Some standard errors in item response theory

The mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for some common situations. It is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter, indicating that if one needs to have accurate estimates of location parameters (say for purposes of test linking/equating or computerized adaptive testing) the sample sizes required for acceptable accuracy may be unattainable in most applications. It is suggested that other estimation methods be used if the three parameter model is applied in these situations.The research reported here was supported, in part, by contract #F41689-81-6-0012 from the Air Force Human Resources Laboratory to McFann-Gray & Associates, Benjamin A. Fairbank, Jr., Principal Investigator. Further support of Wainer's effort was supplied by the Educational Testing Service, Program Statistics Research Project.