The emergence and advancement of modern test theory (e.g., item response theory [IRT]) and the rapid deployment of new computing technologies have completely changed how educational tests are designed, delivered, and administered. One of the most important examples is computerized adaptive testing (CAT). As its name implies, the CAT test form is adaptively assembled on the fly as the test taker answers each test item. Because CAT selects and administers items at the difficulty level that is most relevant to each test taker’s ability level, the test length is usually much shorter than a typical linear version of a test. At the same time, CAT administration retains (or even improves) the precision of test score estimation—in other words, CAT greatly improves measurement efficiency.

CAT has been introduced to a variety of high-stakes testing operations, including medical health licensing examinations in the United States such as the American Society for Clinical Pathology Board of Certification Examinations, the National Council Licensure Examinations (NCLEX-RN exam), National Registry of Emergency Medical Technicians, and the North American Pharmacist Licensure Examination. To adopt CAT for use in other licensing examinations not only in the United States, but in other countries around the world, it is essential to understand the basic processes of CAT administration, of which the item selection algorithm is the most critical component. The purpose of this review is to present knowledge and techniques regarding the 3 components of the conventional CAT item selection algorithm: test content balancing, the item selection criterion, and item exposure control. It is hoped that this review will help opinion leaders of test-providing institutions to understand CAT implementation and administration.

CAT administration involves 3 key processes that iterate for each test item administration, as shown in the illustration in Fig. 1.

The first process determines the latest $\hat{\theta }$ (i.e., the ability estimate). At the beginning of CAT, there are no observed response data from which $\hat{\theta }$ is estimated, so the $\hat{\theta }$ value is initialized at the expected value, which is often the average score. After the response data are collected for one or more items, $\hat{\theta }$ is computed and updated using, for example, the maximum likelihood estimation (MLE) or Bayesianbased methods [1] such as the modal a posteriori [2] or expected a posteriori (EAP) [3]; methods. Test developers often prefer the MLE method because it does not have the estimation biases that Bayesianbased methods usually exhibit due to their use of an informative prior. The MLE method, however, is often unusable in an early-stage CAT administration due to its inability to handle special response patterns such as all correct or all incorrect responses. To overcome this issue, it is not unusual for several different $\hat{\theta }$ estimation methods to be used during CAT in operational settings. For example, in the early stage of CAT administration, when the number of item responses is small and the chance of having all correct or all incorrect responses is high, the EAP method is used. As the CAT progresses toward or reaches the end of a test, the final $\hat{\theta }$ is estimated using the MLE method. A modification of MLE, called MLE with fences (MLEF), was recently proposed by Han [4]. The literature suggests that MLEF results in unbiased estimation just like MLE, but is also capable of handling special response patterns that a typical MLE cannot.

The second CAT process involves the evaluation of test progress against the CAT termination rules that are defined as part of the test specification. In many CAT programs, the test length is fixed for all test takers, and the CAT administration is terminated once the number of items reaches the fixed test length. This is preferable if the goal is to make the test-taking experience, especially test time and workload, equivalent across test takers. In CAT, however, the length of a test and its termination can be adaptive, too, based on other termination rules and policies. For example, some CAT test programs aim to ensure that the precision of the score estimation is as parallel as possible across test takers while shortening the test length as much as possible. In such an example, the CAT termination rule can be defined such that the test administration finishes once the standard error of estimation (SEE) for a test score reaches a target. If the progress and status of the CAT do not meet the termination criteria, then the CAT is set to move on to the third process.

The third process involves the selection and administration of a new item given the latest interim $\hat{\theta }$ from the first process. The item selection process is the core function of CAT, and is where test construction and delivery actually happen. The item selection process involves 3 key components: (1) content balancing, (2) the item selection criterion, and (3) item exposure control, as illustrated in Fig. 2. Many CAT algorithms handle these 3 components separately for ease of implementation, but some CAT approaches combine or handle some or all of the 3 item selection components together at the same time. This paper introduces several of the most widely used or noteworthy methodologies for each of the CAT item selection components, followed by a discussion of other approaches.

In most test form constructions, it is common for a test form to have more than 1 content area from which items are selected, and it is important for CAT to ensure that the composition of test content is parallel across all test takers, even while it adaptively alters the test difficulty for each individual.

