JSM 2005 - Toronto

Abstract #303654

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 30
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract - #303654
Title: Posterior Inference for Computer Adaptive Ability Estimation
Author(s): Kelly Rulison*+ and Eric Loken
Companies: The Pennsylvania State University and The Pennsylvania State University
Address: S113 Henderson Building, University Park, PA, 16802, United States
Keywords: Item Response Theory ; Computer Adaptive Testing ; Bayesian inference
Abstract:

Item response theory models are prevalent in education and psychological assessment. Computerized adaptive tests (CAT) allow for tailored assessment with continually updated "ability" estimates. ML algorithms are problematic for certain response vectors. Estimation also can be influenced by indeterminacies in the model; for example, the IRT model is a nonlinear factor model, so equivalent solutions exist when reversing the factor polarity. Bayesian approaches can work better, but estimates can be biased and difficult to calculate. Viewing the prior as previously collected data, we implement a technique for posterior inference that is robust for tests with few responses. We study a variety of guessing strategies advocated for computerized adaptive testing. Of particular note is the asymmetric impact of correct and incorrect answers when using a three-parameter model. The adaptive algorithm ascends slowly when high-ability students make early mistakes on moderate-difficulty questions; however, it descends quickly after low-ability students make lucky early guesses on difficult questions.

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