Re: st: Can Spearman's rho be used to measure of the degree of association between two binary variables ?

[Dirk Enzmann <dirk.enzmann@uni-hamburg.de>]

Marcos Vinicius asked, whether Spearman's rho can be used to measure the 
degree of association between two binary variables, see:

http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-836.html

to which he received very helpful answers (perhaps more than he 
initially wanted to know):

- from Maarten Buis and Richard Williams
http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-855.html
http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-859.html
who discuss whether multicollinearity should be regarded as a problem at all

- and from Cameron McIntosh, Richard Stoll, and Roger Newson
http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-837.html
http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-838.html
http://www.hsph.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.1205/date/article-858.html
who point at alternative measures for the association of two binary 
variables.

Let me add two comments as to the use of tetrachoric (or polychoric) 
correlation coefficients vs. Pearson (or Spearman) correlation 
coefficients in the case of two binary variables:
1) Tetrachoric and Pearson correlations answer different questions: The 
first estimates the correlation of two *latent* (quasi-continuous) 
variables "behind" the observed dichotomous variables, thus assuming 
that both variables are artificially dichotomous, whereas the Pearson 
coefficients shows how the *observed* values correlate, thus assuming 
naturally dichotomous variables.
2) Ledesma et al. (2011) (see: 
http://openjournal.konradlorenz.edu.co/index.php/rlpsi/article/viewFile/459/463 
) cited by Cameron write: "Stata gives their users a function based on a 
work by Edwards and Edwards (1984), that is basically 'a very rough 
approximation' and
is consequently unsuitable for many applications ..." (p. 182). This is 
not quite correct: Stata computes the tetrachoric correlation "... by 
using the Edwards and Edwards (1984) noniterative estimator as the 
*initial* value" (see: [R] Base Referencence, p. 2196; bold face by me) 
- the coefficient calculated by Stata is at least as precise as the 
coefficient calculated by Ledesma et al.'s Vista-Tetrachor program:

* --- Example from Ledesma et al., p. 183 ------------------------
input y x ncases
1 1 203
1 0 186
0 1 167
0 0 374
end
expand ncases
tetrachoric x y
* --- End of Stata example ---------------------------------------

Dirk

========================================
Dr. Dirk Enzmann
Institute of Criminal Sciences
Dept. of Criminology
Rothenbaumchaussee 33
D-20148 Hamburg
Germany

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email: dirk.enzmann@uni-hamburg.de
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