Several marginal effect size (ES) statistics suitable for quantifying the magnitude of differential item functioning (DIF) have been proposed in the area of item response theory; for instance, the Differential Functioning of Items and Tests (DFIT) statistics, signed and unsigned item difference in the sample statistics (SIDS, UIDS, NSIDS, and…

The current study proposed several variants of simple-structure multidimensional item response theory equating procedures. Four distinct sets of data were used to demonstrate feasibility of proposed equating methods for two different equating designs: a random groups design and a common-item nonequivalent groups design. Findings indicated some…

A common method of checking person-fit in Bayesian item response theory (IRT) is the posterior-predictive (PP) method. In recent years, more powerful approaches have been proposed that are based on resampling methods using the popular L*[subscript z] statistic. There has also been proposed a new Bayesian model checking method based on pivotal…

Back random responding (BRR) behavior is one of the commonly observed careless response behaviors. Accurately detecting BRR behavior can improve test validities. Yu and Cheng (2019) showed that the change point analysis (CPA) procedure based on weighted residual (CPA-WR) performed well in detecting BRR. Compared with the CPA procedure, the…

This study proposed a recursion-based analytical approach to assess measurement precision of ability estimation and classification accuracy in multistage adaptive tests (MSTs). A simulation study was conducted to compare the proposed recursion-based analytical method with an analytical method proposed by Park, Kim, Chung, and Dodd and with the…

The purpose of this study is to develop a nonparametric DIF method that (a) compares focal groups directly to the composite group that will be used to develop the reported test score scale, and (b) allows practitioners to explore for DIF related to focal groups stemming from multicategorical variables that constitute a small proportion of the…

Abstract This study proposes a new Bayesian differential item functioning (DIF) detection method using posterior predictive model checking (PPMC). Item fit measures including infit, outfit, observed score distribution (OSD), and Q1 were considered as discrepancy statistics for the PPMC DIF methods. The performance of the PPMC DIF method was…

The use of multistage adaptive testing (MST) has gradually increased in large-scale testing programs as MST achieves a balanced compromise between linear test design and item-level adaptive testing. MST works on the premise that each examinee gives their best effort when attempting the items, and their responses truly reflect what they know or can…

Estimates of various variance components, universe score variance, measurement error variances, and generalizability coefficients, like all statistics, are subject to sampling variability, particularly in small samples. Such variability is quantified traditionally through estimated standard errors and/or confidence intervals. The paper derived new…

When a response pattern does not fit a selected measurement model, one may resort to robust ability estimation. Two popular robust methods are biweight and Huber weight. So far, research on these methods has been quite limited. This article proposes the maximum a posteriori biweight (BMAP) and Huber weight (HMAP) estimation methods. These methods…

Traditional IRT characteristic curve linking methods ignore parameter estimation errors, which may undermine the accuracy of estimated linking constants. Two new linking methods are proposed that take into account parameter estimation errors. The item- (IWCC) and test-information-weighted characteristic curve (TWCC) methods employ weighting…

This article presents the pseudo-equivalent group approach and discusses how it can enhance the quality of linking in the presence of nonequivalent groups. The pseudo-equivalent group approach allows to achieve pseudo-equivalence using propensity score reweighting techniques. We use it to perform linking to establish scale concordance between two…

Multiple group modeling is one of the methods to address the measurement noninvariance issue. Traditional studies on multiple group modeling have mainly focused on item responses. In computer-based assessments, joint modeling of response times and action counts with item responses helps estimate the latent speed and action levels in addition to…

This study proposes explanatory cognitive diagnostic model (CDM) jointly incorporating responses and response times (RTs) with the inclusion of item covariates related to both item responses and RTs. The joint modeling of item responses and RTs intends to provide more information for cognitive diagnosis while item covariates can be used to predict…

This study applied the mode of on-the-fly assembled multistage adaptive testing to cognitive diagnosis (CD-OMST). Several and several module assembly methods for CD-OMST were proposed and compared in terms of measurement precision, test security, and constrain management. The module assembly methods in the study included the maximum priority index…