Lord-Wingersky algorithm Version 2.5 with applications. 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.

References in zbMATH (referenced in 13 articles , 2 standard articles )

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  1. Huang, Sijia; Cai, Li: Lord-Wingersky algorithm Version 2.5 with applications (2021)
  2. Schalet, Benjamin D.; Lim, Sangdon; Cella, David; Choi, Seung W.: Linking scores with patient-reported health outcome instruments: a validation study and comparison of three linking methods (2021)
  3. Zeigenfuse, Matthew D.; Batchelder, William H.; Steyvers, Mark: An item response theory model of matching test performance (2020)
  4. van Rijn, Peter W.; Ali, Usama S.: A generalized speed-accuracy response model for dichotomous items (2018)
  5. Cai, Li: Lord-Wingersky algorithm version 2.0 for hierarchical item factor models with applications in test scoring, scale alignment, and model fit testing (2015)
  6. Magnano, Guido; Tannoia, Chiara; Andrà, Chiara: A priori reliability of tests with cut score (2015)
  7. van der Linden, Wim J.; Lewis, Charles: Bayesian checks on cheating on tests (2015)
  8. Sinharay, Sandip; Holland, Paul W.: The missing data assumptions of the NEAT design and their implications for test equating (2010)
  9. Ogasawara, Haruhiko: Asymptotic standard errors of IRT observed-score equating methods (2003)
  10. Béguin, A. A.; Glas, C. A. W.: MCMC estimation and some model-fit analysis of multidimensional IRT models (2001)
  11. Thissen, David: Psychometric engineering as art (2001)
  12. van der Linden, Wim J.: A test-theoretic approach to observed-score equating (2000)
  13. van der Linden, Wim J.; Luecht, Richard M.: Observed-score equating as a test assembly problem (1998)