The robustness of Rasch estimates

Abstract

The small scale applicability of Rasch estimates was investigated under simulated conditions of guessing and heterogeneity in item discrimination. The accuracy of the Rasch estimates was evaluated by means of the correlation between the item/person parameters and their estimates, the standard deviations of the estimates, and the difference as well as the root mean squared difference between parameters and estimates. Within the range of the present investigation (from 10 to 50 items and from 25 to 500 persons) these criteria yielded favorable results under conditions of heterogeneous item discrimination. Under conditions of guessing, robustness could only be demonstrated for the correlational criterion. Guessing affects the difference measures between the parameter values and estimates quite strongly in a systematic way. It is argued that, notwithstanding these estimation errors, the Rasch model is to be preferred over nonstandard estimation procedures, from which the validity is unclear, or the use of the three-parameter model with its computational problems in small samples.