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…

This simulation study investigated to what extent departures from construct similarity as well as differences in the difficulty and targeting of scales impact the score transformation when scales are equated by means of concurrent calibration using the partial credit model with a common person design. Practical implications of the simulation…

In line with the journal volume's theme, this essay considers lessons from the past and visions for the future of test validity. In the first part of the essay, a description of historical trends in test validity since the early 1900s leads to the natural question of whether the discipline has progressed in its definition and description of test…

It is desirable for an educational assessment to be constructed of items that can differentiate different performance levels of test takers, and thus it is important to estimate accurately the item discrimination parameters in either classical test theory or item response theory. It is particularly challenging to do so when the sample sizes are…

Low-stakes test performance commonly reflects examinee ability and effort. Examinees exhibiting low effort may be identified through rapid guessing behavior throughout an assessment. There has been a plethora of methods proposed to adjust scores once rapid guesses have been identified, but these have been plagued by strong assumptions or the…

A theoretical and conceptual framework for true-score equating using a simple-structure multidimensional item response theory (SS-MIRT) model is developed. A true-score equating method, referred to as the SS-MIRT true-score equating (SMT) procedure, also is developed. SS-MIRT has several advantages over other complex multidimensional item response…

Reporting standard errors of equating has been advocated as a standard practice when conducting test equating. The two most widely applied procedures for standard errors of equating including the bootstrap method and the delta method are either computationally intensive or confined to the derivations of complicated formulas. In the current study,…

We derive formulas for the differential item functioning (DIF) measures that two routinely used DIF statistics are designed to estimate. The DIF measures that match on observed scores are compared to DIF measures based on an unobserved ability (theta or true score) for items that are described by either the one-parameter logistic (1PL) or…

The R software provides packages and functions that provide data analysis in classical true score, generalizability theory, item response theory, and Rasch measurement theories. A brief list of notable articles in each measurement theory and the first measurement journals is followed by a list of R psychometric software packages. Each psychometric…

The characteristic curve methods have been applied to estimate the equating coefficients in test equating under the graded response model (GRM). However, the approaches for obtaining the standard errors for the estimates of these coefficients have not been developed and examined. In this study, the delta method was applied to derive the…

Building on prior research on the relationships between key concepts in item response theory and classical test theory, this note contributes to highlighting their important and useful links. A readily and widely applicable latent variable modeling procedure is discussed that can be used for point and interval estimation of the individual person…

This study presents new models for item response functions (IRFs) in the framework of the D-scoring method (DSM) that is gaining attention in the field of educational and psychological measurement and largescale assessments. In a previous work on DSM, the IRFs of binary items were estimated using a logistic regression model (LRM). However, the LRM…

Examinees who attempt the same test multiple times are often referred to as "repeaters." Previous studies suggested that repeaters should be excluded from the total sample before equating because repeater groups are distinguishable from non-repeater groups. In addition, repeaters might memorize anchor items, causing item drift under a…

Current procedures for equating number-correct scores using traditional item response theory (IRT) methods assume local independence. However, when tests are constructed using testlets, one concern is the violation of the local item independence assumption. The testlet response theory (TRT) model is one way to accommodate local item dependence.…

Building on previous works by Lord and Ogasawara for dichotomous items, this article proposes an approach to derive the asymptotic standard errors of item response theory true score equating involving polytomous items, for equivalent and nonequivalent groups of examinees. This analytical approach could be used in place of empirical methods like…