Abstract
Item response theory scoring based on summed scores is employed frequently in the practice of educational and psychological measurement. Lord and Wingersky (Appl Psychol Meas 8(4):453–461, 1984) proposed a recursive algorithm to compute the summed score likelihood. Cai (Psychometrika 80(2):535–559, 2015) extended the original Lord–Wingersky algorithm to the case of two-tier multidimensional item factor models and called it Lord–Wingersky algorithm Version 2.0. The 2.0 algorithm utilizes dimension reduction to efficiently compute summed score likelihoods associated with the general dimensions in the model. The output of the algorithm is useful for various purposes, for example, scoring, scale alignment, and model fit checking. In the research reported here, a further extension to the Lord–Wingersky algorithm 2.0 is proposed. The new algorithm, which we call Lord–Wingersky algorithm Version 2.5, yields the summed score likelihoods for all latent variables in the model conditional on observed score combinations. The proposed algorithm is illustrated with empirical data for three potential application areas: (a) describing achievement growth using score combinations across adjacent grades, (b) identification of noteworthy subscores for reporting, and (c) detection of aberrant responses.
Highlights
Generalizing the seminal Lord–Wingersky (1984) algorithm to other settings has been a regular topic in item response theory (IRT) research since its initial publication more than 35 years ago
The two-dimensional MIRT model is treated as a two-tier model with empty specific latent dimensions so that the score combination posteriors can be computed via the Lord–Wingersky algorithm 2.5 implemented in flexMIRT (Cai, 2017) without additional programming
We note that the summaries of the posterior distribution (i.e., μ and ) along with the probability associated with each observed score combination, obtainable from the Lord–Wingersky algorithm 2.5, could be utilized to capture the statistical relationship between ξn and η and thereafter facilitate subscore reporting
Summary
Generalizing the seminal Lord–Wingersky (1984) algorithm to other settings has been a regular topic in item response theory (IRT) research since its initial publication more than 35 years ago. Cai (2015) extended the algorithm to the case of hierarchical item factor models, the two-tier model (Cai, 2010b). The dominating insight of Cai (2015) is that the non-overlapping item clusters are exchangeable conditional on the primary latent dimensions. The algorithm proposed in this study generalizes this idea to scenarios where the underlying IRT models are hierarchical item factor models. With no loss of generality, consider a bifactor model with N specific latent dimensions, wherein each ξn is measured by In dichotomously scored items, and n = 1, . The item parameters are assumed to be known and fixed, usually from a calibration study
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
