The final step of the typical process of developing educational and psychological tests is to place the selected test items in a formatted form. The step involves the grouping and ordering of the items to meet a variety of formatting constraints. As this activity tends to be time-intensive, the use of mixed-integer programming (MIP) has been…

Linking functions adjust for differences between identifiability restrictions used in different instances of the estimation of item response model parameters. These adjustments are necessary when results from those instances are to be compared. As linking functions are derived from estimated item response model parameters, parameter estimation…

Optimal test-design methods are applied to rule-based item generation. Three different cases of automated test design are presented: (a) test assembly from a pool of pregenerated, calibrated items; (b) test generation on the fly from a pool of calibrated item families; and (c) test generation on the fly directly from calibrated features defining…

Automated test assembly uses the methodology of mixed integer programming to select an optimal set of items from an item bank. Automated test-form generation uses the same methodology to optimally order the items and format the test form. From an optimization point of view, production of fully formatted test forms directly from the item pool using…

In automated test assembly (ATA), the methodology of mixed-integer programming is used to select test items from an item bank to meet the specifications for a desired test form and optimize its measurement accuracy. The same methodology can be used to automate the formatting of the set of selected items into the actual test form. Three different…

Developed a method based on 0-1 linear programming to stratify an item pool optimally for use in alpha-stratified adaptive testing. Applied the method to a previous item pool from the computerized adaptive test of the Graduate Record Examinations. Results show the new method performs well in practical situations. (SLD)

Proposes an algorithm for the assembly of multiple test forms in which the multiple-form problem is reduced to a series of computationally less intensive two-form problems. Illustrates how the method can be implemented using 0-1 linear programming and gives two examples. (SLD)

A popular design in large-scale educational assessments is the balanced incomplete block design. The design assumes that the item pool is split into a set of blocks of items that are assigned to assessment booklets. This paper shows how the technique of 0-1 linear programming can be used to calculate a balanced incomplete block design. Several…

Reviews optimal test-assembly literature and introduces the contributions to this special issue. Discusses four approaches to computerized test assembly: (1) heuristic-based test assembly; (2) 0-1 linear programming; (3) network-flow programming; and (4) an optimal design approach. Contains a bibliography of 90 sources on test assembly.…

An algorithm for the assembly of multiple test forms is proposed in which the multiple-form problem is reduced to a series of computationally less intensive two-form problems. At each step one form is assembled to its true specifications; the other form is a dummy assembled only to maintain a balance between the quality of the current form and the…

Proposes a model for constrained computerized adaptive testing in which the information in the test at the trait level (theta) estimate is maximized subject to the number of possible constraints on the content of the test. Test assembly relies on a linear-programming approach. Illustrates the approach through simulation with items from the Law…

A method based on 0-1 linear programming (LP) is presented to stratify an item pool optimally for use in "alpha"-stratified adaptive testing. Because the 0-1 LP model belongs to the subclass of models with a network-flow structure, efficient solutions are possible. The method is applied to a previous item pool from the computerized…

This paper proposes an item selection algorithm that can be used to neutralize the effect of time limits in computer adaptive testing. The method is based on a statistical model for the response-time distributions of the test takers on the items in the pool that is updated each time a new item has been administered. Predictions from the model are…

A set of linear conditions on the item response functions is derived that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly that assembles a new test form to have an observed-score distribution optimally equated to the distribution of the…

Derives a set of linear conditions of item-response functions that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly. An example illustrates the use of the model for an item pool from the Law School Admissions Test (LSAT). (SLD)