Abstract #300490

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JSM 2003 Abstract #300490
Activity Number: 237
Type: Topic Contributed
Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
Sponsor: Social Statistics Section
Abstract - #300490
Title: Small Sample Estimation in the Three-Oarameter Logistic Model Using Auxiliary Information
Author(s): Lisa A. Keller*+ and Hariharan Swaminathan
Companies: University of Massachusetts and Educational Testing Service
Address: 152 Hills South, Amherst, MA, 01003,
Keywords: psychometrics ; item response theory ; Bayesian estimation ; small sample estimation
Abstract:

In a computerized adaptive testing environment, concerns for test security make it difficult to obtain the necessary large sample sizes for accurate item parameter estimation. This simulation study investigates a practical method for small sample estimation that relies upon Bayesian estimation. Item specific priors will be determined via prediction of item location parameters (i.e., b-parameters) from known item characteristics using linear regression. The results of the study indicate that, based on the root mean square error (RMSE) of the estimates, a reduction in sample size to 200 may be possible if item-specific priors are used on the b-parameter. Further, in terms of the bias of the estimates, the estimate of the slope parameters showed a decrease of as much as 75%, while for the location parameter, it was more typical to see a 30% reduction. Furthermore, the use of item-specific priors also leads to an 18-25% decrease in the RMSE of the estimate of the item information function, and a 16-80% decrease in bias. The implication is a more accurate estimate of the standard error of the ability estimate, leading to more precise measurement.

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