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Through simulations, this study investigates the effects of anchor item methods on Type I error and power of detecting differential item functioning (DIF) using the likelihood ratio test within the framework of item response theory. Four anchor item methods were compared: the all-other, 1-item, 4-item, and 10-item methods. The results showed that it is the average signed area between the reference and focal groups rather than the percentage of DIF items in a test that determines the Type I error of the all-other method. The all-other method yields good control over Type I error and reasonable power only when the average signed area approaches zero. The all-other method is not recommended for practical DIF analysis because it is only adequate under very stringent conditions. The other three methods perform appropriately under all the simulated conditions. The more anchor items are used, the higher the power of DIF detection.

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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.

Extreme response style (ERS) is a systematic tendency for a person to endorse extreme options (e.g., strongly disagree, strongly agree) on Likert-type or rating-scale items. In this study, we develop a new class of item response theory (IRT) models to account for ERS so that the target latent trait is free from the response style and the tendency of ERS is quantified. Parameters of these new models can be estimated with marginal maximum likelihood estimation methods or Bayesian methods. In this study, we use the freeware program WinBUGS, which implements Bayesian methods. In a series of simulations, we find that the parameters are recovered fairly well; ignoring ERS by fitting standard IRT models resulted in biased estimates, and fitting the new models to data without ERS did little harm. Two empirical examples are provided to illustrate the implications and applications of the new models.