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Semiparametric Item Response Functions in the Context of Guessing
Author(s) -
Falk Carl F.,
Cai Li
Publication year - 2016
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/jedm.12111
Subject(s) - asymptote , item response theory , monotonic function , context (archaeology) , function (biology) , flexibility (engineering) , mathematics , polynomial , isotonic regression , statistics , polynomial regression , logistic regression , computer science , econometrics , regression , psychometrics , mathematical analysis , paleontology , geometry , evolutionary biology , estimator , biology
We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three‐parameter logistic model. We develop a maximum marginal likelihood‐based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally efficient strategy for choosing the order of the polynomial is demonstrated. Finally, our approach is tested through simulations and compared to response function estimation using smoothed isotonic regression. Results indicate that our approach can result in small gains in item response function recovery and latent trait estimation.