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…

Orlando and Thissen (2000) introduced the "S - X[superscript 2]" item-fit index for testing goodness-of-fit with dichotomous item response theory (IRT) models. This study considers and evaluates an alternative approach for computing "S - X[superscript 2]" values and other factors associated with collapsing tables of observed…

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 study investigates the effect of several design and administration choices on item exposure and person/item parameter recovery under a multistage test (MST) design. In a simulation study, we examine whether number-correct (NC) or item response theory (IRT) methods are differentially effective at routing students to the correct next stage(s)…

Cognitive diagnosis models provide profile information about a set of latent binary attributes, whereas item response models yield a summary report on a latent continuous trait. To utilize the advantages of both models, higher order cognitive diagnosis models were developed in which information about both latent binary attributes and latent…

In observed-score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response…

Many standardized tests are now administered via computer rather than paper-and-pencil format. The computer-based delivery mode brings with it certain advantages. One advantage is the ability to adapt the difficulty level of the test to the ability level of the test taker in what has been termed computerized adaptive testing (CAT). A second…

When cut scores for classifications occur on the total score scale, popular methods for estimating classification accuracy (CA) and classification consistency (CC) require assumptions about a parametric form of the test scores or about a parametric response model, such as item response theory (IRT). This article develops an approach to estimate CA…

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

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…

A practical concern for many existing tests is that subscore test lengths are too short to provide reliable and meaningful measurement. A possible method of improving the subscale reliability and validity would be to make use of collateral information provided by items from other subscales of the same test. To this end, the purpose of this article…

DIMTEST is a widely used and studied method for testing the hypothesis of test unidimensionality as represented by local item independence. However, DIMTEST does not report the amount of multidimensionality that exists in data when rejecting its null. To provide more information regarding the degree to which data depart from unidimensionality, a…

In this study we examined procedures for assessing model-data fit of item response theory (IRT) models for mixed format data. The model fit indices used in this study include PARSCALE's G[superscript 2], Orlando and Thissen's S-X[superscript 2] and S-G[superscript 2], and Stone's chi[superscript 2*] and G[superscript 2*]. To investigate the…

Monte Carlo simulations with 20,000 replications are reported to estimate the probability of rejecting the null hypothesis regarding DIF using SIBTEST when there is DIF present and/or when impact is present due to differences on the primary dimension to be measured. Sample sizes are varied from 250 to 2000 and test lengths from 10 to 40 items.…

In this article, we introduce a person-fit statistic called the hierarchy consistency index (HCI) to help detect misfitting item response vectors for tests developed and analyzed based on a cognitive model. The HCI ranges from -1.0 to 1.0, with values close to -1.0 indicating that students respond unexpectedly or differently from the responses…