Algorithmic test design using classical item parameters

Two optimalization models for the construction of tests with a maximal value of coefficient alpha are given. Both models have a linear form and can be solved by using a branch-and-bound algorithm. The first model assumes an item bank calibrated under the Rasch model and can be used, for instance, when classical test theory has to serve as an interface between the item bank system and a user not familiar with modern test theory. Maximization of alpha was obtained by inserting a special constraint in a linear programming model. The second model has wider applicability and can be used with any item bank for which estimates of the classical item parameter are available. The models can be expanded to meet practical constraints with respect to test composition. An empirical study with simulated data using two item banks of 500 items was carried out to evaluate the model assumptions. For Item Bank 1 the underlying response was the Rasch model, and for Item Bank 2 the underlying model was the three-parameter model. An appendix discusses the relation between item response theory and classical parameter values and adds the case of a multidimensional item bank. Three tables present the simulation study data.