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Regression Analysis and Discriminant Analysis: An Application of R. A. Fisher's Theorem to Data in Political Science

Published online by Cambridge University Press:  01 August 2014

Fred Kort
Fred Kort*
Affiliation:
University of Connecticut
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Abstract

The conversion of multiple regression analysis to discriminant analysis is not only of theoretical interest, but—in view of the extensive use of these methods in political science—it also has considerable value for applications. It is the purpose of this presentation to explain the underlying theoretical relationship and to demonstrate its application in the form of an example chosen from the judicial process. Specifically, the Supreme Court's acceptance or rejection of the fact that the defendant was not advised of his right to counsel in an involuntary confession case is considered as a function of the appearance, nonappearance, or denial of the fact in lower court records and appellate briefs. Since the acceptance or rejection of the fact by the Supreme Court is a dichotomous dependent variable, discriminant analysis is appropriate. It is shown in this study how discriminant analysis can be employed by initially using regression analysis, not only in the example presented for illustration, but in any situation in which a phenomenon with dichotomous manifestations may be examined as a function of specified variables.

Type
Articles
Information
American Political Science Review , Volume 67 , Issue 2 , June 1973 , pp. 555 - 559
Copyright
Copyright © American Political Science Association 1973

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References

1 384 U.S. 436 (1966). The case is purposely excluded from this example, because the particular fact under examination (no advice of the right to counsel) gained significance in a new context as a result of this decision. The example shows the dominant position of this fact in all the involuntary confession cases, and it contributes to the explanation of the immense importance the fact gained in the Miranda case and in subsequent developments.

2 See Tobin, James, “The Application of Multivariate Probit Analysis to Economic Survey Data,” Cowles Foundation Discussion Paper No. 1 (July 14, 1955, as revised December 1, 1955), p. 2.Google Scholar

3 For a concise but complete presentation of multiple regression and discriminant analysis, with a good mathematical exposition, see Tintner, Gerhard, Econometrics (New York: John Wiley & Sons, Inc., 1952), pp. 83–102.Google Scholar

4 See Fisher, R. A., “The Statistical Utilization of Multiple Measurements,” Annals of Eugenics, 8 (1938), 376–386CrossRefGoogle Scholar, and Statistical Methods for Research Workers, 13th ed. (New York: Hafner Publishing Company, Inc., 1958), p. 286. The notation used here differs from that employed by Fisher. For another study which compares regression analysis and discriminant analysis, see Ladd, George W., “Linear Probability Functions and Discriminant Functions,” Econometrica, 34 (1966), 873–885.CrossRefGoogle Scholar

5 The F-test was presented by R. A. Fisher as a test for significance for discriminant analysis (see note 4), with reference to Hotelling's generalized Student distribution (see Hotelling, Harold, “The Generalization of Student's Ratio,” Annals of Mathematical Statistics, 2 [1931], 360–378CrossRefGoogle Scholar). In this connection. Fisher also introduced the applicability of R2 to discriminant analysis (see the proof outlined in the Appendix).

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