parcorVecH2: Vector of hybrid generalized partial correlation...

parcorVecH2R Documentation

Vector of hybrid generalized partial correlation coefficients.


This is a second version to be used when ‘parcorVecH’ fails. (H=hybrid). This hybrid version of parcorVec subtracting only linear effects but using generlized correlation between OLS residuals


parcorVecH2(mtx, dig = 4, verbo = FALSE, idep = 1)



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


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


Make this TRUE for detailed printing of computational steps


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


This function calls parcorHijk2 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).


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


Hybrid Generalized Partial Correlation Coefficients (HGPCC) allow comparison of the relative contribution of each X_j to the explanation of X_i, because HGPCC are 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.


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


Vinod, H. D. 'Generalized Correlations and Instantaneous Causality for Data Pairs Benchmark,' (March 8, 2015)

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:

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.


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
## Not run: 
colnames(mtx)=c('V1', 'v2', 'V3', 'V4')
parcorVecH2(mtx,verbo=TRUE, idep=2)

## End(Not run)

generalCorr documentation built on May 1, 2023, 9:06 a.m.