Two-group classification is discussed when a unidimensional latent trait "theta" is appropriate for explaining data. If data have a monotone likelihood ratio, then optimal allocation rules can be based on its magnitude when allocation must be made to one of the two groups related to the unidimensional latent trait. (SLD)

The purpose of the present paper is to derive linear equating methods for the common item nonequivalent populations design from explicitly stated congeneric type test score models. The equating methods developed are compared with previously developed methods and applied to five professionally constructed examinations administered to approximately…

D.V. Budescu and J.L. Rogers (1981) proposed a method of adjusting correlations of scales to eliminate spurious components resulting from the overlapping of scales. Three reliability correction formulas are derived in this article that are based on more tenable assumptions. (SLD)

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)

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…

A rating scale can be expressed as a chain of dichotomous items. The relationship between the dichotomies depends on the manner in which the rating scale is presented to the test taker. Three models for ordered scales are discussed. In the success model, which represents growth, the lowest or easiest category is presented first. If the test taker…

The problem of obtaining designs that result in the most precise parameter estimates is encountered in at least two situations where item response theory (IRT) models are used. In so-called two-stage testing procedures, certain designs that match difficulty levels of the test items with the ability of the examinees may be located. Such designs…

Use of the Mantel-Haenszel procedure as a test for differential item functioning under the Rasch model of item-response theory is examined. Results of the procedure cannot be generalized to the class of items for which item-response functions are monotonic and local independence holds. (TJH)

The use of confirmatory factor analysis by the LISREL program is demonstrated as an assumption-testing method when computing reliability coefficients under different model assumptions. Results indicate that reliability estimates are robust against departure from the assumption of parallelism of test items. (SLD)

A probabilistic parallelogram model (the PARELLA model) is presented for the measurement of latent traits by proximity items. This unidimensional model assumes that the responses of persons to items result from proximity relations. The model is illustrated in an analysis of three empirical datasets from previous studies. (SLD)

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…

Two methods are proposed for the construction of weakly parallel tests based on a prespecified information function. A method is then described for selecting weakly parallel tests that are optimal with respect to the Maximin criterion. Numerical examples demonstrate the practicality of the tests. (SLD)

Polynomial algorithms are presented that are used to solve selected problems in test theory, and computational results from sample problems with several hundred decision variables are provided that demonstrate the benefits of these algorithms. The algorithms are based on optimization theory in networks (graphs). (SLD)

A model for solving very large item selection problems is presented. The model builds on binary programming applied to test construction. A heuristic for selecting items that satisfy the constraints in the model is also presented, and various problems are solved using the model and heuristic. (SLD)

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…