The Rasch Testlet Model

Abstract

The Rasch testlet model for both dichotomous and polytomous items in testlet-based tests is proposed. It can be viewed as a special case of the multidimensional random coefficients multinomial logit model (MRCMLM). Therefore, the estimation procedures for the MRCMLM can be directly applied. Simulations were conducted to examine parameter recovery under the dichotomous Rasch testlet model and the partial-credit testlet model. Results indicated that the item and person parameters as well as the random testlet effects could be recovered very accurately under all the simulated conditions. As sample sizes were increased, the root mean square errors of the estimates decreased to an acceptable level. An empirical example of an English test with 11 testlets was given. Index terms: multidimensional item response model, item bundle, marginal maximum likelihood estimation, parameter recovery.