Multidimensional computerized adaptive testing (MCAT) has been developed over the past decades, and most of them can only deal with dichotomously scored items. However, polytomously scored items have been broadly used in a variety of tests for their advantages of providing more information and testing complicated abilities and skills. The purpose of this study is to discuss the item selection algorithms used in MCAT with polytomously scored items (PMCAT). Several promising item selection algorithms used in MCAT are extended to PMCAT, and two new item selection methods are proposed to improve the existing selection strategies. Two simulation studies are conducted to demonstrate the feasibility of the extended and proposed methods. The simulation results show that most of the extended item selection methods for PMCAT are feasible and the new proposed item selection methods perform well. Combined with the security of the pool, when two dimensions are considered (Study 1), the proposed modified continuous entropy method (MCEM) is the ideal of all in that it gains the lowest item exposure rate and has a relatively high accuracy. As for high dimensions (Study 2), results show that mutual information (MUI) and MCEM keep relatively high estimation accuracy, and the item exposure rates decrease as the correlation increases.

A testlet-based visual analogue scale (VAS) is a doubly bounded scaling approach (e.g., from 0% to 100% or from 0 to 1) composed of multiple adjectives, nouns, or sentences (statements/items) within testlets for measuring individuals' attitudes, opinions, or career interests. While testlet-based VASs have many advantages over Likert scales, such as reducing response style effects, the development of proper statistical models for analyzing testlet-based VAS data lags behind. This paper proposes a novel beta copula model and a competing logit-normal model based on the item response theory framework, assessed by Bayesian parameter estimation, model comparison, and goodness-of-fit statistics. An empirical career interest dataset based on a testlet-based VAS design was analyzed using the proposed models. Simulation studies were conducted to assess the two models' parameter recovery. The results show that the beta copula model had superior fit in the empirical data analysis, and also exhibited good parameter recovery in the simulation studies, suggesting that it is a promising statistical approach to testlet-based doubly bounded responses.

Differential item functioning (DIF) is a standard analysis for every testing company. Research has demonstrated that DIF can result when test items measure different ability composites, and the groups being examined for DIF exhibit distinct underlying ability distributions on those composite abilities. In this article, we examine DIF from a two-dimensional multidimensional item response theory (MIRT) perspective. We begin by delving into the compensatory MIRT model, illustrating and how items and the composites they measure can be graphically represented. Additionally, we discuss how estimated item parameters can vary based on the underlying latent ability distributions of the examinees. Analytical research highlighting the consequences of ignoring dimensionally and applying unidimensional IRT models, where the two-dimensional latent space is mapped onto a unidimensional, is reviewed. Next, we investigate three different approaches to understanding DIF from a MIRT standpoint: 1. Analytically Uniform and Nonuniform DIF: When two groups of interest have different two-dimensional ability distributions, a unidimensional model is estimated. 2. Accounting for complete latent ability space: We emphasize the importance of considering the entire latent ability space when using DIF conditional approaches, which leads to the mitigation of DIF effects. 3. Scenario-Based DIF: Even when underlying two-dimensional distributions are identical for two groups, differing problem-solving approaches can still lead to DIF. Modern software programs facilitate routine DIF procedures for comparing response data from two identified groups of interest. The real challenge is to identify why DIF could occur with flagged items. Thus, as a closing challenge, we present four items (Appendix A) from a standardized test and invite readers to identify which group was favored by a DIF analysis.

Differential item functioning (DIF) is a common challenge when examining latent traits in large scale surveys. In recent work, methods from the field of machine learning such as model-based recursive partitioning have been proposed to identify subgroups with DIF when little theoretical guidance and many potential subgroups are available. On this basis, we propose and compare recursive partitioning techniques for detecting DIF with a focus on measurement models with multiple latent variables and ordinal response data. We implement tree-based approaches for identifying subgroups that contribute to DIF in multidimensional latent variable modeling and propose a robust, yet scalable extension, inspired by random forests. The proposed techniques are applied and compared with simulations. We show that the proposed methods are able to efficiently detect DIF and allow to extract decision rules that lead to subgroups with well fitting models.

The paper provides a survey of 18 years' progress that my colleagues, students (both former and current) and I made in a prominent research area in Psychometrics-Computerized Adaptive Testing (CAT). We start with a historical review of the establishment of a large sample foundation for CAT. It is worth noting that the asymptotic results were derived under the framework of Martingale Theory, a very theoretical perspective of Probability Theory, which may seem unrelated to educational and psychological testing. In addition, we address a number of issues that emerged from large scale implementation and show that how theoretical works can be helpful to solve the problems. Finally, we propose that CAT technology can be very useful to support individualized instruction on a mass scale. We show that even paper and pencil based tests can be made adaptive to support classroom teaching.

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.