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Bayesian Estimation of the Logistic Positive Exponent IRT Model

Heleno Bolfarine and Jorge Luis Bazan
Journal of Educational and Behavioral Statistics
Vol. 35, No. 6 (December 2010), pp. 693-713
Stable URL: http://www.jstor.org/stable/40959475
Page Count: 21
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Bayesian Estimation of the Logistic Positive Exponent IRT Model
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Abstract

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

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