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Activity Number:
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294
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Type:
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Contributed
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Date/Time:
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Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #301262 |
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Title:
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Simulated Annealing for Scoring Based on Item Response Theory
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Author(s):
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Lianghua Shu*+ and Aviva Lev-Ari and Werner Wothke
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Companies:
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CTB/McGraw-Hill and CTB/McGraw-Hill and CTB/McGraw-Hill
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Address:
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20 Ryan Ranch Rd., Monterey, CA, 93940,
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Keywords:
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scoring ; simulated ; annealing ; item ; response
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Abstract:
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This paper applies simulated annealing (SA) to item response theory (IRT). IRT-based scoring finds an integer pattern score (PS) by maximizing likelihood function over a range of reportable scores for a given student's response vector (RV). It is well known that the traditional Newton method sometimes gets trapped in local maxima. As an optimization technique, SA can statistically guarantee finding correct PS, but it can be slow. To speed it up, we modified SA (MSA) by using the random integer generator instead of random real number generator in the standard SA. Over a quarter of a million RVs are used to evaluate the three algorithms: SA, exhaustive search (ES) and grid search (GS). ES always guarantee finding the correct PS. The MSA runs more than 4 times faster than ES with the same accuracy. GS algorithm initially (grid) searches function slopes to set the starting points for the Newton algorithm. The scoring accuracy of GS depends on the number of initial grid points. With the appropriate grid points, GS runs 3 times faster than MSA. Result also shows that SA is insensitive to the starting point. Further research on improving the speed of the above 3 algorithms is under way.
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