Hostname: page-component-6bf8c574d5-9nwgx Total loading time: 0 Render date: 2025-02-20T23:28:01.175Z Has data issue: false hasContentIssue false
  • English
  • Français

Marginal Maximum Likelihood Estimation for the One-Parameter Logistic Model

Published online by Cambridge University Press:  01 January 2025

David Thissen
David Thissen*
Affiliation:
University of Kansas
*
Requests for reprints should be sent to David Thissen, Department of Psychology, University of Kansas, Lawrence, Ks. 66045.
Get access Rights & Permissions [Opens in a new window]

Abstract

Two algorithms are described for marginal maximum likelihood estimation for the one-parameter logistic model. The more efficient of the two algorithms is extended to estimation for the linear logistic model. Numerical examples of both procedures are presented.

Keywords

Rasch modellinear logistic model
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 2 , June 1982 , pp. 175 - 186
Copyright
Copyright © 1982 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

Portions of this research were presented at the meeting of the Psychometric Society in Chapel Hill, N.C. in May, 1981. Thanks to R. Darrell Bock, Gerhard Fischer, and Paul Holland for helpful comments in the course of this research.

References

Andersen, E. B. The numerical solution of a set of conditional estimation equations. Journal of the Royal Statistical Society, Series B, 1972, 34, 42–54.CrossRefGoogle Scholar
Andersen, E. B. & Madsen, Mette Estimating the parameters of the latent population distribution. Psychometrika, 1977, 42, 357–374.CrossRefGoogle Scholar
Bock, R. D. Multivariate statistical methods in behavioral research, 1975, N.Y.: McGraw-Hill.Google Scholar
Bock, R. D. & Aitkin, Murray Marginal maximum likelihood estimation of item parameters: an application of an EM algorithm. Psychometrika, 1981, 46, 443–459.CrossRefGoogle Scholar
Bock, R. D. & Lieberman, M. Fitting a response model forn dichotomously scored items. Psychometrika, 1970, 35, 179–197.CrossRefGoogle Scholar
Dempster, A. P., Laird, N. M. & Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm (with Discussion). Journal of the Royal Statistical Society, Series B, 1977, 39, 1–38.CrossRefGoogle Scholar
Fischer, G. Linear logistic test model as an instrument in educational research. Acta Psychologica, 1973, 37, 359–374.CrossRefGoogle Scholar
Gustaffson, J. E. The Rasch model for dichotomous items: Theory, applications and a computer program. Report from the Institute of Education, 1977, Goteborg, Sweden: University of Goteborg.Google Scholar
Kemper, S. & Thissen, D. Memory for the dimensions of requests. Journal of Verbal Learning and Verbal Behavior, 1981, 20, 552–563.CrossRefGoogle Scholar
Lord, F. M. Applications of item response theory to practical testing problems, 1980, Hillsdale, N.J.: Erlbaum.Google Scholar
Mislevey, R. J. & Bock, R. D. Biweight estimates of latent ability. Journal of Educational and Psychological Measurement, in press.Google Scholar
Ramsay, J. O. Solving implicit equations in psychometric data analysis. Psychometrika, 1975, 40, 337–360.CrossRefGoogle Scholar
Rasch, G. Probabilistic models for some intelligence and achievement tests, 1960, Copenhagen: Nielsen and Lydiche.Google Scholar
Wainer, H. & Wright, B. D. Robust estimation of ability in the Rasch model. Psychometrika, 1980, 45, 373–391.CrossRefGoogle Scholar