This study explored two methods that are used to assess the dimensionality of item response data. The paper begins with a discussion of the assessment dimensionality and the use of factor-analytic procedures. A number of problems associated with using linear factor analyses to assess dimensionality are also considered. A procedure is presented for hierarchical cluster analysis in combination with a new proximity measure. A simulation was performed to study how well the different cluster methods (group average, centroid, and Ward's cluster method) recovered unidimensional and multidimensional data and whether different cluster methods over- or underestimated the number of dimensions in unidimensional or multidimensional data. In the simulation, only the centroid cluster method recovered the true dimensionality of simulated unidimensional data reasonably well and only in shorter tests. For all other conditions, the three cluster methods consistently overshadowed the true dimensionality of the simulated data. For three-dimensional data, Ward's cluster method was the best performing, and only the group average and Ward's cluster method recovered the multidimensional data well. Implications for practitioners are discussed. (Contains 6 tables and 46 references.) (SLD)