[R] bivariate normal cdf and rho

John Fox jfox at mcmaster.ca
Wed May 1 21:20:13 CEST 2002

Dear Thomas and Jun Yan,

The Encyclopedia of Statistical Sciences (Kotz and Johnson, eds.) has an 
article on tetrachoric correlation, including many references.


At 08:39 AM 5/1/2002 -0700, Thomas Lumley wrote:
>On Wed, 1 May 2002, Jun Yan wrote:
> > Suppose F(x, y; rho) is the cdf of a bivariate normal distribution, with
> > standardized marginals and correlation parameter rho. For any fixed x and
> > y, I wonder if F(x, y; rho) is a monotone increasing function of rho,
> > i.e., there is a 1 to 1 map from rho to F(x, y; rho).
> >
>It is true.  You want references to the tetrachoric correlation.  The
>tetrachoric correlation is the estimate of rho based on F(x,y), and it
>wouldn't be any use if it weren't 1-1. I don't have any specific
>references. I tried Kendall & Stuart, but it doesn't give details.

John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox

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