parcor_ridg function

Compute generalized (ridge-adjusted) partial correlation coefficients from matrix R*. (deprecated)

This function calls parcor_ijkOLD function which uses a generalized correlation matrix R* as input to compute generalized partial correlations between $X_i$ and $X_j$

where j can be any one of the remaining variables. Computation removes the effect of all other variables in the matrix. It further adjusts the resulting partial correlation coefficients to be in the appropriate [-1,1] range by using an additive constant in the fashion of ridge regression.

parcor_ridg(gmc0, dig = 4, idep = 1, verbo = FALSE, incr = 3)

Arguments

• gmc0: This must be a p by p matrix R* of generalized correlation coefficients.
• dig: The number of digits for reporting (=4, default)
• idep: The column number of the first variable (=1, default)
• verbo: Make this TRUE for detailed printing of computational steps
• incr: incremental constant for iteratively adjusting ridgek' where ridgek is the constant times the identity matrix used to make sure that the gmc0 matrix is positive definite. If not iteratively increas the incr` till all partial correlations are within the [-1,1] interval.

Returns

A five column out' matrix containing partials. The first column has the name of the idep` variable. The second column has the name of the j variable, while the third column has r*(i,j | k). The 4-th column has r*(j,i | k) (denoted partji), and the 5-th column has rijMrji, that is the difference in absolute values (abs(partij) - abs(partji)).

Note

The ridgek constant created by the function during the first round may not be large enough to make sure that that other pairs of r*(i,j | k) are within the [-1,1] interval. The user may have to choose a suitably larger input incr to get all relevant partial correlation coefficients in the correct [-1,1] interval.

Examples

set.seed(234)
z=runif(10,2,11)# z is independently created
x=sample(1:10)+z/10  #x is partly indep and partly affected by z
y=1+2*x+3*z+rnorm(10)# y depends on x and z not vice versa
mtx=cbind(x,y,z)
g1=gmcmtx0(mtx)
parcor_ijkOLD(g1,1,2) # ouji> ouij implies i=x is the cause of j=y
parcor_ridg(g1,idep=1)
 
   
## Not run:

set.seed(34);x=matrix(sample(1:600)[1:99],ncol=3)
colnames(x)=c('V1', 'v2', 'V3')
gm1=gmcmtx0(x)
parcor_ridg(gm1, idep=1)
## End(Not run)

References

Vinod, H. D. 'Generalized Correlations and Instantaneous Causality for Data Pairs Benchmark,' (March 8, 2015) https://www.ssrn.com/abstract=2574891

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. "A Survey of Ridge Regression and Related Techniques for Improvements over Ordinary Least Squares," Review of Economics and Statistics, Vol. 60, February 1978, pp. 121-131.

See Also

See Also parcor_ijkOLD.

Author(s)

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