Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T13:42:07.679Z Has data issue: false hasContentIssue false
  • English
  • Français

Factorizations of the residual likelihood criterion in discriminant analysis

Published online by Cambridge University Press:  24 October 2008

J. Radcliffe
J. Radcliffe
Affiliation:
University CollegeLondon
Get access Rights & Permissions [Opens in a new window]

Extract

Certain exact tests were developed by Williams (1952) to deal with the goodness of fit of a single hypothetical discriminant function. Bartlett (1951) generalized these results by the use of the geometric method to any number of dependent and independent variables. Bartlett's paper is divided into two parts. The first deals with an approximate factorization of the residual likelihood criterion into an effect due to the difference between the hypothetical and sample functions, and an effect due to non-collinearity. A method is given for constructing confidence intervals from the first factor. The second part of the paper gives two possible exact factorizations of the likelihood criterion, expressing the results in terms of the sample canonical variables. Kshirsagar (1964a) has expressed these results in terms of the original variables and given an analytic proof of the distribution of the factors. Williams (1955, 1961) has outlined a generalization of these results to several discriminant functions and given the result for one of the possible factorizations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 743 - 752
Copyright
Copyright © Cambridge Philosophical Society 1966

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

REFERENCES

Bartlett, M. S. (1951). The goodness of fit of a single hypothetical discriminant function in the case of several groups. Ann. Eugen. 16, 199–214.CrossRefGoogle ScholarPubMed
Kshirsagar, A. M. (1962). A note on direction and collinearity factors in canonical analysis. Biometrika 49, 255–259.CrossRefGoogle Scholar
Kshirsagar, A. M. (1964 a). Distributions of the direction and collinearity factors in discriminant analysis. Proc. Cambridge Philos. Soc. 60, 217–225.CrossRefGoogle Scholar
Kshirsagar, A. M. (1964 b). Wilks' A criterion. J. Indian Stat. Assoc. 2, 1–20.Google Scholar
Lawley, D. N. (1956). A general method of approximating to the distribution of likelihood ratio criteria. Biometrika 43, 295–303.CrossRefGoogle Scholar
Lawley, D. N. (1959). Tests of significance in canonical analysis. Biometrika 46, 59–66.CrossRefGoogle Scholar
Williams, E. J. (1952). Some exact tests in multivariate analysis. Biometrika 39, 17–31.CrossRefGoogle Scholar
Williams, E. J. (1955). Significance tests for discriminant functions and linear functional relationships. Biometrika 42, 360–381.CrossRefGoogle Scholar
Williams, E. J. (1961). Tests for discriminant functions. J. Aust. Math. Soc. 2, 243–252.CrossRefGoogle Scholar