Abstract
We consider the problem of comparingm 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.
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Reference note
Andersen, E. B. & Madsen, M.A Computer Program for Comparing Several Population Distributions of a Latent Variable (Res. Rep. No. 37). Copenhagen: Department of Statistics, University of Copenhagen, 1977.
References
Andersen, E. B. A goodness of fit test for the Rasch model.Psychometrika, 1973a,38, 123–140.
Andersen, E. B. Conditional inference and multiple choice questionnaires,British Journal of Statistical Psychology, 1973b,26, 31–44.
Andersen, E. B. & Madsen, M. Estimating the parameters of the latent population distribution.Psychometrika, 1977,42, 357–374.
Birch, M. W. A new proof of the Pearson-Fisher theorem.Annals of Mathematical Statistics 1964,35, 817–824.
Bock, R. D. Estimating item parameters and latent ability when responses are scored in two or more nominal categories.Psychometrika, 1972,37, 29–51.
Christoffersen, A. Factor analysis of dichotomized variables.Psychometrika. 1975,40, 5–32.
Kearns, J. & Meredith, W. Empirical Bayes point estimates of latent trait scores without knowledge of the trait distribution.Psychometrika, 1973,38, 533–554.
Kearns, J. & Meredith, W. Methods for evaluating empirical Bayes point estimates of latent trait scores.Psychometrika, 1975,40, 373–394.
Lord, F. M. A theory of test scores.Psychometric Monograph, 1952 (Whole No. 7).
Lord, F. M. Estimating true-score distributions in psychological testing. (An empirical Bayes estimation problem).Psychometrika, 1969,34, 259–299.
Lord, F. M. & Novick, M. R.Statistical Theories of Mental Test Scores. Reading: Addison & Wesley, 1968.
Rao, C. C.Linear statistical inference and its applications. New York: J. Wiley and Sons, 1973.
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.
Rasch, G. An individualistic approach to item analysis. In P. Lazarsfeld & N. W. Henry (Eds.),Readings in mathematical social sciences. Chicago: Science Research Associates, 1966a.
Rasch, G. An item analysis which takes individual differences into account.British Journal of Mathematical and Statistical Psychology, 1966b,19, 49–57.
Sanathanan, L. & Blumenthal, S. The logistic model and estimation of latent structure.Journal of the American Statistical Association 1978,73, 794–799.
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This work was supported in part by a grant from the Danish Social Science Research Council.
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Andersen, E.B. Comparing latent distributions. Psychometrika 45, 121–134 (1980). https://doi.org/10.1007/BF02293602
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DOI: https://doi.org/10.1007/BF02293602