Hostname: page-component-7dd5485656-2pp2p Total loading time: 0 Render date: 2025-10-31T20:35:40.146Z Has data issue: false hasContentIssue false
  • English
  • Français

A Maximum Likelihood Solution for the Method of Successive Intervals Allowing for Unequal Stimulus Dispersions

Published online by Cambridge University Press:  01 January 2025

Peter H. Schönemann  and
Ledyard R Tucker
Peter H. Schönemann
Affiliation:
Ohio State University
Ledyard R Tucker
Affiliation:
University of Illinois
Get access Rights & Permissions [Opens in a new window]

Abstract

A maximum likelihood solution for the method of successive intervals is presented together with an iterative procedure for obtaining estimates for stimulus scale values, boundary scale values, and stimulus dispersions. The method applies without modification to incomplete data matrices. The method was programmed for ILLIAC and a brief description of the program and a numerical illustration are included.

Information

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 4 , December 1967 , pp. 403 - 417
Copyright
Copyright © 1967 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.)

Article purchase

Temporarily unavailable

Footnotes

*

This research was jointly supported by the University of Illinois and the Office of Naval Research under contracts Nonr 1834(39) and N00014-66-C0010A03.

References

Adams, E. and Messick, S. An axiomatic formulation and generalization of successive interval scaling. Psychometrika, 1958, 23, 355–368.CrossRefGoogle Scholar
Anderson, T. W. An introduction to multivariate statistical analysis, New York: Wiley, 1958.Google Scholar
Bock, R. D. Note on the least squares solution for the method of successive categories. Psychometrika, 1957, 22, 231–240.CrossRefGoogle Scholar
Bock, R. D. and Jones, L. V. The measurement and prediction of judgmental response, Chapel Hill: Psychometric Laboratory, University of North Carolina, 1963.Google Scholar
Burros, R. H. The estimation of the discriminal dispersion in the method of successive intervals. Psychometrika, 1955, 20, 299–305.CrossRefGoogle Scholar
Dear, R. E. A comparison of Thurstone's method of absolute scaling with several other methods of estimating intelligence test parameters. 1957, mimeo.Google Scholar
Diederich, G. W., Messick, S. J., and Tucker, L. R. A general least squares solution for successive intervals. Psychometrika, 1957, 22, 159–173.CrossRefGoogle Scholar
Edwards, A. L. The scaling of stimuli by the method of successive intervals. Journal of Applied Psychology, 1952, 36, 118–122.CrossRefGoogle Scholar
Edwards, A. L. and Thurstone, L. L. An internal consistency check for the method of successive intervals and the method of graded dichotomies. Psychometrika, 1952, 17, 169–180.CrossRefGoogle Scholar
Galanter, E. and Messick, S. The relation between category and magnitude scales of loudness. Psychological Review, 1961, 68, 363–372.CrossRefGoogle ScholarPubMed
Gulliksen, H. A least squares solution for successive intervals assuming unequal standard deviations. Psychometrika, 1954, 19, 117–140.CrossRefGoogle Scholar
Hicks, J. M. and Campbell, D. T. Zero-point scaling as affected by social object, scaling method, and context. Journal of Personnel Psychology, 1965, 2, 793–808.CrossRefGoogle ScholarPubMed
Jones, L. V. Some invariant findings under the method of successive intervals. In H., Gulliksen and S., Messick (Eds.), Psychological scaling: theory and applications. New York: Wiley, 1960, 7–20.Google Scholar
Jones, L. V. The problem of successive intervals scale origin. Natick, Mass.: QM Research and Engineering Command, P-1113, Report No. 4, 1959.Google Scholar
Jones, L. V. A rational origin in paired comparison and successive interval scaling. Chicago: QM Food and Container Inst. for the Armed Forces, P-1101, Report No. 3, 1957.Google Scholar
Jones, L. V. and Thurstone, L. L. The psychophysics of semantics: an experimental investigation. Journal of Applied Psychology, 1955, 39, 31–36.CrossRefGoogle Scholar
Luce, R. D. Individual choice behavior, New York: Wiley, 1959.Google Scholar
Luce, R. D., Bush, R. R., and Galanter, E.. Handbook of mathematical psychology, Vols. I-III. New York: Wiley, 1963.Google Scholar
Luce, R. D. and Galanter, E. Psychological scaling. In Luce, R. D., Bush, R. R. and Galanter, E. (Eds.), Handbook of mathematical psychology, New York: Wiley, 1963.Google Scholar
Messick, S. J. An empirical evaluation of multidimensional successive intervals. Psychometrika, 1956, 21, 367–376.CrossRefGoogle Scholar
Messick, S. J., Tucker, L. R. and Garrison, H. W. A punched card procedure for the method of successive intervals. Res. Bull.. Princeton: Educational Testing Service, 1955, RB55–25.Google Scholar
Mosier, C. I. A modification of the method of successive intervals. Psychometrika, 1940, 5, 101–108.CrossRefGoogle Scholar
Noble, B. Numerical methods: Iteration, programming and algebraic equations Vol. I, Edinburgh: Oliver and Boyd, 1964.Google Scholar
Rimoldi, H. J. A.and Hormaeche, M. The law of comparative judgment in successive intervals and graphic rating scale methods. Psychometrika, 1955, 20, 307–318.CrossRefGoogle Scholar
Rozeboom, W. W. and Jones, L. V. The validity of the successive intervals method of psychometric scaling. Psychometrika, 1956, 21, 165–183.CrossRefGoogle Scholar
Saffir, M. A. A comparative study of scales constructed by three psychophysical methods. Psychometrika, 1937, 2, 179–199.CrossRefGoogle Scholar
Schönemann, P. H. A maximum likelihood solution for successive intervals scaling, Urbana, Illinois: University of Illinois, 1964.Google Scholar
Stevens, S. S. Ratio scales, partition scale and confusion scales. In Gulliksen, H. and Messick, S. (Eds.), Psychological scaling: theory and applications. New York: Wiley, 1960, 49–66.Google Scholar
Stevens, S. S. and Galanter, E. H. Ratio scales and category scales for a dozen perceptual continua. Journal of Experimental Psychology, 1957, 54, 377–411.CrossRefGoogle ScholarPubMed
Thurstone, L. L. and Jones, L. V. The rational origin for measuring subjective values. Journal of the American Statistical Association, 1957, 52, 458–471.CrossRefGoogle Scholar
Torgerson, W. S. The theory and methods of scaling, New York: Wiley, 1958.Google Scholar
Torgerson, W. S. A law of categorical judgment. In Clark, L. S. (Eds.), Consumer behavior, New York: New York University Press, 1954.Google Scholar
Tucker, L. R. A maximum likelihood solution for paired comparisons scaling by Thurstone's Case V, Urbana, Illinois: University of Illinois, 1964.Google Scholar