An Efficiency Balanced Information Criterion for Item Selection in Computerized Adaptive Testing

Successful administration of computerized adaptive testing (CAT) programs in educational settings requires that test security and item exposure control issues be taken seriously. Developing an item selection algorithm that strikes the right balance between test precision and level of item pool utilization is the key to successful implementation and long‐term quality control of CAT. This study proposed a new item selection method using the “efficiency balanced information” criterion to address issues with the maximum Fisher information method and stratification methods. According to the simulation results, the new efficiency balanced information method had desirable advantages over the other studied item selection methods in terms of improving the optimality of CAT assembly and utilizing items with low a‐values while eliminating the need for item pool stratification.     

Increasing the Homogeneity of CAT's Item-Exposure Rates by Minimizing or Maximizing Varied Target Functions While Assembling Shadow Tests

A computerized adaptive testing (CAT) algorithm that has the potential to increase the homogeneity of CAT's item-exposure rates without significantly sacrificing the precision of ability estimates was proposed and assessed in the shadow-test ( van der Linden & Reese, 1998 ) CAT context. This CAT algorithm was formed by a combination of maximizing or minimizing varied target functions while assembling shadow tests. There were four target functions to be separately used in the first, second, third, and fourth quarter test of CAT. The elements to be used in the four functions were associated with (a) a random number assigned to each item, (b) the absolute difference between an examinee's current ability estimate and an item difficulty, (c) the absolute difference between an examinee's current ability estimate and an optimum item difficulty, and (d) item information. The results indicated that this combined CAT fully utilized all the items in the pool, reduced the maximum exposure rates, and achieved more homogeneous exposure rates. Moreover, its precision in recovering ability estimates was similar to that of the maximum item-information method. The combined CAT method resulted in the best overall results compared with the other individual CAT item-selection methods. The findings from the combined CAT are encouraging. Future uses are discussed.     

Cognitive Diagnostic Multistage Testing by Partitioning Hierarchically Structured Attributes

In cognitive diagnostic models (CDMs), a set of fine-grained attributes is required to characterize complex problem solving and provide detailed diagnostic information about an examinee. However, it is challenging to ensure reliable estimation and control computational complexity when The test aims to identify the examinee's attribute profile in a large-scale map of attributes. To address this problem, this study proposes a cognitive diagnostic multistage testing by partitioning hierarchically structured attributes (CD-MST-PH) as a multistage testing for CDM. In CD-MST-PH, multiple testlets can be constructed based on separate attribute groups before testing occurs, which retains the advantages of multistage testing over fully adaptive testing or the on-the-fly approach. Moreover, testlets are offered sequentially and adaptively, thus improving test accuracy and efficiency. An item information measure is proposed to compute the discrimination power of an item for each attribute, and a module assembly method is presented to construct modules anchored at each separate attribute group. Several module selection indices for CD-MST-PH are also proposed by modifying the item selection indices used in cognitive diagnostic computerized adaptive testing. The results of simulation study show that CD-MST-PH can improve test accuracy and efficiency relative to the conventional test without adaptive stages.     

Improving Item-Exposure Control in Adaptive Testing

One of the methods of controlling test security in adaptive testing is imposing random item-ineligibility constraints on the selection of the items with probabilities automatically updated to maintain a predetermined upper bound on the exposure rates. Three major improvements of the method are presented. First, a few modifications to improve the initialization of the method and accelerate the impact of its feedback mechanism on the observed item-exposure rates are introduced. Second, the case of conditional item-exposure control given the uncertainty of examinee's ability parameter is addressed. Third, although rare for a well-designed item pool, when applied in combination with the shadow-test approach to adaptive testing the method may meet occasional infeasibility of the shadow-test model. A big M method is proposed that resolves the issue. The practical advantages of the improvements are illustrated using simulated adaptive testing from a real-world item pool under a variety of conditions.     

Constructing Rotating Item Pools for Constrained Adaptive Testing

Preventing items in adaptive testing from being over- or underexposed is one of the main problems in computerized adaptive testing. Though the problem of overexposed items can be solved using a probabilistic item-exposure control method, such methods are unable to deal with the problem of underexposed items. Using a system of rotating item pools, on the other hand, is a method that potentially solves both problems. In this method, a master pool is divided into (possibly overlapping) smaller item pools, which are required to have similar distributions of content and statistical attributes. These pools are rotated among the testing sites to realize desirable exposure rates for the items. A test assembly model, motivated by Gulliksen's matched random subtests method, was explored to help solve the problem of dividing a master pool into a set of smaller pools. Different methods to solve the model are proposed. An item pool from the Law School Admission Test was used to evaluate the performances of computerized adaptive tests from systems of rotating item pools constructed using these methods.     

