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June, 1961 Multivariate Correlation Models with Mixed Discrete and Continuous Variables
I. Olkin, R. F. Tate
Ann. Math. Statist. 32(2): 448-465 (June, 1961). DOI: 10.1214/aoms/1177705052


A model which frequently arises from experimentation in psychology is one which contains both discrete and continuous variables. The concern in such a model may be with finding measures of association or with problems of inference on some of the parameters. In the simplest such model there is a discrete variable $x$ which takes the values 0 or 1, and a continuous variable $y$. Such a random variable $x$ is often used in psychology to denote the presence or absence of an attribute. Point-biserial correlation, which is the ordinary product-moment correlation between $x$ and $y$, has been used as a measure of association. This model, when $x$ has a binomial distribution, and the conditional distribution of $y$ for fixed $x$ is normal, was studied in some detail by Tate [13]. In the present paper, we consider a multivariate extension, in which $x = (x_0, x_1, \cdots, x_k)$ has a multinomial distribution, and the conditional distribution of $y = (y_1, \cdots, y_p)$ for fixed $x$ is multivariate normal.


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I. Olkin. R. F. Tate. "Multivariate Correlation Models with Mixed Discrete and Continuous Variables." Ann. Math. Statist. 32 (2) 448 - 465, June, 1961.


Published: June, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0113.35101
MathSciNet: MR152062
Digital Object Identifier: 10.1214/aoms/1177705052

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 2 • June, 1961
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