Many organizations utilize some form of automation in the test assembly process; either fully algorithmic or heuristically constructed. However, one issue with heuristic models is that when the test assembly problem changes the entire model may need to be re-conceptualized and recoded. In contrast, mixed-integer programming (MIP) is a mathematical…

For trinary partial credit items, the shape of the item information and item discrimination functions is examined in relation to the item parameters. Conditions under which these functions are unimodal and bimodal are discussed, and the locations and values of maxima are derived. Practical relevance of the results is discussed. (SLD)

This discussion of new methods for calibrating item response theory (IRT) models looks into new optimization procedures, such as the Genetic Algorithm (GA) to improve on the use of the Newton-Raphson procedure. The advantages of using a global optimization procedure like GA is that this kind of procedure is not easily affected by local optima and…

This paper describes and evaluates the use of decision theory as a tool for classifying examinees based on their item response patterns. Decision theory, developed by A. Wald (1947) and now widely used in engineering, agriculture, and computing, provides a simple model for the analysis of categorical data. Measurement decision theory requires only…

Two-group classification is discussed when a unidimensional latent trait "theta" is appropriate for explaining data. If data have a monotone likelihood ratio, then optimal allocation rules can be based on its magnitude when allocation must be made to one of the two groups related to the unidimensional latent trait. (SLD)

An item response theory model based on the Rasch model is proposed for composite tasks, those decomposed into subtasks of different kinds. The model, which is illustrated with an application to spelling tasks, constrains the difficulties of the composite tasks to be linear combinations of the difficulties of the subtask items. (SLD)

Following a brief discussion of test construction by linear programing, the results of a study by F. B. Baker and others (1988) with respect to a uniform target is replicated. It is demonstrated that the result depends on characteristics of the item pool. (SLD)

How item bias indexes based on item response theory (IRT) identify bias that results from multidimensionality is demonstrated. Simulation results suggest that IRT-based bias indexes detect multidimensional items with bias but do not detect multidimensional items without bias. They also do not confound between-group differences on the primary test.…

The capability of the DIMTEST statistical test in assessing essential unidimensionality of item responses to real tests was investigated for 22 real tests of at least 25 items and 700 or more examinees. DIMTEST results on real tests were able to discriminate between essentially unidimensional and multidimensional tests. (SLD)

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 equating of results from the PC-BILOG computer program to an underlying metric was studied through simulation when a two-parameter item response theory model was used. Results are discussed in terms of the identification problem and implications for test equating. (SLD)

A method for detecting and interpreting disturbances of the local-independence assumption among items that share common stimulus material or other features is presented. Dichotomous and polytomous Rasch models are used to analyze structure of the learning outcome superitems. (SLD)

It is demonstrated, theoretically and empirically, that item sets can be selected that meet the unidimensionality assumption of most item response theory models, even though they require more than one ability for a correct response. A method for identifying such item sets for test development purposes is presented. (SLD)

D.V. Budescu and J.L. Rogers (1981) proposed a method of adjusting correlations of scales to eliminate spurious components resulting from the overlapping of scales. Three reliability correction formulas are derived in this article that are based on more tenable assumptions. (SLD)

At the Educational Testing Service, the Mantel-Haenszel procedure is used for differential item functioning (DIF) detection, and the standardization procedure is used to describe DIF. This report describes these procedures. First, an important distinction is made between DIF and impact, pointing to the need to compare the comparable. Then, these…