While linear programming is a common tool in business and industry, there have not been many applications in educational assessment and only a handful of individuals have been actively involved in conducting psychometric research in this area. Perhaps this is due, at least in part, to the complexity of existing software packages. This article…

Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…

Generating a test from an item bank using a criterion based on classical test theory parameters poses considerable problems. A mathematical model is formulated that maximizes the reliability coefficient alpha, subject to logical constraints on the choice of items. Theorems ensuring appropriate application of the Lagragian relation techniques are…

An alternative item-selection procedure for use with Owen's Bayesian adaptive testing strategy is proposed. This procedure is, by design, faster than Owen's original procedure because it searches only part of the total item pool. Item selections are, however, identical for both methods. After a conceptual development of the rapid-search procedure,…

A method is described for simultaneous test construction using the Operations Research technique zero-one programming. The model for zero-one programming consists of two parts. The first contains the objective function that describes the aspect to be optimized. The second part contains the constraints under which the objective function should be…

The construction of parallel tests from item-response-theory-based item banks is discussed. Two methods for sequentially selecting parallel tests and two methods for simultaneously constructing tests using 0-1 linear programing are compared. Advantages and disadvantages of these techniques are reviewed. (SLD)

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…

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…

A procedure for the sequential optimization of the calibration of an item bank is given. The procedure is based on an empirical Bayes approach to a reformulation of the Rasch model as a model for paired comparisons between the difficulties of test items in which ties are allowed to occur. First, it is indicated how a paired-comparisons design…

Statistical properties of person fit indices are reviewed as indicators of the extent to which a person's score pattern is in agreement with a measurement model. Distribution of a fit index and ability-free fit evaluation are discussed. The null distribution was simulated for a test of 20 items. (SLD)

Designing a test using three-parameter item response theory (IRT) is discussed. A brief review of IRT is followed by a discussion of two types of test design: (1) selecting items using confidence envelopes (confidence envelope method); and (2) using item characteristic curves and their confidence intervals (test envelope method). The confidence…

A new test construction method based on integer linear programming is described. This method selects optimal tests in small amounts of computer time. The new method, called the Cluster-Based Method, assumes that the items in the bank have been grouped according to their item information curves so that items within a group, or cluster, are…

A method is presented and illustrated for simultaneously generating multiple tests with similar characteristics from the item bank by using binary programing techniques. The parallel tests are created to match an existing seed test item for item and to match user-supplied taxonomic specifications. (SLD)

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)

Since 1985 several procedures for computerized test construction using linear programing techniques have been described in the literature. To apply these procedures successfully, suitable item banks are needed. The problem of designing item banks based on item response theory (IRT) is addressed. A procedure is presented that determines whether an…