Abstract
We introduce an extended multivariate logistic response model for multiple choice items; this model includes several earlier proposals as special cases. The discussion includes a theoretical development of the model, a description of the relationship between the model and data, and a marginal maximum likelihood estimation scheme for the item parameters. Comparisons of the performance of different versions of the full model with more constrained forms corresponding to previous proposals are included, using likelihood ratio statistics and empirical data.
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This research was supported in part by ONR contract N00014-83-C-0283 to the University of Chicago, R, Darrell Bock, Principal Investigator, and AFHRL contract F41689-82-C-00020 to the Educational Testing Service, Howard Wainer, Principal Investigator. This project was facilitated by a sabbatical leave provided David Thissen by the University of Kansas, during which time some of this work was done with the Research Statistics Group of the Educational Testing Service. Conversations with Darrell Bock, Howard Wainer, Paul Holland, Frederic Lord, Donald Rubin, James Ramsay and Malcolm Ree have also been important and useful in shaping the research and its presentation here. While all those mentioned have helped us gain wisdom in these matters, any error that remains is, of course, our own.
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Thissen, D., Steinberg, L. A response model for multiple choice items. Psychometrika 49, 501–519 (1984). https://doi.org/10.1007/BF02302588
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DOI: https://doi.org/10.1007/BF02302588