The recovery of the density scale using a stochastic quasi-realization of additive conjoint measurement

This paper attempts to illuminate some of the practical limitations that the Rasch model (and by extension, Item Response Theory models) may have by focusing on the recovery of the density scale. Five simulation trials were conducted: the first four to recover the density scale with different deviations from the assumptions implicit in the use of the Rasch model and the fifth trial with an almost ideal data set. Results demonstrate that when error distributions are insufficient the results may be ordinal at best, and when error distributions are non-symmetrical, the positions of items may be biased with respect to the positions of persons. Results also confirm that errors of estimation, and test and sample information functions are sample dependent.