A Comparison of Item Exposure Control Methods in Computerized Adaptive Testing

Two new methods for item exposure control were proposed. In the Progressive method, as the test progresses, the influence of a random component on item selection is reduced and the importance of item information is increasingly more prominent. In the Restricted Maximum Information method, no item is allowed to be exposed in more than a predetermined proportion of tests. Both methods were compared with six other item-selection methods (Maximum Information, One Parameter, McBride and Martin, Randomesque, Sympson and Hetter, and Random Item Selection) with regard to test precision and item exposure variables. Results showed that the Restricted method was useful to reduce maximum exposure rates and that the Progressive method reduced the number of unused items. Both did well regarding precision. Thus, a combined Progressive-Restricted method may be useful to control item exposure without a serious decrease in test precision.     

Stratified and Maximum Information Item Selection Procedures in Computer Adaptive Testing

In this study we evaluated and compared three item selection procedures: the maximum Fisher information procedure (F), the a-stratified multistage computer adaptive testing (CAT) (STR), and a refined stratification procedure that allows more items to be selected from the high a strata and fewer items from the low a strata (USTR), along with completely random item selection (RAN). The comparisons were with respect to error variances, reliability of ability estimates and item usage through CATs simulated under nine test conditions of various practical constraints and item selection space. The results showed that F had an apparent precision advantage over STR and USTR under unconstrained item selection, but with very poor item usage. USTR reduced error variances for STR under various conditions, with small compromises in item usage. Compared to F, USTR enhanced item usage while achieving comparable precision in ability estimates; it achieved a precision level similar to F with improved item usage when items were selected under exposure control and with limited item selection space. The results provide implications for choosing an appropriate item selection procedure in applied settings.     

Multidimensional CAT Item Selection Methods for Domain Scores and Composite Scores With Item Exposure Control and Content Constraints

The intent of this research was to find an item selection procedure in the multidimensional computer adaptive testing (CAT) framework that yielded higher precision for both the domain and composite abilities, had a higher usage of the item pool, and controlled the exposure rate. Five multidimensional CAT item selection procedures (minimum angle; volume; minimum error variance of the linear combination; minimum error variance of the composite score with optimized weight; and Kullback‐Leibler information) were studied and compared with two methods for item exposure control (the Sympson‐Hetter procedure and the fixed‐rate procedure, the latter simply refers to putting a limit on the item exposure rate) using simulated data. The maximum priority index method was used for the content constraints. Results showed that the Sympson‐Hetter procedure yielded better precision than the fixed‐rate procedure but had much lower item pool usage and took more time. The five item selection procedures performed similarly under Sympson‐Hetter. For the fixed‐rate procedure, there was a trade‐off between the precision of the ability estimates and the item pool usage: the five procedures had different patterns. It was found that (1) Kullback‐Leibler had better precision but lower item pool usage; (2) minimum angle and volume had balanced precision and item pool usage; and (3) the two methods minimizing the error variance had the best item pool usage and comparable overall score recovery but less precision for certain domains. The priority index for content constraints and item exposure was implemented successfully.     

An Automated Item Pool Assembly Framework for Maximizing Item Utilization for CAT

Computerized adaptive testing (CAT) has gained deserved popularity in the administration of educational and professional assessments, but continues to face test security challenges. To ensure sustained quality assurance and testing integrity, it is imperative to establish and maintain multiple stable item pools that are consistent in terms of psychometric characteristics and content specifications. This study introduces the Honeycomb Pool Assembly (HPA) framework, an innovative solution for the construction of multiple parallel item pools for CAT that maximizes item utilization in the item bank. The HPA framework comprises two stages—cell assembly and pool assembly—and uses a mixed integer programming modeling approach. An empirical study demonstrated HPA's effectiveness in creating a large number of parallel pools using a real-world high-stakes CAT assessment item bank. The HPA framework offers several advantages, including (a) simultaneous creation of multiple parallel pools, (b) simplification of item pool maintenance, and (c) flexibility in establishing statistical and operational constraints. Moreover, it can help testing organizations efficiently manage and monitor the health of their item banks. Thus, the HPA framework is expected to be a valuable tool for testing professionals and organizations to address test security challenges and maintain the integrity of high-stakes CAT assessments.     

