Abstract
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.
Similar content being viewed by others
Reference notes
Swaminathan, H. & Gifford, J. A.Bayesian estimation in item response models. A talk given at the annual meeting of the Psychometric Society, Chapel Hill, North Carolina, 1981.
Wood, R. L., Wingersky, M. S. & Lord, F. M.LOGIST: A computer program for estimating examinee ability on item characteristic curve parameters. Princeton, N.J.: Educational Testing Service, 1976. Research Memorandum 76-6 (modified 1/78).
References
Andersen, E. B. A goodness-of-fit test for the Rasch model.Psychometrica, 1973,38, 123–140.
Bock, R. D. & Aitkin, M. Marginal maximum likelihood estimation of item parameters: application of an EM algorithm.Psychometrika, 1981,46, 443–459.
Kendall, M. G. & Stuart, A.The advanced theory of statistics, Volume II. Third edition. London: Griffin & Co., 1960.
Lord, F. M.Applications of item response theory to practical testing problems. Hillsdale, N.J.: Lawrence Erlbaum Associates, 1980.
Thissen, D. Marginal maximum likelihood estimation for the one-parameter logistic model.Psychometrika, 1982,47, 175–186.
Wainer, H., Morgan, A., & Gustafsson, J. E. A review of estimation procedures for the Rasch Model with an eye toward longish tests.Journal of Educational Statistics 1980, (5), 35–64.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
Thissen, D., Wainer, H. Some standard errors in item response theory. Psychometrika 47, 397–412 (1982). https://doi.org/10.1007/BF02293705
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02293705