Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2025-01-05T15:01:12.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Constructing Measures with Maximum Reliability

Published online by Cambridge University Press:  01 January 2025

M. Knott  and
D. J. Bartholomew
M. Knott*
Affiliation:
London School of Economics and Political Science
D. J. Bartholomew
Affiliation:
London School of Economics and Political Science
*
Requests for reprints should be sent to M. Knott, Statistics Department, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, ENGLAND.
Get access Rights & Permissions [Opens in a new window]

Abstract

The scoring of response vectors to give maximum test-retest correlation is investigated. Simple sufficiency arguments show that the form of the best scores is very restricted. A general method is given for finding the best scores, deriving the best scores for the normal factor model, and showing by calculation of several particular cases that for a standard model for binary response it is easy to approximate the best scores.

Keywords

correlationbinary responsefactor analysisrepeated testing
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 2 , June 1993 , pp. 331 - 338
Copyright
Copyright © 1993 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.)

References

Bartholomew, D. J. (1984). Scaling binary data using a factor model. Journal of The Royal Statistical Society, 46, 120–123.CrossRefGoogle Scholar
Bartholomew, D. J. (1987). Latent variable models and factor analysis, London: Charles Griffin & Company.Google Scholar
Bartholomew, D. J., Schuessler, K. F. (1991). Reliability of attitude scores based on a latent trait model. In Marsden, P. (Eds.), Sociological methodology (pp. 97–123). Oxford: Blackwell.Google Scholar
Bentler, P. M. (1968). Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis. Psychometrika, 33, 335–345.CrossRefGoogle ScholarPubMed
Bentler, P. M. (1972). A lower bound for the dimension-free measurement of internal consistency. Social Science Research, 1, 343–357.CrossRefGoogle Scholar
Bentler, P. M., Woodward, J. A. (1980). Inequalities among lower bounds to reliability with applications to test construction and factor analysis. Psychometrika, 45, 249–267.CrossRefGoogle Scholar
Dunn, G. (1989). Design and analysis of reliability studies, London: Edward Arnold.Google Scholar
Guttman, L. (1945). A basis for analyzing test-retest reliability. Psychometrika, 10, 255–262.CrossRefGoogle ScholarPubMed
Lancaster, H. O. (1966). Kolmogorov's remark on the Hotelling canonical correlations. Biometrika, 53, 585–588.Google Scholar
Lancaster, H. O. (1969). The chi-squared distribution, New York: John Wiley & Sons.Google Scholar
Lehmann, E. L. (1983). Theory of point estimation, New York: John Wiley & Sons.CrossRefGoogle Scholar
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Reading MA: Addison-Wesley.Google Scholar
Rao, C. R. (1965). Linear statistical inference and its applications, New York: John Wiley & Sons.Google Scholar
Renyi, A. (1959). On measures of dependence. Acta Mathematica Academiae Scientiarum Hungaricae, 10, 441–451.CrossRefGoogle Scholar
Sarmanov, O. V. (1946). Sur les solutions monotones des équations intégrales de corrélation [On monotone solutions of the integral equations of correlation]. Doklady Akademii. nauk. SSSR, 53, 781–784.Google Scholar