It has previously been shown that the Bock-Aitkin procedure (R. Bock and M. Aitkin, 1981) is an instance of the EM algorithm when trying to find the marginal maximum likelihood estimate for a discrete latent ability variable (latent trait). In this paper, it is shown that the Bock-Aitkin procedure is a numerical implementation of the EM algorithm…

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,…

An adaptive test can usually match or exceed the measurement precision of conventional tests several times its length. This increased efficiency is not without costs, however, as the models underlying adaptive testing make strong assumptions about examinees and items. Most troublesome is the assumption that item pools are unidimensional. Truly…

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…

This paper examines the effect of using unidimensional item response theory (IRT) item parameter estimates of multidimensional items to create weakly parallel test forms using target information curves. To date, all computer-based algorithms that have been devised to create parallel test forms assume that the items are unidimensional. This paper…

A didactic example is provided, using a Monte Carlo method, of how differential item functioning (DIF) can be eliminated (and thus better understood) when the complete latent space is used. The main source of DIF is that the matching single criterion used in some DIF procedures, Mantel Haenszel or Simultaneous Item Bias (SIBTEST), does not account…

Many researchers have suggested that the main cause of item bias is the misspecification of the latent ability space. That is, items that measure multiple abilities are scored as though they are measuring a single ability. If two different groups of examinees have different underlying multidimensional ability distributions and the test items are…

One of the important underlying assumptions of all item response theory (IRT) models is that of local independence. This assumption requires that the response to an item on a test not be influenced by the response to any other items. This assumption is often taken for granted, with little or no scrutiny of the response process required to answer…

The concept of a user-specified validity sector is discussed. The idea of the validity sector combines the work of M. D. Reckase (1986) and R. Shealy and W. Stout (1991). Reckase developed a methodology to represent an item in a multidimensional latent space as a vector. Item vectors are computed using multidimensional item response theory item…

The relationship between levels of reliability and the power of two bias and differential item functioning (DIF) detection methods is examined. Both methods, the Mantel-Haenszel (MH) procedure of P. W. Holland and D. T. Thayer (1988) and the Simultaneous Item Bias (SIB) procedure of R. Shealy and W. Stout (1991), use examinees' raw scores as a…

The purpose of this study was to investigate the effect of using multidimensional items in a computer adaptive test (CAT) setting which assumes a unidimensional item response theory (IRT) framework. Previous research has suggested that the composite of multidimensional abilities being estimated by a unidimensional IRT model is not constant…

The difference between item bias and item impact and the way they relate to item validity are discussed from a multidimensional item response theory perspective. The Mantel-Haenszel procedure and the Simultaneous Item Bias strategy are used in a Monte Carlo study to illustrate detection of item bias. (SLD)

This paper demonstrates the relationship between the concept of unidimensionality and direction of an item in a multidimensional space. The basic premise is that if items that measure in the same direction are combined to form a test, that test will meet the item response theory requirements of unidimensionality. This will be true even if the…