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Estimating Ability With Three Item Response Models When the Models Are Wrong and Their Parameters are Inaccurate IRT

Jones, Douglas H.; Kaplan, Bruce A.; Wainer, Howard
Publication Year:
Report Number:
RR-84-26, PSRTR-84-46
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
United States Air Force Human Resources Laboratory, Armed Services Vocational Aptitude Battery., Goodness of Fit, Item Response Theory (IRT), Mathematical Models, Maximum Likelihood Statistics, Statistical Analysis


How accurately ability is estimated when the test model does not fit the data is considered. To address this question, this study investigated the accuracy of the maximum likelihood estimator of ability for the one-, two- and three-parameter logistic (PL) mod- els. The models were fitted into generated item characteristic curves derived from the Armed Services Vocational Aptitude Battery. Results indicated that the 3-PL model is the least biased, but that for lower abilities it had both the highest mean square error and was the most fragile with respect to sampling fluctuations of the parameter estimates. It is recommended that the current practice of utilizing some method of restricting the variability of parameters continue to be employed (such as Bayesian priors, robust estimation, or fixing some parameters to be constant). (AUTHOR/BS). (55pp.)

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