode counting and found that trimming distributions' tails helped. However, parallel analyses of comparison data achieved much greater accuracy, improved base rate estimation, and afforded consistency checks with other taxometric procedures. Two additional studies apply this approach to empirical data either known to be categorical or presumed to be dimensional. Each study supports this new method for factor-analytic research on the latent structure of constructs and measures in psychological assessment. (Contains 4 footnotes, 2 tables, and 7 figures.)