This study investigated the effect on examinees' ability estimate under item response theory (IRT) when they are presented an item, have ample time to answer the item, but decide not to respond to the item. Simulation data were modeled on an empirical data set of 25,546 examinees that was calibrated using the 3-parameter logistic model. The study…

Previous work on the effects of dimensionality on parameter estimation for dichotomous models is extended to the graded response model. Datasets are generated that differ in the number of latent factors as well as their interdimensional association, number of test items, and sample size. (SLD)

When the item response theory (IRT) model uses the marginal maximum likelihood estimation, person parameters are usually treated as random parameters following a certain distribution as a prior distribution to estimate the structural parameters in the model. For example, both PARSCALE (Muraki & Bock, 1999) and BILOG 3 (Mislevy & Bock,…

The relationship between examinee ability and the accuracy of maximum likelihood item parameter estimation is explored in terms of the expected (Fisher) information. Information functions are used to find the optimum ability levels and maximum contributions to information for estimating item parameters in three commonly used logistic item response…

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item parameters. Simulated data sets were analyzed using two different Bayes estimation procedures, the two-stage hierarchical Bayes estimation (HB2) and the marginal Bayesian with known hyperparameters (MB), and marginal maximum…

A definition of essential independence is proposed for sequences of polytomous items. For items which satisfy the assumption that the expected amount of credit awarded increases with examinee ability, a theory of essential unidimensionality is developed that closely parallels that of W. F. Stout (1987, 1990). Essentially unidimensional item…

Explored are two theoretical approaches that attempt to cope with omitted responses, that is, when an examinee omits (fails to respond to) an item and therefore the item response formula cannot be used. Preliminary considerations are discussed, and it is shown that a conveniently simple application of equivalent items leads to internal…

This study investigated the efficiency of item selection in a computerized adaptive test (CAT), where efficiency was defined in terms of the accumulated test information at an examinee's true ability level. A simulation methodology compared the efficiency of 2 item selection procedures with 5 ability estimation procedures for CATs of 5, 10, 15,…

Maximum likelihood and Bayesian estimates of proficiency, typically used in adaptive testing, use item weights that depend on test taker proficiency to estimate test taker proficiency. In this study, several methods were explored through computer simulation using fixed item weights, which depend mainly on the items difficulty. The simpler scores…

The analytically derived expected asymptotic standard errors (SEs) of maximum likelihood (ML) item estimates can be predicted by a mathematical function without examinees' responses to test items. The empirically determined SEs of marginal maximum likelihood estimation/Bayesian item estimates can be obtained when the same set of items is…

Type I error rates for the likelihood ratio test for detecting differential item functioning (DIF) were investigated using Monte Carlo simulations. Type I error rates for the two-parameter model were within theoretically expected values at each alpha level, but those for the three-parameter model were not. (SLD)

A method is proposed to assess the importance of differential item functioning (DIF) by estimating the largest possible fraction of the population in which DIF does not occur, or equivalently, the smallest possible portion of the population in which DIF may occur. The approach is based on latent class (C. C. Clogg, 1981) or mixture concepts, and…

This paper presents a method for estimating certain characteristics of test items which are designed to measure ability, or knowledge, in a particular area. Under the assumption that ability parameters are sampled from a normal distribution, the EM algorithm is used to derive maximum likelihood estimates to item parameters of the two-parameter…

Lord's bias function and the weighted likelihood estimation method are effective in reducing the bias of the maximum likelihood estimate of an examinee's ability under the assumption that the true item parameters are known. This paper presents simulation studies to determine the effectiveness of these two methods in reducing the bias when the item…

The similarity of item and ability parameter estimations was investigated using two numerical analysis techniques via marginal maximum likelihood estimation (MMLE) with a large simulated data set (n=1,000 examinees) and changing the number of quadrature points. MMLE estimation uses a numerical analysis technique to integrate examinees' abilities…