Hostname: page-component-6dbcb7884d-64ff6 Total loading time: 0 Render date: 2025-02-13T17:50:23.294Z Has data issue: false hasContentIssue false
  • English
  • Français

An Application of Order Restricted Inference Methodology to a Problem in Psychiatry

Published online by Cambridge University Press:  01 January 2025

Tim Robertson  and
Giles Warrack
Tim Robertson*
Affiliation:
Department of Statistics and Actuarial Science, The University of Iowa
Giles Warrack
Affiliation:
Department of Mathematics, University of North Carolina, At Greensboro
*
Requests for reprints should be sent to Tim Robertson, Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA 52242.
Get access Rights & Permissions [Opens in a new window]

Abstract

Using data which reflects upon the genetic makeup of patients, Cadoret, Woolson and Winokur (1977) test two theories regarding the genetic makeup of patients suffering from unipolar affective disorder. This hypothesis test is a good example of a problem in order restricted inference. Using some recently developed techniques in order restricted inference we analyze these data and compare the analyses.

Keywords

unipolar affective disorderlikelihood ratio testsleast favorablechi-bar-square distribution
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 4 , December 1985 , pp. 421 - 427
Copyright
Copyright © 1985 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 research was sponsored by the Office of Naval Research under contract N00014-80-C-0321.

References

Barlow, R. E., Bartholomew, D. J., Bremner, J. M., Brunk, H. D. (1972). Statistical Inference Under Order Restrictions, New York: Wiley.Google Scholar
Bartholomew, D. J. (1983). Isotonic inference. Encyclopedia of Statistical Sciences, 4, 260–265.Google Scholar
Cadoret, R. J., Woolson, R., Winokur, G. (1977). Relationship of age of onset in unipolar affective disorder to the risk of alcoholism and depression in parents. Journal of Psychiatric Research, 13, 137–142.CrossRefGoogle Scholar
Chacko, V. J. (1966). Modified chi-square test for ordered alternatives. Sankhya (B), 28, 185–190.Google Scholar
Cox, D. R., Hinkley, D. V. (1977). Problems and Solutions in Theoretical Statistics, London: Chapman and Hall.Google Scholar
Robertson, T. (1978). Testing for and against an order restriction on multinomial parameters. Journal of the American Statistical Association, 73, 197–202.CrossRefGoogle Scholar
Robertson, T. (1985). Monotone relationships. Encyclopedia of Statistical Sciences, 5, 609–611.Google Scholar
Robertson, T., Wright, F. T. (1985). On approximation of the level probabilities and associated distributions in order restricted inference. Biometrika, 70, 597–606.CrossRefGoogle Scholar
van Zwet, W. R., Oosterhoff, J. (1967). On the combination of independent test statistics. Annual Mathematical Statistian, 38, 659–680.CrossRefGoogle Scholar
Warrack, G., Robertson, T. (1984). A likelihood ratio test regarding two nested but oblique order restricted hypotheses. Journal of the American Statistical Association, 79, 881–886.CrossRefGoogle Scholar