One of the most widely used approaches for balancing test content involves the use of a test script. A test script specifies which items are eligible for item selection based on content area given the item administration sequence. For example, if we were to administer 5 test items from 3 different content areas— say, 1 item from content area 1, 2 items from content area 2, and 2 items from content area 3—the test script would look like the one shown in Table 1. If, for test security reasons, it is preferable to differentiate the sequence of test content across test takers, one could employ multiple test scripts and randomly select one of them for use when CAT testing starts. The test script method is easy to understand, straightforward to implement, and greatly simplifies the item pool assembly process since each item belongs to a single content category and content categories are mutually exclusive (i.e., no overlap of content areas is allowed). As a result, the test script method is widely used in various CAT applications. However, 2 critical shortcomings are associated with the test script method. First, because the test script specifies a content area for each sequence of item administration, each test script is specific to the test length. If, for example, a CAT is of a variable length instead of a fixed length, the test script method may not achieve a completely consistent content balance across test takers. Second, because the test script method requires that all items belong to a single content category, the method may not be directly applicable if there are multiple layers in the content structure. For example, if there are 2 layers of content categories (content area and type) as shown in Table 2, one would need to reclassify all items into 1 of the 6 possible content combinations (3 content areas by 2 content types). The test script method often is still practical for content balancing if there are 2 or 3 content layers after reclassifying items. If there are 4 or more layers, however, the number of available items in each mutually exclusive category across all layers can become very small, making the test script method impractical.

Another popular method for content balancing in CAT is the constrained CAT (CCAT) method proposed by Kingsbury and Zara [5]. In CCAT, the percentage of items administered thus far from each content area is first evaluated against the content specification/ target. After that, the items from a content area that show the greatest proportional difference compared with the content specification/ target are identified as eligible for item selection for the next CAT administration. Because CCAT evaluates the test content composition by percentage instead of the actual count of items, it can be used in both fixed-length CAT and flexible-length CAT. In addition, multiple layers of content balancing can be easily handled by implementing CCAT as many times as the number of content layers. One undesirable property of CCAT, however, is that the sequence of test content areas during CAT administration is always the same across all test takers.

To address this downside of the CCAT method, Leung et al. [6] proposed a modified CCAT (MCCAT) method. Unlike CCAT, MCCAT considers all items eligible for item selection except those from content areas where the maximum number of items has already been reached. With the MCCAT approach, the sequencing of content areas during CAT is much less predictable. One could also expect this approach to improve the adaptiveness of CAT, since MCCAT tends to have a greater number of eligible items to select from in comparison with CCAT.

When test content is specified by a range of numbers or percentages instead of exact numbers or percentages, the penalty function approach proposed by Segall and Davey [7] or its variations such as the weighted penalty model [8] can be considered as alternative options for content balancing.

Other approaches exist that perform both content balancing and item selection simultaneously instead of handling them separately. These approaches will be introduced later in this paper.

Once test items are determined to be eligible based on the content specification in the content balancing component of the CAT algo-rithm, these eligible items are then evaluated for selection as the next item to be administered. An extensive array of item selection criteria has been developed in the test measurement field, but only a very few are used in actual CAT implementation. An introduction to a few noteworthy item selection criteria is presented below.

Unlike linear tests whose test items are designed for a single use during 1 testing event, CAT reuses all items in the item bank/pool over time. However, some items may be selected and used too frequently. Such excessive exposure of items to a test population couldchange a person’s test-taking behavior regarding those compromised items. For example, if a test taker obtained prior knowledge of the compromised test items and their correct answers, he or she could likely respond based on memorization of the items rather than on his or her true problem-solving skills. Unintended changes in testtaking behavior due to excessive item exposure could seriously threaten the test’s fairness and validity. In many high-stakes exams, maintaining proper item exposure is one of most important considerations for ensuring test security. It should be noted that for some CAT applications, such as medical diagnostic questionnaires, personality measures, and adaptive learning tools, controlling item exposure is not necessary.

Item exposure control is the last of the 3 components of the CAT item selection algorithm (Fig. 2). Once eligible items are identified in the first component (content balancing), and an optimal item is selected in the second component (item selection), then, in the third component (exposure control), some random factors are introduced to the item selection process to prevent excessive item use. The following section introduces a few widely used exposure control methods.

Earlier sections of this report explained each of the 3 separate components of CAT item selection algorithms (Fig. 2). As noted, a majority of operational CAT programs currently implement and run those 3 item selection components separately. There are other CAT approaches, however, that construct adaptive test forms and handle the content balancing and item selection components simultaneously. These CAT approaches view and formulate the content balancing component and item selection component as the constraints and objective, respectively, of a mathematical programming model such as mixed integer programming (MIP), an optimization method often used for automated test assembly (ATA) practices [22-26].

The shadow-test approach (STA) offers a framework for iterative ATA performed on the fly given the latest interim $\hat{\theta }$ for CAT [27,28]. In this framework, either minimizing the deviation of the test information function (TIF) from the TIF target or maximizing the TIF itself at a single or multiple evaluation points on the θ scale is set to be an objective for the MIP, and the test content balancing and other test specifications are formulated as constraints. For example, if the goal is to implement an STA that is equivalent to a 10-item-long CAT using the MFI item selection criterion (see Equation 1) with the content balancing scenario shown in Table 2, then the MIP model can be expressed as:

where i = {1, 2, 3, …, I}, I is the number of items in the item pool, n is the test length, x_i is a binary variable indicating whether item i is included in the constructed test form (1 if included and 0 if not included), g is the number of items administered so far, and C_1i, C_2i, C_3i, C_4i, and C5i are binary (0 or 1) identifiers for item i for each content type/area (for example, if C_1i is 1, the item i content type is “pure”).

