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…

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,…

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…

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…

Power analysis is a fundamental prerequisite for conducting scientific research. Without power analysis the researcher has no way of knowing whether the sample size is large enough to detect the effect he or she is looking for. This paper demonstrates how psychometric factors such as measurement error and equating error affect the power of…

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…

Using simulated data, this study examined the impact of different levels of stringency of the valid case inclusion criterion on item response theory (IRT)-based true score equating over 5 years in the context of K-12 assessment when growth in student achievement is expected. Findings indicate that the use of the most stringent inclusion criterion…

The main purposes of this study were to develop bi-factor multidimensional item response theory (BF-MIRT) observed-score equating procedures for mixed-format tests and to investigate relative appropriateness of the proposed procedures. Using data from a large-scale testing program, three types of pseudo data sets were formulated: matched samples,…

This module describes and extends X-to-Y regression measures that have been proposed for use in the assessment of X-to-Y scaling and equating results. Measures are developed that are similar to those based on prediction error in regression analyses but that are directly suited to interests in scaling and equating evaluations. The regression and…

In the framework of the observed-score equating methods for the nonequivalent groups with anchor test design, there are 3 fundamentally different ways of using the information provided by the anchor scores to equate the scores of a new form to those of an old form. One method uses the anchor scores as a conditioning variable, such as the Tucker…

This study investigates a sequence of item response theory (IRT) true score equatings based on various scale transformation approaches and evaluates equating accuracy and consistency over time. The results show that the biases and sample variances for the IRT true score equating (both direct and indirect) are quite small (except for the mean/sigma…

The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the multidimensional item response theory (MIRT) framework. Three equating procedures--two observed score procedures and one true score procedure--were created and described in detail. One observed score procedure was…