This research simulated responses of 75 subjects to 30 items under the Birnbaum model and attempted a fit to the data using the Rasch model. When item discriminations varied from a variance of .05 to .25, there was only a slight increase in lack of fit as the variances increased. (Author/CTM)

The construction of parallel tests from item response theory (IRT) based item banks is discussed. Tests are considered parallel whenever their information functions are identical. After the methods for constructing parallel tests are considered, the computational complexity of 0-1 linear programming and the heuristic procedure applied are…

Fisher's information measure for the item difficulty parameter in the Rasch model and its marginal and conditional formulations are investigated. It is shown that expected item information in the unconditional model equals information in the marginal model, provided the assumption of sampling examinees from an ability distribution is made. For the…

The usefulness of a latent trait model designed for use with multidimensional test data was investigated in two stages. The first stage consisted of generating simulation data to fit the multidimensional extension of the two-parameter logistic model, applying the model to the data, and comparing the resulting estimates with the known parameters.…

The theoretical differences between the traditional definition of dimensionality and the more recently defined notion of essential dimensionality are presented. Monte Carlo simulations are used to demonstrate the utility of W. F. Stout's procedure to assess the essential unidimensionality of the latent space underlying a set of terms. The…

Two iterative procedures for constructing Rasch scales are presented. A log-likelihood ratio test based on a quasi-loglinear formulation of the Rasch model is given by which one item at a time can be deleted from or added to an initial item set. In the so-called "top-down" algorithm, items are stepwise deleted from a relatively large…

Using simulated item response data, the performance of several "robust" and conventional schemes for ability estimation was evaluated in conjunction with logistic item response theory models (one, two, and three parameter models). The simulated item response data were generated using a model that is more complex than are the usual…

Simultaneous estimation of many parameters can often be improved, sometimes dramatically so, if it is reasonable to consider one or more subsets of parameters as exchangeable members of corresponding populations. While each observation may provide limited information about the parameters it is modeled directly in terms of, it also contributes…

This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for 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…

The application of latent trait theory to classroom tests necessitates the use of small sample sizes for parameter estimation. Computer generated data were used to assess the accuracy of estimation of the slope and location parameters in the two parameter logistic model with fixed abilities and varying small sample sizes. The maximum likelihood…

National Assessment of Educational Progress reading data were scaled using a unidimensional item response theory model. Bock's full-information factor analysis and Rosenbaum's test of unidimensionality were applied. Conclusions about unidimensionality for balanced incomplete block spiralled data were the same as for complete data. (Author/GDC)

A two-stage study was conducted to compare the ability estimates yielded by tailored testing procedures based on the one-parameter logistic (1PL) and three-parameter logistic (3PL) models. The first stage of the study employed real data, while the second stage employed simulated data. In the first stage, response data for 3,000 examinees were…

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…

A latent trait model is described that is appropriate for use with tests that measure more than one dimension, and its application to both real and simulated test data is demonstrated. Procedures for estimating the parameters of the model are presented. The research objectives are to determine whether the two-parameter logistic model more…