generalCorr (version 1.2.6)

gmcmtx0: Matrix R* of generalized correlation coefficients captures nonlinearities.

Description

This function checks for missing data for each pair individually. It then uses the kern function to kernel regress x on y, and conversely y on x. It needs the R package `np', which reports the R-squares of each regression. gmcmtx0() function reports their square roots after assigning them the observed sign of the Pearson correlation coefficient. Its threefold advantages are: (i) It is asymmetric, yielding causal direction information by relaxing the assumption of linearity implicit in usual correlation coefficients. (ii) The r* correlation coefficients are generally larger upon admitting arbitrary nonlinearities. (iii) max(|R*ij|, |R*ji|) measures (nonlinear) dependence. For example, let x=1:20 and y=sin(x). This y has a perfect (100 percent) nonlinear dependence on x, and yet Pearson correlation coefficient r(xy) -0.0948372 is near zero, and the 95% confidence interval (-0.516, 0.363) includes zero, implying that r(xy) is not significantly different from zero. This shows a miserable failure of traditional r(x,y) to measure dependence when nonlinearities are present. gmcmtx0(cbind(x,y)) will correctly reveal perfect (nonlinear) dependence with generalized correlation coefficient =-1.

Usage

gmcmtx0(mym, nam = colnames(mym))

Value

A non-symmetric R* matrix of generalized correlation coefficients

Arguments

mym

A matrix of data on variables in columns

nam

Column names of the variables in the data matrix

Author

Prof. H. D. Vinod, Economics Dept., Fordham University, NY

References

Vinod, H. D.'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, tools:::Rd_expr_doi("10.1080/03610918.2015.1122048")

Vinod, H. D. 'Matrix Algebra Topics in Statistics and Economics Using R', Chapter 4 in 'Handbook of Statistics: Computational Statistics with R', Vol.32, co-editors: M. B. Rao and C.R. Rao. New York: North Holland, Elsevier Science Publishers, 2014, pp. 143-176.

Vinod, H. D. 'New exogeneity tests and causal paths,' Chapter 2 in 'Handbook of Statistics: Conceptual Econometrics Using R', Vol.32, co-editors: H. D. Vinod and C.R. Rao. New York: North Holland, Elsevier Science Publishers, 2019, pp. 33-64.

Zheng, S., Shi, N.-Z., and Zhang, Z. (2012). 'Generalized measures of correlation for asymmetry, nonlinearity, and beyond,' Journal of the American Statistical Association, vol. 107, pp. 1239-1252.

See Also

See Also as gmcmtxBlk for a more general version using blocking allowing several bandwidths.

Examples

gmcmtx0(mtcars[,1:3])

if (FALSE) {
set.seed(34);x=matrix(sample(1:600)[1:99],ncol=3)
colnames(x)=c('V1', 'v2', 'V3')
gmcmtx0(x)}