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Estimating the Parameters of the Latent Population Distribution

Published online by Cambridge University Press:  01 January 2025

Erling Andersen  and
Mette Madsen
Erling Andersen*
Affiliation:
University of Copenhagen
Mette Madsen
Affiliation:
University of Copenhagen
*
Requests for reprints should be sent to Dr. Erling B. Andersen, Institute of Statistics, University of Copenhagen, Studiestraede 6, DK-1455 Copenhagen K, DENMARK.
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Abstract

Under consideration is a test battery of binary items. The responses of n individuals are assumed to follow a Rasch model. It is further assumed that the latent individual parameters are distributed within a given population in accordance with a normal distribution. Methods are then considered for estimating the mean and variance of this latent population distribution. Also considered are methods for checking whether a normal population distribution fits the data. The developed methods are applied to data from an achievement test and from an attitude test.

Keywords

Rasch modellatent variablepopulation likelihoodnormal distribution
Type
Original Paper
Information
Psychometrika , Volume 42 , Issue 3 , September 1977 , pp. 357 - 374
Copyright
Copyright © 1977 The Psychometric Society

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References

Reference Notes

Birnbaum, A. On the estimation of mental ability, 1958, Randolph Air Force Base: USAF School of Aviation Medicine.Google Scholar
Haberman, S. Maximum likelihood estimates in exponential response models, 1975, Chicago: University of Chicago.Google Scholar

References

Andersen, E. B. Conditional inference and multiple choice questionnaires. British Journal of Mathematical and Statistical Psychology, 1973, 26, 31–44. (a)CrossRefGoogle Scholar
Andersen, E. B. A goodness of fit test for the Rasch model. Psychometrika, 1973, 38, 123–140. (b)CrossRefGoogle Scholar
Barndorff-Nielsen, O. Exponential families and conditioning, 1973, Arhus: S. Møller Christensen.Google Scholar
Bock, R. D. Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 1972, 37, 29–51.CrossRefGoogle Scholar
Bock, R. D. & Lieberman, M. Fitting a response model for n dichotomously scored items. Psychometrika, 1970, 35, 179–197.CrossRefGoogle Scholar
Christofferson, A. Factor analysis of dichotomized variables. Psychometrika, 1975, 40, 5–32.CrossRefGoogle Scholar
Lawley, D. N. On problems connected with item selection and test construction. Proceedings of the Royal Society of Edinburgh, 1973, 61, 273–287.Google Scholar
Lord, F. M. A theory of test scores. Psychometric Monograph No. 7, 1952.Google Scholar
Rao, C. R. Linear statistical inference and its applications, 1975, New York: J. Wiley and Sons.Google Scholar
Rasch, G. Probabilistic models for some intelligence and attainment tests, 1960, Copenhagen: Danmarks Paedagogiske Institut.Google Scholar
Rasch, G. On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability Theory, 1961, 5, 321–333.Google Scholar
Stouffer, S. A. & Toby, J. Role conflict and personality. American Journal of Sociology, 1951, 56, 395–406.CrossRefGoogle Scholar