For computerized adaptive tests (CATs) to work well, they must have an item pool with sufficient numbers of good quality items. Many researchers have pointed out that, in developing item pools for CATs, not only is the item pool size important but also the distribution of item parameters and practical considerations such as content distribution…

A new indicator of item difficulty, which identifies effectiveness ranges, overcomes the limitations of other item difficulty indexes in describing the difficulty of an item or a test as a whole and in aiding the selection of appropriate ability level items for a test. There are three common uses of the term "item difficulty": (1) the probability…

The concept of item discrimination is generalized to the case in which more than one ability is required to determine the correct response to an item, using the conceptual framework of item response theory and the definition of multidimensional item difficulty previously developed by M. Reckase (1985). (SLD)

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…

Real test data of unknown structure were analyzed using both a unidimensional and a multidimensional latent trait model in an attempt to determine the underlying components of the test. The models used were the three-parameter logistic model and a multidimensional extension of the two-parameter logistic model. The basic design for the analysis of…

A study was undertaken to develop guidelines for the interpretation of the parameters of three multidimensional item response theory models and to determine the relationship between the parameters and traditional concepts of item difficulty and discrimination. The three models considered were multidimensional extensions of the one-, two-, and…

A study was conducted to compare the quality of the item parameter estimates obtained from the ANCILLES and LOGIST estimation procedures using goodness of fit as a criterion. Statistics used to compare the fit included a chi-square statistic and a mean square deviation statistic. Other analyses performed included comparisons of the distributions…

Factor analysis is the traditional method for studying the dimensionality of test data. However, under common conditions, the factor analysis of tetrachoric correlations does not recover the underlying structure of dichotomous data. The purpose of this paper is to demonstrate that the factor analyses of tetrachoric correlations is unlikely to…

One of the major assumptions of latent trait theory is that the items in a test measure a single dimension. This report describes an investigation of procedures for forming a set of items that meet this assumption. Factor analysis, nonmetric multidimensional scaling, cluster analysis and latent trait analysis were applied to simulated and real…

An application of the two-paramenter logistic (Rasch) model to tailored testing is presented. The model is discussed along with the maximum likelihood estimation of the ability parameters given the response pattern and easiness parameter estimates for the items. The technique has been programmed for use with an interactive computer terminal. Use…

Multidimensional item difficulty (MID) is proposed as a means of describing test items which measure more than one ability. With mathematical story problems, for instance, both mathematical and verbal skills are required to obtain a correct answer. The proposed measure of MID is based upon three general assumptions: (1) the probability of…

The work presented in this paper defined conceptually the concepts of multidimensional discrimination and information, derived mathematical expressions for the concepts for a particular multidimensional item response theory (IRT) model, and applied the concepts to actual test data. Multidimensional discrimination was defined as a function of the…

An experiment was performed with computer-generated data to investigate some of the operational characteristics of tailored testing as they are related to various provisions of the computer program and item pool. With respect to the computer program, two characteristics were varied: the size of the step of increase or decrease in item difficulty…