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Cognitive diagnostic computerized adaptive testing (CD-CAT) aims to obtain more useful diagnostic information by taking advantages of computerized adaptive testing (CAT). Cognitive diagnosis models (CDMs) have been developed to classify examinees into the correct proficiency classes so as to get more efficient remediation, whereas CAT tailors optimal items to the examinee’s mastery profile. The item selection method is the key factor of the CD-CAT procedure. In recent years, a large number of parametric/nonparametric item selection methods have been proposed. In this article, the authors proposed a series of stratified item selection methods in CD-CAT, which are combined with posterior-weighted Kullback–Leibler (PWKL), nonparametric item selection (NPS), and weighted nonparametric item selection (WNPS) methods, and named S-PWKL, S-NPS, and S-WNPS, respectively. Two different types of stratification indices were used: original versus novel. The performances of the proposed item selection methods were evaluated via simulation studies and compared with the PWKL, NPS, and WNPS methods without stratification. Manipulated conditions included calibration sample size, item quality, number of attributes, number of strata, and data generation models. Results indicated that the S-WNPS and S-NPS methods performed similarly, and both outperformed the S-PWKL method. And item selection methods with novel stratification indices performed slightly better than the ones with original stratification indices, and those without stratification performed the worst.

E-learning systems are capable of providing more adaptive and efficient learning experiences for learners than traditional classroom settings. A key component of such systems is the learning policy. The learning policy is an algorithm that designs the learning paths or rather it selects learning materials for learners based on information such as the learners’ current progresses and skills, learning material contents. In this article, the authors address the problem of finding the optimal learning policy. To this end, a model for learners’ hierarchical skills in the E-learning system is first developed. Based on the hierarchical skill model and the classical cognitive diagnosis model, a framework to model various mastery levels related to hierarchical skills is further developed. The optimal learning path in consideration of the hierarchical structure of skills is found by applying a model-free reinforcement learning method, which does not require any assumption about learners’ learning transition processes. The effectiveness of the proposed framework is demonstrated via simulation studies.

An informational distance/divergence-based approach is proposed to detect the presence of parameter drift in multidimensional computerized adaptive testing (MCAT). The study presents significance testing procedures for identifying changes in multidimensional item response functions (MIRFs) over time based on informational distance/divergence measures that capture the discrepancy between two probability functions. To approximate the MIRFs from the observed response data, the k-nearest neighbors algorithm is used with the random search method. A simulation study suggests that the distance/divergence-based drift measures perform effectively in identifying the instances of parameter drift in MCAT. They showed moderate power with small samples of 500 examinees and excellent power when the sample size was as large as 1,000. The proposed drift measures also adequately controlled for Type I error at the nominal level under the null hypothesis.

Cognitive diagnostic computerized adaptive testing (CD-CAT) purports to obtain useful diagnostic information with great efficiency brought by CAT technology. Most of the existing CD-CAT item selection algorithms are evaluated when test length is fixed and relatively long, but some applications of CD-CAT, such as in interim assessment, require to obtain the cognitive pattern with a short test. The mutual information (MI) algorithm proposed by Wang is the first endeavor to accommodate this need. To reduce the computational burden, Wang provided a simplified scheme, but at the price of scale/sign change in the original index. As a result, it is very difficult to combine it with some popular constraint management methods. The current study proposes two high-efficiency algorithms, posterior-weighted cognitive diagnostic model (CDM) discrimination index (PWCDI) and posterior-weighted attribute-level CDM discrimination index (PWACDI), by modifying the CDM discrimination index. They can be considered as an extension of the Kullback–Leibler (KL) and posterior-weighted KL (PWKL) methods. A pre-calculation strategy has also been developed to address the computational issue. Simulation studies indicate that the newly developed methods can produce results comparable with or better than the MI and PWKL in both short and long tests. The other major advantage is that the computational issue has been addressed more elegantly than MI. PWCDI and PWACDI can run as fast as PWKL. More importantly, they do not suffer from the problem of scale/sign change as MI and, thus, can be used with constraint management methods together in a straightforward manner.

