Current methods for fitting cognitive diagnosis models to educational data are based on maximum-likelihood estimation (MLE) methods such as Expectation Maximization (EM) and Markov Chain Monte Carlo that often suffer from practical limitations. As an alternative to MLE, parameter-free, nonmodel-based classification techniques have been proposed as heuristic or approximate methods for fitting cognitive diagnosis models; the asymptotic classification theory of cognitive diagnosis by Chiu, Douglas, and Li provides a theoretical foundation for this approach. However, both MLE methods and nonmodel-based classification heuristics can be applied only if the ``Q-matrix'' underlying a given test is known a priori. The binary Q-matrix specifies the relation between individual test items and the cognitive skills required to respond correctly to them and thus represents an integral component of all cognitive diagnosis models. Unfortunately, in practice, for most tests, the Q-matrix is unknown so that the item-attribute associations must be estimated based on the (fallible) judgment of experts. A misspecified Q-matrix results in the incorrect classification of examinees regardless of whether MLE or nonmodel-based heuristics are used. The asymptotic classification theory, for example, assumes that examinees' test item scores have been aggregated into sum-scores, an item-profile statistic that reflects the item-attribute associations and, so requires the Q-matrix of the test in question to be known. In avoiding any complications arising from an unknown and possibly misspecified Q-matrix, we propose to classify examinees directly based on their raw-score item profiles. Extensive simulation studies show that using nonaggregated item profiles results in superior recovery rates of the true underlying cluster structure, as compared to grouping examinees based on their sum-score profiles.