parcorVec function

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

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 $X_k$.

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

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)

Returns

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

Note

Generalized Partial Correlation Coefficients (GPCC) allow comparison of the relative contribution of each $X_j$ to the explanation of $X_i$, because GPCC 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)
parcorVec(mtx)
 
   
## Not run:

set.seed(34);x=matrix(sample(1:600)[1:99],ncol=3)
colnames(x)=c('V1', 'v2', 'V3')#some names needed
parcorVec(x)
## 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 a hybrid version parcorVecH.

Author(s)

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