Recently, multistage testing (MST) has been adopted by several important large-scale testing programs and become popular among practitioners and researchers. Stemming from the decades of history of computerized adaptive testing (CAT), the rapidly growing MST alleviates several major problems of earlier CAT applications. Nevertheless, MST is only one among all possible solutions to these problems. This article presents a new adaptive testing design, “on-the-fly assembled multistage adaptive testing” (OMST), which combines the benefits of CAT and MST and offsets their limitations. Moreover, OMST also provides some unique advantages over both CAT and MST. A simulation study was conducted to compare OMST with MST and CAT, and the results demonstrated the promising features of OMST. Finally, the “Discussion” section provides suggestions on possible future adaptive testing designs based on the OMST framework, which could provide great flexibility for adaptive tests in the digital future and open an avenue for all types of hybrid designs based on the different needs of specific tests.

Differential item functioning (DIF) analysis is an important step in the data analysis of large-scale testing programs. Nowadays, many such programs endorse matrix sampling designs to reduce the load on examinees, such as the balanced incomplete block (BIB) design. These designs pose challenges to the traditional DIF analysis methods. For example, as difficulty levels often vary across booklets, examinees with same booklet scores may be disparate in ability. Consequently, DIF procedures based on matching total scores at the booklet level may cause misplacement of examinees and inflation in measurement errors. Therefore, modification to traditional DIF procedures to better accommodate the BIB design becomes important. This article introduces modification of current simultaneous item bias test (SIBTEST) procedure for the DIF analysis method when multiple booklets are used. More specifically, examinees will be pooled across booklets, and the matching will be based on transformed booklet scores after common block equating/linking. Simulations are conducted to compare the performance of this new method, the equated pooled booklet method against that of the current pooled booklet method, in terms of both Type I error control and power. Four factors are considered in the simulation—the DIF effect size, item difficulty, impact, and the length of common block. Results show that the equated pooled booklet method in general improves power while keeping Type I error under control. The advantage of the new method is the most pronounced when the traditional method struggles, for example, when the item is difficult or there is impact.

Multidimensional computerized adaptive testing (MCAT) is able to provide a vector of ability estimates for each examinee, which could be used to provide a more informative profile of an examinee’s performance. The current literature on MCAT focuses on the fixed-length tests, which can generate less accurate results for those examinees whose abilities are quite different from the average difficulty level of the item bank when there are only a limited number of items in the item bank. Therefore, instead of stopping the test with a predetermined fixed test length, the authors use a more informative stopping criterion that is directly related to measurement accuracy. Specifically, this research derives four stopping rules that either quantify the measurement precision of the ability vector (i.e., minimum determinant rule [D-rule], minimum eigenvalue rule [E-rule], and maximum trace rule [T-rule]) or quantify the amount of available information carried by each item (i.e., maximum Kullback–Leibler divergence rule [K-rule]). The simulation results showed that all four stopping rules successfully terminated the test when the mean squared error of ability estimation is within a desired range, regardless of examinees’ true abilities. It was found that when using the D-, E-, or T-rule, examinees with extreme abilities tended to have tests that were twice as long as the tests received by examinees with moderate abilities. However, the test length difference with K-rule is not very dramatic, indicating that K-rule may not be very sensitive to measurement precision. In all cases, the cutoff value for each stopping rule needs to be adjusted on a case-by-case basis to find an optimal solution.

Criteria had been proposed for assessing the severity of possible test security violations for computerized tests with high-stakes outcomes. However, these criteria resulted from theoretical derivations that assumed uniformly randomized item selection. This study investigated potential damage caused by organized item theft in computerized adaptive testing (CAT) for two realistic item selection methods, maximum item information and a-stratified with content blocking, using the randomized method as a baseline for comparison. Damage caused by organized item theft was evaluated by the number of compromised items each examinee could encounter and the impact of the compromised items on examinees' ability estimates. Severity of test security violation was assessed under self-organized and organized item theft simulation scenarios. Results indicated that though item theft could cause severe damage to CAT with either item selection method, the maximum item information method was more vulnerable to the organized item theft simulation than was the a-stratified method.

Content balancing is an important issue in the design and implementation of computerized adaptive testing (CAT). Content-balancing techniques that have been applied in fixed content balancing, where the number of items from each content area is fixed, include constrained CAT (CCAT), the modified multinomial model (MMM), modified constrained CAT (MCCAT), and others. In this article, four methods are proposed to address the flexible content-balancing issue with the a-stratification design, named STR_C. The four methods are MMM+, an extension of MMM; MCCAT+, an extension of MCCAT; the TPM method, a two-phase content-balancing method using MMM in both phases; and the TPF method, a two-phase content-balancing method using MMM in the first phase and MCCAT in the second. Simulation results show that all of the methods work well in content balancing, and TPF performs the best in item exposure control and item pool utilization while maintaining measurement precision.

