Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-07T18:51:11.621Z Has data issue: false hasContentIssue false
  • English
  • Français

Assessing Statistical Accuracy in Ability Estimation: A Bootstrap Approach

Published online by Cambridge University Press:  01 January 2025

Michelle Liou  and
Lien-Chi Yu
Michelle Liou*
Affiliation:
Academia Sinica, University of California, Berkeley
Lien-Chi Yu
Affiliation:
North Carolina State University, Raleigh
*
Requests for reprints should be sent to Michelle Liou, Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, R.O.C.
Get access Rights & Permissions [Opens in a new window]

Abstract

Given known item parameters, the bootstrap method can be used to determine the statistical accuracy of ability estimates in item response theory. Through a Monte Carlo study, the method is evaluated as a way of approximating the standard error and confidence limits for the maximum likelihood estimate of the ability parameter, and compared to the use of the theoretical standard error and confidence limits developed by Lord. At least for short tests, the bootstrap method yielded better estimates than the corresponding theoretical values.

Keywords

ability estimatesitem response theorymaximum likelihoodstatistical accuracythe bootstrap method
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 1 , March 1991 , pp. 55 - 67
Copyright
Copyright © 1991 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This paper was originally presented at the Annual Meeting of American Educational Research Association, Washington, D.C., April 1987. The authors are indebted to Patricia Busk, the editor, and two anonymous referees for helpful comments on the earlier drafts of the manuscript.

References

Bradley, R. A., & Gart, J. J. (1962). The asymptotic properties of ML estimators when sampling from associated population. Biometrika, 49, 205–214.CrossRefGoogle Scholar
Chao, M. T. (1984). Generalized bootstrap methods, Taipei: Institute of Statistical Science, Academia Sinica, R.O.C..Google Scholar
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1–26.CrossRefGoogle Scholar
Efron, B. (1981). Nonparametric standard errors and confidence intervals. The Canadian Journal of Statistics, 9, 139–172.CrossRefGoogle Scholar
Efron, B. (1981). Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods. Biometrika, 68, 589–599.CrossRefGoogle Scholar
Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans. Society of Industrial and Applied Mathematics CBMS-NSF Monographs, 38.CrossRefGoogle Scholar
Efron, B. (1984). Better bootstrap confidence intervals, Palo Alto, CA: Stanford University, Department of Statistics.CrossRefGoogle Scholar
Efron, B., & Tibshiran, R. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, 17, 1–35.Google Scholar
IMSL (1987). International Mathematical and Statistical Libraries (Stat/Library Vol. I), User's Manual, Houston, TX: Author.Google Scholar
Lloyd, E. (1984). Maximum likelihood estimates. In Lloyd, E. (Eds.), Handbook of applicable mathematics, Volume VI: Statistics (Part A) (pp. 283–354). New York: Wiley.Google Scholar
Lord, F. M. (1980). Application of item response theory to practical testing problems, Hillsdale, NJ: Erlbaum.Google Scholar
Lord, F. M. (1983). Unbiased estimators of ability parameters, of their variance, and of their parallel-form reliability. Psychometrika, 48, 233–245.CrossRefGoogle Scholar
Miller, K. S. (1960). An introduction to the calculus of finite differences & difference equations, New York: Holt.Google Scholar
Parr, W. C. (1983). A note on the jackknife, the bootstrap and the delta method estimators of bias and variance. Biometrika, 70, 719–722.CrossRefGoogle Scholar
Shenton, L. R., & Bowman, K. O. (1977). Maximum likelihood estimation in small samples, New York: Macmillan.Google Scholar
Tucker, L. R., Humphreys, L. G., & Roznowski, M. A. (1986). Comparative accuracy of five indices of dimensionality of binary items, Springfield, VA: National Technology Information Service.Google Scholar
Wainer, H., & Wright, B. D. (1980). Robust estimation of ability in the Rasch model. Psychometrika, 45, 373–391.CrossRefGoogle Scholar