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…

Confidence envelopes for one-parameter, two-parameter, and three-parameter logistic item response models are illustrated. M-line plots showing the genesis of the envelope and the density of lines in the confidence region are described and illustrated. (Author/SLD)

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)

E.J. Bedrick recently derived the asymptotic distribution of the modified sample biserial correlation estimator of F.M. Lord and studied its efficacy for bivariate normal populations. A more detailed examination of the properties of Lord's estimator is provided, and the small sample bias and variance are studied. (SLD)

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…

Information functions are used to find the optimum ability levels and maximum contributions to information for estimating item parameters in three commonly used logistic item response models. Implications are discussed for applications such as adaptive testing and test construction. (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…

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 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)

Scoring of response vectors to give maximum test-retest correlation is investigated. A general method is given for finding the best scores, deriving them for the normal factor model, and showing that for a standard model for binary response it is easy to approximate the best scores. (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)

The psychometric objections to using essays and other subjective tests for measurement can be overcome by a many-facet Rasch model. This model enables judge-awarded grades to be transformed from their arbitrary, local, non-linear rating scale form into linear measures with explicit generalizable meaning of specifiable reliability (standard error)…

Mixed integer linear programing models for customizing two-stage tests are presented. Model constraints are imposed with respect to test composition, administration time, inter-item dependencies, and other practical considerations. The models can be modified for use in the construction of multistage tests. (Author/TJH)