parcorVecH2 function

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)

Arguments

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

Returns

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

Details

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).

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 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.

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)
parcorVecH2(mtx)
 
   
## Not run:

set.seed(34);mtx=matrix(sample(1:600)[1:80],ncol=4)
colnames(mtx)=c('V1', 'v2', 'V3', 'V4')
parcorVecH2(mtx,verbo=TRUE, idep=2)
## 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. '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.

Author(s)

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