A recursive equation for computing higher-order derivatives of the elementary symmetric functions in the Rasch model is proposed. The formula is conceptually simple and relatively more efficient than the sum algorithm (Gustafsson, 1980). A simulation study indicated that the proposed formula has a small loss in accuracy, compared to the sum algorithm, for computing higher-order derivatives when tests contained 60 items or less. Index terms: difference algorithm, elementary symmetric functions, Formann's equation, Jansen's equation, Rasch model, sum algorithm.
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