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This paper describes an R package, rpartOrdinal, that implements alternative splitting functions for fitting a classification tree when interest lies in predicting an ordinal response. This includes the generalized Gini impurity function, which was introduced as a method for predicting an ordinal response by including costs of misclassification into the impurity function, as well as an alternative ordinal impurity function due to Piccarreta (2008) that does not require the assignment of misclassification costs. The ordered twoing splitting method, which is not defined as a decrease in node impurity, is also included in the package. Since, in the ordinal response setting, misclassifying observations to adjacent categories is a less egregious error than misclassifying observations to distant categories, this package also includes a function for estimating an ordinal measure of association, the gamma statistic.