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A Note on the Equivalence Between Observed and Expected Information Functions With Polytomous IRT Models

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  • David Magis

Abstract

The purpose of this note is to study the equivalence of observed and expected (Fisher) information functions with polytomous item response theory (IRT) models. It is established that observed and expected information functions are equivalent for the class of divide-by-total models (including partial credit, generalized partial credit, rating scale, and nominal response models) but not for the class of difference models (including the graded response and modified graded response models). Yet, observed information function remains positive in both classes. Straightforward connections with dichotomous IRT models and further implications are outlined.

Suggested Citation

  • David Magis, 2015. "A Note on the Equivalence Between Observed and Expected Information Functions With Polytomous IRT Models," Journal of Educational and Behavioral Statistics, , vol. 40(1), pages 96-105, February.
    • Handle: RePEc:sae:jedbes:v:40:y:2015:i:1:p:96-105
    DOI: 10.3102/1076998614558122
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    1. Fumiko Samejima, 1973. "A comment on Birnbaum's three-parameter logistic model in the latent trait theory," Psychometrika, Springer;The Psychometric Society, vol. 38(2), pages 221-233, June.
    2. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    3. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer;The Psychometric Society, vol. 37(1), pages 29-51, March.
    4. David Thissen & Lynne Steinberg, 1986. "A taxonomy of item response models," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 567-577, December.
    5. Magis, David & Raîche, Gilles, 2012. "Random Generation of Response Patterns under Computerized Adaptive Testing with the R Package catR," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i08).
    6. Wendy Yen & George Burket & Robert Sykes, 1991. "Nonunique solutions to the likelihood equation for the three-parameter logistic model," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 39-54, March.
    7. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    8. Fumiko Samejima, 1994. "Some critical observations of the test information function as a measure of local accuracy in ability estimation," Psychometrika, Springer;The Psychometric Society, vol. 59(3), pages 307-329, September.
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