Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2025-01-05T16:12:02.286Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparing Latent Distributions

Published online by Cambridge University Press:  01 January 2025

Erling B. Andersen
Erling B. Andersen*
Affiliation:
University of Copenhagen
*
Requests for reprints should be sent to Professor Erling B. Andersen, Department of Statistics, University of Copenhagen, 6 Studiestraede, 1455 Copenhagen K, Denmark.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the problem of comparing m latent population distributions when the observed values are scores on a test battery with binary items. The latent densities are assumed to be normal densities, and we consider a test for equality of the means as well as a test equality of the variances. In addition, we consider a longitudinal model, where the test battery has been applied to the same individuals at different points in time. This model allows for correlations between the latent variable at different time points, and methods are discussed for estimating the correlation coefficient.

Keywords

Latent distributionRasch modelpopulation distributionlongitudinal model
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 1 , March 1980 , pp. 121 - 134
Copyright
Copyright © 1980 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 work was supported in part by a grant from the Danish Social Science Research Council.

References

Reference Note

Andersen, E. B. & Madsen, M. A Computer Program for Comparing Several Population Distributions of a Latent Variable, 1977, Copenhagen: Department of Statistics, University of Copenhagen.Google Scholar

References

Andersen, E. B. A goodness of fit test for the Rasch model. Psychometrika, 1973, 38, 123–140.CrossRefGoogle Scholar
Andersen, E. B. Conditional inference and multiple choice questionnaires. British Journal of Statistical Psychology, 1973, 26, 31–44.Google Scholar
Andersen, E. B. & Madsen, M. Estimating the parameters of the latent population distribution. Psychometrika, 1977, 42, 357–374.CrossRefGoogle Scholar
Birch, M. W. A new proof of the Pearson-Fisher theorem. Annals of Mathematical Statistics, 1964, 35, 817–824.CrossRefGoogle 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
Christoffersen, A. Factor analysis of dichotomized variables. Psychometrika, 1975, 40, 5–32.CrossRefGoogle Scholar
Kearns, J. & Meredith, W. Empirical Bayes point estimates of latent trait scores without knowledge of the trait distribution. Psychometrika, 1973, 38, 533–554.Google Scholar
Kearns, J. & Meredith, W. Methods for evaluating empirical Bayes point estimates of latent trait scores. Psychometrika, 1975, 40, 373–394.CrossRefGoogle Scholar
Lord, F. M. A theory of test scores. Psychometric Monograph, 1952 (Whole No. 7).Google Scholar
Lord, F. M. Estimating true-score distributions in psychological testing. (An empirical Bayes estimation problem). Psychometrika, 1969, 34, 259–299.CrossRefGoogle Scholar
Lord, F. M. & Novick, M. R. Statistical Theories of Mental Test Scores, 1968, Reading: Addison & Wesley.Google Scholar
Rao, C. C. Linear statistical inference and its applications, 1973, New York: J. Wiley and Sons.CrossRefGoogle Scholar
Rasch, G. On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Probability and Mathematical Statistics, 1961, 5, 321–333.Google Scholar
Rasch, G. An individualistic approach to item analysis. In Lazarsfeld, P. & Henry, N. W. (Eds.), Readings in mathematical social sciences, 1966, Chicago: Science Research Associates.Google Scholar
Rasch, G. An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology, 1966, 19, 49–57.CrossRefGoogle ScholarPubMed
Sanathanan, L. & Blumenthal, S. The logistic model and estimation of latent structure. Journal of the American Statistical Association, 1978, 73, 794–799.CrossRefGoogle Scholar