In selected-response assessments such as attitude surveys with Likert-type rating scales, examinees often select from rating scale categories to reflect their locations on a construct. Researchers have observed that some examinees exhibit "response styles," which are systematic patterns of responses in which examinees are more likely to…

Item response theory (IRT) refers to a family of mathematical models which describe the relationship between latent continuous variables (attributes or characteristics) and their manifestations (dichotomous/polytomous observed outcomes or responses) with regard to a set of item characteristics. Researchers typically use parametric IRT (PIRT)…

This article aims to provide a theoretical framework for computerized adaptive tests (CAT) and item response theory models for polytomous items. Besides that, it aims to introduce the simulation and live CAT software to the related researchers. Computerized adaptive test algorithm, assumptions of item response theory models, nominal response…

In testing factorial invariance, researchers have often used a reference variable strategy in which the factor loading for a variable (i.e., reference variable) is fixed to 1 for identification. This commonly used method can be misleading if the chosen reference variable is actually a noninvariant item. This simulation study suggests an…

This comprehensive "Handbook" focuses on the most used polytomous item response theory (IRT) models. These models help us understand the interaction between examinees and test questions where the questions have various response categories. The book reviews all of the major models and includes discussions about how and where the models…

Numerous studies have shown increasing item reliabilities as an effect of the item position in personality scales. Traditionally, these context effects are analyzed based on item-total correlations. This approach neglects that trends in item reliabilities can be caused either by an increase in true score variance or by a decrease in error…

A model of test item dependency is presented and used to illustrate the effect that violations of local independence have on the behavior of item characteristic curves. The dependency model is flexible enough to simulate the interaction of a number of factors including item difficulty and item discrimination, varying degrees of item dependence,…

A common problem in practical educational research is that of perfect scores which result when latent trait models are used. A simple procedure for managing the perfect and zero response problem encountered in converting test scores into measures is presented. It allows the test user to chose among two or three reasonable finite representations of…

Concern has been expressed over the item response theory (IRT) assumption that a person's ability can be estimated in a unidimensional latent space. To examine whether or not the response to an item requires only a single latent ability, unidimensional ability estimates were compared for data generated from the multidimensional item response…

An alternative definition has been developed of the delta scale of item difficulty used at Educational Testing Service. The traditional delta scale uses an inverse normal transformation based on normal ogive models developed years ago. However, no use is made of this fact in typical uses of item deltas. It is simply one way to make the probability…

The models and procedures discussed in this paper are related to those presented in Bock and Aitkin (1981), where they considered the 2-parameter probit model and approximated a normally distributed prior distribution of abilities by a finite and discrete distribution. One purpose of this paper is to clarify the nature of the general EM (GEM)…

The purpose of this paper is to present a generalization of the concept of item difficulty to test items that measure more than one dimension. Three common definitions of item difficulty were considered: the proportion of correct responses for a group of individuals; the probability of a correct response to an item for a specific person; and the…

The effects of variations in degree of range restriction and different subgroup sample sizes on the validity of several item bias detection procedures based on Item Response Theory (IRT) were investigated in a simulation study. The degree of range restriction for each of two subpopulations was varied by cutting the specified subpopulation ability…

This report documents a computer program for simulation evaluation of item response theory (IRT) ability estimators. This Honeywell DPS version is a very slight modification of the program originally developed in FORTRAN-77 on a DEC VAX 11/780. The model of the world simulated by the program involves a unidimensional test in which the probability…

Significant to a latent trait or item response theory analysis of a mental test is the determination of exactly what is being quantified. The following are practical problems to be considered in the formulation of a good theory: (1) deciding whether two tests measure the same trait or traits; (2) analyzing the relative contributions of a pair of…