Methods and models for the construction of weakly parallel tests

Several methods are proposed for the construction of weakly parallel tests [i.e., tests with the same test information function (TIF)]. A mathematical programming model that constructs tests containing a prespecified TIF and a heuristic that assigns items to tests with information functions that are equal are important components of these methods. Numerical examples demonstrate that tests can be constructed quickly and that the heuristic produces good results. However, the heuristic is not applicable for every set of practical constraints (e.g., constraints with respect to test administration time, test composition, or dependencies between items). Index terms: item banking, heuristics, mathematical programming, test construction, weakly parallel tests

A note on solving large-scale zero-one programming problems

A heuristic for solving large-scale zero-one programming problems is provided. The heuristic is based on the modifications made by H. Crowder et al. (1983) to the standard branch-and-bound strategy. First, the initialization is modified. The modification is only useful if the objective function values for the continuous and the zero-one programming problems are close to each other. Given the initialization, the branch-and-bound method is stopped when a feasible solution to the problem is found. The heuristic also uses the reduced costs to fix non-basic variables to 1 or 0. An example taken from achievement test construction illustrates the efficiency of the proposed heuristic. Several test construction problems were implemented and solved by the proposed heuristic for item banks with 400 items. Modifications were introduced in the LANDO computer program. A table illustrates that the central processing unit times for solving the zero-one programming problem were close to the times needed to solve the continuous problem

Implementations of the branch-and-bound method for test construction problems

Item banks, large sets of test items, can be used for the construction of achievement tests. Mathematical programming models have been proposed for the selection of items from an item bank for a test. These models make automated test construction possible. However, to find an optimal or even an approximate optimal solution to a test construction model can be time consuming. This paper shows how test construction models, and in particular the Maximin Model, are solvable by the program MPSX/370 V2. This program offers the user several implementations of the branch-and-bound method, which can be used for solving test construction models. Several implementations are compared. The results show that test construction models are solvable in a practical amount of time if the user applies the options offered by the program in an intelligent way. An appendix describes the Extended Control Language (ECL) computer program

The construction of two-stage tests

Although two-stage testing is not the most efficient form of adaptive testing, it has some advantages. In this paper, linear programming models are given for the construction of two-stage tests. In these models, practical constraints with respect to, among other things, test composition, administration time, and inter-item dependencies play an important role. Research indicates that two-stage tests can be constructed both sequentially and simultaneously. Models based on the maximin model for test construction developed by W. J. van der Linden and E. Boekkooi-Timminga (1989) are formulated for the sequential case, with constraints specified at test and subtest levels. It is assumed that a bank of items calibrated under the item response model is available and that "information" is used in accordance with G. H. Fischer's information model. The maximin design is used in order to select the items that maximize the information in the test, while the resulting test information function still has the desired shape. The paper concludes that simultaneous test construction has the disadvantage of having a large number of variables; hence, constraints must be considered

Achievement test construction using 0-1 linear programming

In educational testing the work of professional test agencies has shown a trend towards item banking. Achievement test construction is viewed as selecting items from a test item bank such that certain specifications are met. As the number of possible tests is large and practice usually imposes various constraints on the selection process, a mathematical programming approach is obvious. In this paper it is shown how to formulate achievement test construction as a 0¿1 linear programming problem. A heuristic for solving the problem is proposed and two examples are given. It is concluded that a 0¿1 linear programming approach fits the problem of test construction in an appropriate way and offers test agencies the possibility of computerizing their services

Algorithms for computerized test construction using classical item parameters

Recently, linear programming models for test construction were developed. These models were based on the information function from item response theory. In this paper another approach is followed. Two 0-1 linear programming models for the construction of tests using classical item and test parameters are given. These models are useful, for instance, when classical test theory has to serve as an interface between an IRT-based item banking system and a test constructor not familiar with the underlying theory

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

TLR1/TLR2 Heterodimers Play an Important Role in the Recognition of Borrelia Spirochetes

After infection with Borrelia species, the risk for developing Lyme disease varies significantly between individuals. Recognition of Borrelia by the immune system is mediated by pattern recognition receptors (PRRs), such as TLRs. While TLR2 is the main recognition receptor for Borrelia spp., little is known about the role of TLR1 and TLR6, which both can form functionally active heterodimers with TLR2. Here we investigated the recognition of Borrelia by both murine and human TLR1 and TLR6. Peritoneal macrophages from TLR1- and TLR6- gene deficient mice were isolated and exposed to Borrelia. Human PBMCs were stimulated with Borrelia with or without specific TLR1 and TLR6 blocking using specific antibodies. Finally, the functional consequences of TLR polymorphisms on Borrelia-induced cytokine production were assessed. Splenocytes isolated from both TLR1−/− and TLR6−/− mice displayed a distorted Th1/Th2 cytokine balance after stimulation with B.burgdorferi, while no differences in pro-inflammatory cytokine production were observed. In contrast, blockade of TLR1 with specific neutralizing antibodies led to decreased cytokine production by human PBMCs after exposure to B.burgdorferi. Blockade of human TLR6 did not lead to suppression of cytokine production. When PBMCs from healthy individuals bearing polymorphisms in TLR1 were exposed to B.burgdorferi, a remarkably decreased in vitro cytokine production was observed in comparison to wild-type controls. TLR6 polymorphisms lead to a minor modified cytokine production. This study indicates a dominant role for TLR1/TLR2 heterodimers in the induction of the early inflammatory response by Borrelia spirochetes in humans