Multiple Objective Test Assembly Problems

Mathematical programming techniques for optimal test assembly are discussed. Most methods optimize a single objective: for instance, the amount of information in a test, subject to a number of constraints. However, some test assembly problems have multiple objectives. A recent example in the literature is the problem of assembling test that measure multiple traits, where the amount of information in the test about each different trait has to be maximized. The present paper proposes methods appropriate for solving multiple objective test assembly problems. An overview of multiple objective optimization methods is given. The impact of the method on the optimality of the solution is shown and the appropriateness of the methods is discussed. The methods are illustrated using an empirical example of a test assembly problem for a two-dimensional mathematics item pool.     

Minimizing the Influence of Item Parameter Estimation Errors in Test Development: A Comparison of Three Selection Procedures

In test development, item response theory (IRT) is a method to determine the amount of information that each item (i.e., item information function) and combination of items (i.e., test information function) provide in the estimation of an examinee's ability. Studies investigating the effects of item parameter estimation errors over a range of ability have demonstrated an overestimation of information when the most discriminating items are selected (i.e., item selection based on maximum information). In the present study, the authors examined the influence of item parameter estimation errors across 3 item selection methods—maximum no target, maximum target, and theta maximum—using the 2- and 3-parameter logistic IRT models. Tests created with the maximum no target and maximum target item selection procedures consistently overestimated the test information function. Conversely, tests created using the theta maximum item selection procedure yielded more consistent estimates of the test information function and, at times, underestimated the test information function. Implications for test development are discussed.     

Item Selection and Ability Estimation Procedures for a Mixed-Format Adaptive Test

In this study we compared five item selection procedures using three ability estimation methods in the context of a mixed-format adaptive test based on the generalized partial credit model. The item selection procedures used were maximum posterior weighted information, maximum expected information, maximum posterior weighted Kullback-Leibler information, and maximum expected posterior weighted Kullback-Leibler information procedures. The ability estimation methods investigated were maximum likelihood estimation (MLE), weighted likelihood estimation (WLE), and expected a posteriori (EAP). Results suggested that all item selection procedures, regardless of the information functions on which they were based, performed equally well across ability estimation methods. The principal conclusions drawn about the ability estimation methods are that MLE is a practical choice and WLE should be considered when there is a mismatch between pool information and the population ability distribution. EAP can serve as a viable alternative when an appropriate prior ability distribution is specified. Several implications of the findings for applied measurement are discussed.     

A Conditional Exposure Control Method for Multidimensional Adaptive Testing

In computerized adaptive testing (CAT), ensuring the security of test items is a crucial practical consideration. A common approach to reducing item theft is to define maximum item exposure rates, i.e., to limit the proportion of examinees to whom a given item can be administered. Numerous methods for controlling exposure rates have been proposed for tests employing the unidimensional 3-PL model. The present article explores the issues associated with controlling exposure rates when a multidimensional item response theory (MIRT) model is utilized and exposure rates must be controlled conditional upon ability. This situation is complicated by the exponentially increasing number of possible ability values in multiple dimensions. The article introduces a new procedure, called the generalized Stocking-Lewis method, that controls the exposure rate for students of comparable ability as well as with respect to the overall population. A realistic simulation set compares the new method with three other approaches: Kullback-Leibler information with no exposure control, Kullback-Leibler information with unconditional Sympson-Hetter exposure control, and random item selection.     

Restrictive Stochastic Item Selection Methods in Cognitive Diagnostic Computerized Adaptive Testing

This paper proposes two new item selection methods for cognitive diagnostic computerized adaptive testing: the restrictive progressive method and the restrictive threshold method. They are built upon the posterior weighted Kullback‐Leibler (KL) information index but include additional stochastic components either in the item selection index or in the item selection procedure. Simulation studies show that both methods are successful at simultaneously suppressing overexposed items and increasing the usage of underexposed items. Compared to item selection based upon (1) pure KL information and (2) the Sympson‐Hetter method, the two new methods strike a better balance between item exposure control and measurement accuracy. The two new methods are also compared with Barrada et al.'s (2008) progressive method and proportional method.     

Procedures for Selecting Items for Computerized Adaptive Tests

Many procedures have been developed for selecting the "best" items for a computerized adaptive test. There is a trend toward the use of adaptive testing in applied settings such as licensure tests, program entrance tests, and educational tests. It is useful to consider procedures for item selection and the special needs of applied testing settings to facilitate test design. The current study reviews several classical approaches and alternative approaches to item selection and discusses their relative merit. This study also describes procedures for constrained computerized adaptive testing (C-CAT) that may be added to classical item selection approaches to allow them to be used for applied testing, while maintaining the high measurement precision and short test length that made adaptive testing attractive to practitioners initially.     

