## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 32, Number 2 (1961), 448-465.

### Multivariate Correlation Models with Mixed Discrete and Continuous Variables

I. Olkin and R. F. Tate

#### Abstract

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.

#### Article information

**Source**

Ann. Math. Statist., Volume 32, Number 2 (1961), 448-465.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177705052

**Digital Object Identifier**

doi:10.1214/aoms/1177705052

**Mathematical Reviews number (MathSciNet)**

MR152062

**Zentralblatt MATH identifier**

0113.35101

**JSTOR**

links.jstor.org

#### Citation

Olkin, I.; Tate, R. F. Multivariate Correlation Models with Mixed Discrete and Continuous Variables. Ann. Math. Statist. 32 (1961), no. 2, 448--465. doi:10.1214/aoms/1177705052. https://projecteuclid.org/euclid.aoms/1177705052

#### Corrections

- See Correction: I. Olkin, R. F. Tate. Correction Note: Correction to "Multivariate Correlation Models with Mixed Discrete and Continuous Variables". Ann. Math. Statist., Volume 36, Number 1 (1965), 343--344.Project Euclid: euclid.aoms/1177700300