Approximating Bifactor IRT True-Score Equating With a Projective Item Response Model

Abstract

Item response theory (IRT) true-score equating for the bifactor model is often conducted by first numerically integrating out specific factors from the item response function and then applying the unidimensional IRT true-score equating method to the marginalized bifactor model. However, an alternative procedure for obtaining the marginalized bifactor model is through projecting the nuisance dimensions of the bifactor model onto the dominant dimension. Projection, which can be viewed as an approximation to numerical integration, has an advantage over numerical integration in providing item parameters for the marginalized bifactor model; therefore, projection could be used with existing equating software packages that require item parameters. In this paper, IRT true-score equating results obtained with projection are compared to those obtained with numerical integration. Simulation results show that the two procedures provide very similar equating results.

Several Variations of Simple‐Structure MIRT Equating

“…More specifically, bias tended to decrease with the increased degree of multidimensionality for the SMO procedure, while a reverse pattern was observed for the UNO procedure. Recently, developed an SS-MIRT true-score (SMT) equating procedure that bypasses arbitrary reduction of dimensions or projection which is often required by other MIRT true-score equating methods (e.g., Brossman & Lee, 2013;Kim & Cho, 2020;Lee et al, 2015). Though several recent developments exist for equating procedures based on MIRT models such as a full MIRT model (Brossman & Lee, 2013), a bi-factor model (Lee & Lee, 2016), and a testlet-response model (Tao & Cao, 2016), the primary focus of the current study is the equating procedures based on the SS-MIRT models.…”

Full-information item bifactor model for mathematical ability assessment in Chinese compulsory education quality monitoring

“…In addition, as a special case of confirmatory MIRT modeling, FIBF models have been used to address some important problems in psychological and educational measurement. For instance, modeling test response data and identifying the local dependence of item responses (DeMars, 2006 ; Liu and Thissen, 2012 ), assessing the dimension of test scales (Immekus and Imbrie, 2008 ), and equating and vertical scaling of test scores (Li and Lissitz, 2012 ; Kim and Cho, 2020 ). It is apparent that the advantages and values of bifactor analysis have been largely verified and are widely recognized.…”

Item Response Theory True Score Equating for the Bifactor Model Under the Common-Item Nonequivalent Groups Design

“…Such difficulty for applying IRT true score equating to MIRT models arises because numerous combinations of the latent variables can yield the same true score. To manage this issue, many research studies proposed IRT true score equating procedures for various MIRT models under the random groups design, including the complex structure model (Brossman & Lee, 2013; Peterson & Lee, 2014), the simple structure model (Kim et al, 2019a; Lee & Brossman, 2012), the bifactor model (Lee & Lee, 2016; Lee et al, 2015; Kim & Cho, 2020; Kim et al, 2019b; Peterson & Lee, 2014), and the testlet response model (Cao et al, 2014; Kim et al, 2019b; Tao & Cao, 2016).…”

“…Although the common-item nonequivalent groups (CINEG) design is widely used in practice, IRT true score equating procedures for MIRT models under the CINEG design have been an infrequent topic of discussion in the literature. Thus, the purpose of the current study was to extend the integration procedure (Lee et al, 2015; Kim & Cho, 2020; Kim et al, 2019b) and the projective IRT (PIRT) based procedure (Kim & Cho, 2020) for the bifactor model, both of which were initially proposed for the bifactor model under the random groups design, to the CINEG design and compare the performance of the two equating procedures using both simulated and real data. For the simulation study, the two equating procedures were compared over several factors, including the level of local item dependence (LID), the number of common items, and the distribution of latent variables.…”

“…Under the random groups design, the PIRT-based procedure can be viewed as an approximation to the integration procedure (Kim & Cho, 2020), and therefore, the two equating procedures provide comparable results. However, there might be some discrepancies in the equating results produced by the integration and PIRT-based procedures under the CINEG design because the two equating procedures link different latent variable scales prior to equating; the integration procedure links the latent variable scales for the bifactor model, whereas the PIRT-based procedure links the latent variable scales for a locally dependent UIRT model that is discussed in more detail later.…”