Abstract
The hypothesis that two variables have a perfect disattenuated correlation and hence measure the same trait, except for errors of measurement, is discussed. Equivalently, the underlying variables, the true scores, are related linearly. We show that several previously proposed ad hoc tests are in fact likelihood ratio tests. The cases when the linear relation is specified and when it is unspecified are both discussed.
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Healy, J. D.Estimation and tests for unknown linear restrictions in multivariate linear models (Tech. Rep. 471). Lafayette, Indiana: Purdue University, 1976.
References
Anderson, T. W. Estimating linear restrictions on regression coefficients for multivariate normal distributions.Annals of Mathematical Statistics, 1951,22, 327–351.
Anderson, T. W.An introduction to multivariate statistical analysis. New York: John Wiley & Sons Inc., 1958.
Cochran, W. G. The comparison of different scales of measurement for experimental results.Annals of Mathematical Statistics, 1943,14, 205–216.
Gleser, L. J. & Watson, G. S. Estimation of a linear transformation.Biometrika, 1973,60, 525–534.
Kristof, W. Testing a linear relation between true scores of two measures.Psychometrika, 1973,38, 101–111.
Lord, F. M. Testing if two measuring procedures measure the same dimension.Psychological Bulletin, 1973,79, 71–72.
Madansky, A. The fitting of straight lines when both variables are subject to error.Journal of the American Statistical Association, 1959,54, 173–205.
Moran, P. A. P. Estimating structural and functional relationships.Journal of Multivariate Analysis, 1971,1, 232–255.
Sprent, P. A generalized least squares approach to linear functional relationships.Journal of the Royal Statistical Society, Series B, 1966,28, 278–297.
Villegas, C. Maximum likelihood estimation of a linear functional relationship.Annals of Mathematical Statistics, 1961,32, 1048–1062.
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This work was done while the author was at Purdue University Under Air Force Grant AFOSR-72-2350B.
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Healy, J.D. On kristof's test for a linear relation between true scores of two measures. Psychometrika 44, 235–238 (1979). https://doi.org/10.1007/BF02293974
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DOI: https://doi.org/10.1007/BF02293974