Once the MIP model is set, the MIP solver does most (if not all) of the heavy lifting of test form construction for STA-CAT. Unlike all previously mentioned CAT approaches, where a single item is eventually selected and administered during each cycle of the CAT process (Fig. 1), in CAT with STA, a complete test form given $\hat{\theta }$ is constructed each time. The complete test form always satisfies all content and other constraints, which is its huge advantage over other approaches. In STA-CAT, each item can have multiple content categories and/or multiple layers of content categories. The MIP solver is not restricted to selecting 1 item at a time, which could degrade the level of CAT adaptiveness. Because the MIP solver is required to compute a completely new full test form in real time whenever $\hat{\theta }$ is updated, however, the computational resources requirement for STA-CAT can be extremely high. Thus, it is often necessary to tune the solver and constraints to make STA-CAT operationally feasible.

Stocking and Swanson [29] also proposed another approach to CAT within a linear-programming framework. They focused on developing an MIP model that, unlike STA-CAT, could tolerate violations of content constraints to enable the CAT system to be more robust against possible item selection failures even when, in the view of STA-CAT, there would be no feasible solution for meeting all content constraints. In their method, called the weighted deviation model (WDM), Stocking and Swanson [29] treated the content constraints as part of the object function, where the violations of the content constraints are to be minimized as the object. The IIF is also considered in the WDM-CAT as one of the weighted deviations from the target. Even though the WDM-CAT can be implemented using an MIP solver to find the optimal solution, as with STA-CAT, Stocking and Swanson instead proposed the use of a heuristic algorithm [30], in which items are evaluated and selected one at a time based on the object function of WDM as opposed to items for a whole test form. Using the WDM with the heuristic algorithm, the computational load for CAT administration is much lower than STA-CAT, but un-like STA-CAT, each test form based on WMD is not guaranteed to meet all content constraints.

When it comes time to implement a test program, it is common for some less experienced practitioners to view this as a contest of selecting among different CAT methods to find the ‘best’ method before even asking themselves whether CAT is the right solution. As with any other test construction task, the development of a CAT-based test requires the consideration of many important factors, including the purpose of the test, skills to be measured, nature of the test population, time limit, test time window, test-taking experience, test security, development time and cost, test volume, and communication with test users and stakeholders.

A key question to ask before delving into the details of CAT design decisions is whether CAT is the right design for the test program. Although CAT has joined the mainstream of test industry methods and is used in many psychological and educational applications, it is not necessarily the silver bullet for all testing applications. For exam-ple, if the goal of a test is to render a pass/fail decision for test takers, then using a fixed test form or linear-on-the-fly test (LOFT) developed to maximize the TIF at the cut score (of pass/fail decision) can be more efficient than CAT. If the desired test outcome is simply to classify test takers into one of multiple categories, then a multistage testing (MST) design may be a reasonable alternative to CAT. If maximizing score reliability across a wide-ranging score scale is the goal, however, then CAT is usually the best option compared with less adaptive options such as MST or LOFT.

CAT is usually best suited for large-scale assessments with huge test volumes and continuous or multiple test windows. If the test volume is very small, however (e.g., fewer than 100 test takers per year), it will take a long time or likely be impossible to build up a usable item bank. Even with a large test volume and response data to calibrate items, CAT requires significant lead time for the item bank to grow large enough to address test security concerns through item exposure control. Therefore, it is not unusual for a test program to start initially with a non-CAT fixed test form and later transition to CAT-based test administration once the item bank is well established.

The fundamental logic behind CAT (especially under the IRT framework) was developed more than 50 years ago, but CAT has only gained wide acceptance in the educational and psychological measurement field and in various applications across large-scale test programs in the last 20 years. Extensive research in CAT is actively underway. Topics currently under investigation include new item selection methods, new ATA methods, new CAT designs that improve the test-taking experiences (e.g., allowing response review and change), live item calibration during CAT, new multidimensional CAT methods, new diagnostic CAT methods, and test security measures specialized for CAT administration. In addition, the logic of CAT is now being adopted in the field of adaptive learning, which integrates the learning aspect and the (formative) assessment aspect of education into a continuous, individualized learning experience, and is gaining traction throughout the K-12 educational system. It is a truly exciting time to be involved in the CAT field. Understanding the key elements of CAT reviewed and discussed in this paper is critically important, and, at the same time, efforts to stay current with the new and upcoming CAT research are also very important for measurement experts.