parcorVecH {generalCorr}

Vector of hybrid generalized partial correlation coefficients.

Description

This is a hybrid version of parcorVec subtracting only the linear effects (OLS residuals instead of kernel regression residuals), but using the generalized correlation between the OLS residuals for the last stage of the generalized partial correlation.

Usage

parcorVecH(mtx, ctrl = 0, dig = 4, verbo = FALSE, idep = 1)

Arguments

mtx

Input data matrix with p (> or = 3) columns, the first column must have the dependent variable

ctrl

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

dig

The number of digits for reporting (=4, default)

verbo

Make this TRUE for detailed printing of computational steps

idep

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

Details

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 OLS regressions of X_i on X_k equal the residuals u(i,k). Analogously define u(j,k). It is a hybrid of OLS and generalized. Finally, partial correlation is generalized (kernel) correlation between u(i,k) and u(j,k).

Value

A p by 1 ‘out’ vector containing hybrid partials r*(i,j | k).

Note

Hybrid Generalized Partial Correlation Coefficients (HGPCC) allow comparison of the relative contribution of each X_j to the explanation of X_i, because HGPCC has scale-free pure numbers.

We want to get all partial correlation coefficient pairs removing other column effects. Vinod (2018) shows why one needs more than one criterion to decide the causal paths or exogeneity.

Author(s)

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 parcorVec.

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)
parcorVecH(mtx)
 
   
## Not run: 
set.seed(34);mtx=matrix(sample(1:600)[1:80],ncol=4)
colnames(mtx)=c('V1', 'v2', 'V3', 'V4')
parcorVecH(mtx,verbo=TRUE, idep=2)

## End(Not run)