A Comparative Study of Item Exposure Control Methods in Computerized Adaptive Testing

This study compared the properties of five methods of item exposure control within the purview of estimating examinees' abilities in a computerized adaptive testing (CAT) context. Each exposure control algorithm was incorporated into the item selection procedure and the adaptive testing progressed based on the CAT design established for this study. The merits and shortcomings of these strategies were considered under different item pool sizes and different desired maximum exposure rates and were evaluated in light of the observed maximum exposure rates, the test overlap rates, and the conditional standard errors of measurement. Each method had its advantages and disadvantages, but no one possessed all of the desired characteristics. There was a clear and logical trade-off between item exposure control and measurement precision. The Stocking and Lewis conditional multinomial procedure and, to a slightly lesser extent, the Davey and Parshall method seemed to be the most promising considering all of the factors that this study addressed.     

计算机自适应考试系统研究

本文结合专家经验确定法和项目反应理论,设计出一种简明、实用的计算机自适应考试系统的试题难度确定方法,同时重点分析计算机自适应考试系统的测试起点、终点选择,选题策略和能力值估计方法。最后列举了一个自适应测试的步骤实例。本系统能够根据不同能力被试者随机选择试题项目,减少了测试长度,与传统在线考试系统相比提高了考试效率。     

Item Selection in Computerized Adaptive Testing: Should More Discriminating Items be Used First?

During computerized adaptive testing (CAT), items are selected continuously according to the test-taker's estimated ability. The traditional method of attaining the highest efficiency in ability estimation is to select items of maximum Fisher information at the currently estimated ability. Test security has become a problem because high-discrimination items are more likely to be selected and become overexposed. So, there seems to be a tradeoff between high efficiency in ability estimations and balanced usage of items. This series of four studies with simulated data addressed the dilemma by focusing on the notion of whether more or less discriminating items should be used first in CAT. The first study demonstrated that the common maximum information method with Sympson and Hetter (1985) control resulted in the use of more discriminating items first. The remaining studies showed that using items in the reverse order (i.e., less discriminating items first), as described in Chang and Ying's (1999) stratified method had potential advantages: (a) a more balanced item usage and (b) a relatively stable resultant item pool structure with easy and inexpensive management. This stratified method may have ability-estimation efficiency better than or close to that of other methods, particularly for operational item pools when retired items cannot be totally replenished with similar highly discriminating items. It is argued that the judicious selection of items, as in the stratified method, is a more active control of item exposure, which can successfully even out the usage of all items.     

Effects of Practical Constraints on Item Selection Rules at the Early Stages of Computerized Adaptive Testing

The purpose of this study was to compare the effects of four item selection rules—(1) Fisher information (F), (2) Fisher information with a posterior distribution (FP), (3) Kullback-Leibler information with a posterior distribution (KP), and (4) completely randomized item selection (RN)—with respect to the precision of trait estimation and the extent of item usage at the early stages of computerized adaptive testing. The comparison of the four item selection rules was carried out under three conditions: (1) using only the item information function as the item selection criterion; (2) using both the item information function and content balancing; and (3) using the item information function, content balancing, and item exposure control. When test length was less than 10 items, FP and KP tended to outperform F at extreme trait levels in Condition 1. However, in more realistic settings, it could not be concluded that FP and KP outperformed F, especially when item exposure control was imposed. When test length was greater than 10 items, the three nonrandom item selection procedures performed similarly no matter what the condition was, while F had slightly higher item usage.     

A Framework for Measuring the Amount of Adaptation of Rasch‐based Computerized Adaptive Tests

A key consideration when giving any computerized adaptive test (CAT) is how much adaptation is present when the test is used in practice. This study introduces a new framework to measure the amount of adaptation of Rasch‐based CATs based on looking at the differences between the selected item locations (Rasch item difficulty parameters) of the administered items and target item locations determined from provisional ability estimates at the start of each item. Several new indices based on this framework are introduced and compared to previously suggested measures of adaptation using simulated and real test data. Results from the simulation indicate that some previously suggested indices are not as sensitive to changes in item pool size and the use of constraints as the new indices and may not work as well under different item selection rules. The simulation study and real data example also illustrate the utility of using the new indices to measure adaptation at both a group and individual level. Discussion is provided on how one may use several of the indices to measure adaptation of Rasch‐based CATs in practice.