help for sginicorrP. Van Kerm (April 2020, March 2010)

Title

sginicorr -- Generalized Gini correlations

Syntax

sginicorr
varlist
[weight]
[if exp]
[in range]
[, options]

parameter(real) specifies Gini sensitivity parameter

format(%fmt) display format; default is format(%5.4f)

varlist may contain time-series operators; see tsvarlist.

bootstrap, jackknife, svy bootstrap, and svy jackknife prefixes are allowed; see prefix.

fweight, aweight and pweight are allowed; see help weights.

Description

sginicorr computes generalized Gini correlations for all pairs of variables in varlist.
Gini correlation coefficients are developed and discussed in Schechtman and Yitzhaki (1987, 1999, 2003).

The Gini correlation between two random variables X and Y is defined as R(X,Y)=Cov(X,1-G(Y))/Cov(X,1-F(X))
where F() and G() denote the cumulative distribution functions of X and Y, respectively.
The generalized Gini correlation coefficient replaces 1-G(Y) and 1-F(X) by (1-G(Y))^(v-1) and (1-F(X))^(v-1)
where v is a fixed parameter.
Their properties can be understood as a mixture of Pearson's and Spearman's correlations.
Note that unlike these two correlation measures, Gini correlation coefficients are not symmetric: R(X,Y) is
not equal to R(Y,X).

All pairwise correlations for the variables in varlist are computed, but sginicorr will
discard observations with missing data on any of the input variables and compute all coefficients on the
resulting sample.

An accompanying online manual provides details on formulas and usage examples.

Options

parameter(real) specifies the sensitivity parameter v. Default is 2 leading to the Gini correlation.

format(%fmt) controls the display format; default is format(%5.4f).

Saved Results

Matrices

r(Rho) correlation matrix

Scalars

r(N) number of observations

r(sum_w) sum of weights

r(rho) correlation R(X,Y) between first variable in varlist (X) and second variable in varlist (Y)

r(param) value of the v parameter

Macros

r(varlist) varlist

Dependencies

sginicorr requires installation of the companion package sgini.

Example

. sysuse auto , clear

. sginicorr price turn weight mpg

References

Schechtman, E. & Yitzhaki, S. (1987), A measure of association based on Gini's mean difference, Communications in Statistics - Theory and Methods, 16(1): 207-231.

Schechtman, E. & Yitzhaki, S. (1999), On the proper bounds of the Gini correlation, Economics Letters, 63(2): 133-138.

Schechtman, E. & Yitzhaki, S. (2003), A family of correlation coefficients based on the extended Gini index, Journal of Economic
Inequality, 1(2): 129-146.

Also see

Manual: [R] correlate, [R] spearman

Online: sgini (if installed)

Author

Philippe Van Kerm, CEPS/INSTEAD, Lux

Philippe Van Kerm, Luxembourg Institute of Socio-Economic Research (LISER) and University of Luxembourg, philippe.vankerm@liser.luembourg, philippe.vankerm@ceps.lu

Acknowledgments

This package was originally written for the MeDIM project
(Advances in the Measurement of Discrimination, Inequality and Mobility)
supported by the Luxembourg Fonds National de la Recherche (contract FNR/06/15/08)
and by core funding for CEPS/INSTEAD by the
Ministry of Culture, Higher Education and Research of Luxembourg.