A New Algorithm For Computing Elementary Symmetric Functions And Their F irst And Second Derivatives

Such functions are used extensively in item response models, such as the Rasch model ( Fischer, 1974; Rasch, 1960; Verhelst, Glas & van der Sluis, 1984). Specifically, these functions, together with their first
and second derivatives, are needed in deriving conditional maximum likelihood estimators and their standard errors in these models. As the number of functions needed grows rapidly with the number of arguments, an algorithm is called for which cuts down computing time, without significantly increasing core requirements.