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Small -sample item parameter estimation in the three parameter logistic model: Using collateral information

Lisa Ann Keller Stowe, University of Massachusetts Amherst


The appeal of computer adaptive testing (CAT) is growing in the licensure, credentialing, and educational fields. A major promise of CAT is the more efficient measurement of an examinee's ability. However, for CAT to be successful, a large calibrated item bank is essential. As item selection depends on the proper calibration of items, and accurate estimation of the item information functions, obtaining accurate and stable estimates of item parameters is paramount. However, concerns of item exposure and test security require item parameter estimation with much smaller samples than is recommended. Therefore, the development of methods for small sample estimation is essential. The purpose of this study was to investigate a technique to improve small sample estimation of item parameters, as well as recovery of item information functions by using auxiliary information about item in the estimation process. A simulation study was conducted to examine the improvements in both item parameter and item information recovery. Several different conditions were simulated, including sample size, test length, and quality of collateral information. The collateral information was used to set prior distributions on the item parameters. Several prior distributions were placed on both the a - and b-parameters and were compared to each other as well as to the default options in BILOG. The results indicate that with some relatively good collateral information, nontrivial gains in both item parameter and item information recovery can be made. The current literature in automatic item generation indicates that such information is available for the prediction of item difficulty. The largest improvements were made in the bias of both the a-parameters and the information functions. The implications are that more accurate item selection can occur, leading to more accurate estimates of examinee ability.

Subject Area

Educational evaluation

Recommended Citation

Keller Stowe, Lisa Ann, "Small -sample item parameter estimation in the three parameter logistic model: Using collateral information" (2002). Doctoral Dissertations Available from Proquest. AAI3068572.