There is recent interest in classification procedures intended for use only when the response is ordinal. Ordinal response, however, is evident in the parameters estimated by either multinomial logistic or normal discriminant analyses, both of which classify either ordinal or non-ordinal responses. Further, there may be harm in applying ordinal models inappropriately and ample opportunity to assume mistakenly ordinality in real data sets. Therefore, it becomes important to ascertain whether there is benefit obtained in the appropriate application of ordinal models. This paper presents the results of a simulation study designed to compare classification accuracy of various models. We show that ordinal models classify less accurately than the multinomial logistic and normal discriminant procedures under a variety of circumstances. Until further studies become available, we presently conclude that ordinal models confer no advantage when the main purpose of the analysis is classification.