caa a22 4500 606242236 CHVBK 20210128101317.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s11336-014-9411-3 doi (NATIONALLICENCE)springer-10.1007/s11336-014-9411-3 Cai Li CRESST, University of California, 90095-1521, Los Angeles, CA, USA aut Lord-Wingersky Algorithm Version 2.0 for Hierarchical Item Factor Models with Applications in Test Scoring, Scale Alignment, and Model Fit Testing [Elektronische Daten] [Li Cai] Lord and Wingersky's (Appl Psychol Meas 8:453-461, 1984) recursive algorithm for creating summed score based likelihoods and posteriors has a proven track record in unidimensional item response theory (IRT) applications. Extending the recursive algorithm to handle multidimensionality is relatively simple, especially with fixed quadrature because the recursions can be defined on a grid formed by direct products of quadrature points. However, the increase in computational burden remains exponential in the number of dimensions, making the implementation of the recursive algorithm cumbersome for truly high-dimensional models. In this paper, a dimension reduction method that is specific to the Lord-Wingersky recursions is developed. This method can take advantage of the restrictions implied by hierarchical item factor models, e.g., the bifactor model, the testlet model, or the two-tier model, such that a version of the Lord-Wingersky recursive algorithm can operate on a dramatically reduced set of quadrature points. For instance, in a bifactor model, the dimension of integration is always equal to 2, regardless of the number of factors. The new algorithm not only provides an effective mechanism to produce summed score to IRT scaled score translation tables properly adjusted for residual dependence, but leads to new applications in test scoring, linking, and model fit checking as well. Simulated and empirical examples are used to illustrate the new applications. The Psychometric Society, 2014 multidimensional item response theory nationallicence bifactor model nationallicence testlet nationallicence linking nationallicence scale alignment nationallicence test equating nationallicence goodness-of-fit testing nationallicence summed score nationallicence Psychometrika Springer US; http://www.springer-ny.com 80/2(2015-06-01), 535-559 0033-3123 80:2<535 2015 80 11336 https://doi.org/10.1007/s11336-014-9411-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11336-014-9411-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cai Li CRESST, University of California, 90095-1521, Los Angeles, CA, USA aut NATIONALLICENCE 773 0- Psychometrika Springer US; http://www.springer-ny.com 80/2(2015-06-01), 535-559 0033-3123 80:2<535 2015 80 11336