Item exposure control, test-overlap minimization, and the efficient use of item pool are some of the important issues in computerized adaptive testing (CAT) designs. The overexposure of some items and high test-overlap rate may cause both item and test security problems. Previously these problems associated with the maximum information (Max-I) item selection method have been partially solved by incorporating the Sympson-Hetter (SH) probabilistic procedure that attempts to control the actual usage of the popular high-discrimination items. On a different line of thought, Chang and Ying proposed the a-stratified design (STR) and advocated the use of less discriminating items in the earlier stages of testing. The method has been demonstrated to be effective in improving the utilization of the entire pool without sacrificing the efficiency in ability estimation. Nevertheless, the problem of item overexposure still persists when the ratio of pool size to test length is small. In four simulation studies, the possible benefits of incorporating the SH procedure in the STR method were investigated. The performance of such an enhanced stratified method (STR-SH) was compared with that of STR as well as Max-I-SH. The results indicated the potential advantages of the STR-SH design over the original STR in yielding a more balanced item exposure distribution, lowering the test-overlap rate, and remarkably reducing the number of overexposed items.

The use of more performance items in large-scale testing has led to an increase in the research investigating the use of polytomously scored items in computer adaptive testing (CAT). Because this research has yet to be complimented with information pertaining to exposure control, the present research investigated the impact of using .ve different exposure control algorithms in two sized item pools calibrated using the generalized partial credit model. The results of the simulation study indicated that the a-stratified design, in comparison to a no-exposure control condition, could be used to reduce item exposure and overlap, increase pool utilization, and only minorly degrade measurement precision. Use of the more restrictive exposure control algorithms, such as the Sympson-Hetter and conditional Sympson-Hetter, controlled exposure to a greater extent but at the cost of measurement precision. Because convergence of the exposure control parameters was problematic for some of the more restrictive exposure control algorithms, use of the more simplistic exposure control mechanisms, particularly when the test length to item pool size ratio is large, is recommended.

The effects of five item selection rules—Fisher information (FI), Fisher interval information (FII), Fisher information with a posterior distribution (FIP), Kullback-Leibler information (KL), and Kullback-Leibler information with a posterior distribution (KLP)—were compared with respect to the efficiency and precision of trait (Θ) estimation at the early stages of computerized adaptive testing (CAT). FII, FIP, KL, and KLP performed marginally better than FI at the early stages of CAT for Θ= -3 and -2. For tests longer than 10 items,there appeared to be no precision advantage for any of the selection rules.

Computerized adaptive tests (CAT) commonly use item selection methods that select the item which provides maximum information at an examinees estimated trait level. However, these methods can yield extremely skewed item exposure distributions. For tests based on the three-parameter logistic model, it was found that administering items with low discrimination parameter (a) values early in the test and administering those with high a values later was advantageous; the skewness of item exposure distributions was reduced while efficiency was maintained in trait level estimation. Thus, a new multistage adaptive testing approach is proposed that factors a into the item selection process. In this approach, the items in the item bank are stratified into a number of levels based on their a values. The early stages ofa test use items with lower as and later stages use items with higher as. At each stage, items are selected according to an optimization criterion from the corresponding level. Simulation studies were performed to compare a-stratified CATs with CATs based on the Sympson-Hetter method for controlling item exposure. Results indicated that this new strategy led to tests that were well-balanced, with respect to item exposure, and efficient. The a-stratifiedCATs achieved a lower average exposure rate than CATs based on Bayesian or information-based item selection and the Sympson-Hetter method.

Most item selection in computerized adaptive testing is based on Fisher information (or item information). At each stage, an item is selected to maximize the Fisher information at the currently estimated trait level (θ). However, this application of Fisher information could be much less efficient than assumed if the estimators are not close to the true θ, especially at early stages of an adaptive test when the test length (number of items) is too short to provide an accurate estimate for true θ. It is argued here that selection procedures based on global information should be used, at least at early stages of a test when θ estimates are not likely to be close to the true θ. For this purpose, an item selection procedure based on average global information is proposed. Re sults from pilot simulation studies comparing the usual maximum item information item selection with the pro posed global information approach are reported, indicat ing that the new method leads to improvement in terms of bias and mean squared error reduction under many circumstances. Index terms: computerized adaptive testing, Fisher information, global information, infor mation surface, item information, item response theory, Kullback-Leibler information, local information, test in formation.