generalCorr (version 1.2.6)

parcorVec: Vector of generalized partial correlation coefficients (GPCC), always leaving out control variables, if any.

Description

This function calls parcor_ijk function which uses original data to compute generalized partial correlations between \(X_i\), the dependent variable, and \(X_j\) which is the current regressor of interest. Note that j can be any one of the remaining variables in the input matrix mtx. Partial correlations remove the effect of variables \(X_k\) other than \(X_i\) and \(X_j\). Calculation merges control variable(s) (if any) into \(X_k\). Let the remainder effect from kernel regressions of \(X_i\) on \(X_k\) equal the residuals u*(i,k). Analogously define u*(j,k). (asterisk for kernel regressions) Now partial correlation is generalized correlation between u*(i,k) and u*(j,k). Calculation merges control variable(s) (if any) into \(X_k\).

Usage

parcorVec(mtx, ctrl = 0, verbo = FALSE, idep = 1)

Value

A p by 1 `out' vector containing partials r*(i,j | k).

Arguments

mtx

Input data matrix with p (> or = 3) columns

ctrl

Input vector or matrix of data for control variable(s), default is ctrl=0 when control variables are absent

verbo

Make this TRUE for detailed printing of computational steps

idep

The column number of the dependent variable (=1, default)

Author

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

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. 'New Exogeneity Tests and Causal Paths,' (June 30, 2018). Available at SSRN: https://www.ssrn.com/abstract=3206096

Vinod, H. D. (2021) 'Generalized, Partial and Canonical Correlation Coefficients' Computational Economics, 59(1), 1--28.

See Also

See Also parcor_ijk.

See Also a hybrid version parcorVecH.

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