Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2025-01-05T14:20:04.383Z Has data issue: false hasContentIssue false

Estimation of Latent Ability and Item Parameters when there are Omitted Responses

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord*
Affiliation:
Educational Testing Service

Abstract

Omitted items cannot properly be treated as wrong when estimating ability and item parameters. A convenient method for utilizing the information provided by omissions is presented. Theoretical and empirical justifications are presented for the estimates obtained by the new method.

Type
Original Paper
Copyright
Copyright © 1974 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

*

Research reported in this paper has been supported by grant GB-32781X from National Science Foundation.

References

Birnbaum, A. Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., and Novick, M. R. (Eds.), Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Bock, R. D. Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 1972, 37, 2951.CrossRefGoogle Scholar
Bock, R. D. and Lieberman, M. Fitting a response model for n dichotomously scored items. Psychometrika, 1970, 35, 179197.CrossRefGoogle Scholar
Cramér, H. Mathematical methods of statistics, 1946, Princeton, N. J.: Princeton University Press.Google Scholar
Hambleton, R. K. and Rovinelli, R. A FORTRAN IV program for generating examinee response data from logistic test models. Behavioral Science, 1973, 18, 7474.Google Scholar
Hoadley, B. Asymptotic properties of maximum likelihood estimators for the independent not identically distributed case. The Annals of Mathematical Statistics, 1971, 42, 19771991.CrossRefGoogle Scholar
Kendall, M. G. and Stuart, A. The advanced theory of statistics. Vol. 1, 1958, New York: Hafner.Google Scholar
Lord, F. M. An application of confidence intervals and of maximum likelihood to the estimation of an examinee's ability. Psychometrika, 1953, 18, 5776.CrossRefGoogle Scholar
Lord, F. M. An analysis of the Verbal Scholastic Aptitude Test using Birnbaum's threeparameter logistic model. Educational and Psychological Measurement, 1968, 28, 9891020.CrossRefGoogle Scholar
Lord, F. M. Estimating true-score distributions in psychological testing (An empirical Bayes estimation problem). Psychometrika, 1969, 34, 259299.CrossRefGoogle Scholar
Lord, F. M. Item characteristic curves estimated without knowledge of their mathematical form—a confrontation of Birnbaum's logistic model. Psychometrika, 1970, 35, 4350.CrossRefGoogle Scholar
Lord, F. M. Power scores estimated by item characteristic curves. Educational and Psychological Measurement, 1973, 33, 219224.CrossRefGoogle Scholar
Meredith, W. Some results based on a general stochastic model for mental tests. Psychometrika, 1965, 30, 419440.CrossRefGoogle ScholarPubMed
Samejima, F. A comment on Birnbaum's three-parameter logistic model in the latent trait theory. Psychometrika, 1973, 38, 221233.CrossRefGoogle Scholar
Slakter, M. J. The effect of guessing strategy on objective test scores. Journal of Educational Measurement, 1968, 5, 217221.CrossRefGoogle Scholar
Torgerson, W. S. Theory and methods of scaling, 1958, New York: Wiley.Google Scholar
Wingersky, M. S., Lees, D. M., Lennon, V. and Lord, F. M. A computer program for estimating true-score distributions and graduating observed-score distributions. Educational and Psychological Measurement, 1969, 29, 689692.CrossRefGoogle Scholar
Wingersky, M. S. and Lord, F. M. A computer program for estimating examinee ability and item characteristic curve parameters when there are omitted responses, 1973, Princeton, N. J.: Educational Testing Service.Google Scholar