parcorVec {generalCorr} | R Documentation |
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)
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) |
Value
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.
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 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)
## 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)